Q&a Wo

Find two positive integers such that their sum is 16, and the sum of their squares is maximized.

Luz R.

asked • 03/26/16

3 Answers By Expert Tutors

Here is an algebraic solution:

Let x = one of the numbers. Then 14-x is the other

So, we are to maximize y = x(14-x) = -x2+14x

The graph of y = -x2+14x is a parabola opening downward with x-intercepts (0,0) and (14,0).

The x-coordinate of the maximum point lies halfway between 0 and 14.

So, the two numbers are 7 and 7.

Michael J. answered • 03/26/16

Best Afterschool Tutor to Prepare You For Your Regents

Lets make a chart of x and y in which the sum is 14, and shows their product.

Based on this chart, look for the maximum product. Then look for the x and y values that give that product.

For situations like this, the maximum product is one that is a square.

So if the sum is 14, the two numbers have to be 7 and 7. This way we get a product of 49.

Just to be sure, check the other combinations of addend for their product.

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The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x

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find two positive integers such that the sum of the first number and 4 times the second number is 1000 and the product of the numbers is as large as possible
Write an expression for the sum of the squares of two consecutive integers. (Use x for the integer.) 1 Simplify that expression. 2
Using each of the 10 digits 0 to 9 just once, is it possible to form positive integers who se sum is exactly 100?
Question: 1 The product of two positive numbers is 15876 and the large one is 9 times the other. Find the numbers. Question:2 Th sum of the squares of two positive whole numbers is 794. If one of the numbers is 13 , find the other.
The sum of two positive numbers is 20. Find the numbers if the sum of their squares is as large as possible; as small as possible. What does it mean? This is from applications of derivatives. How do I solve this. Two numbers, x, and 20-x Sumsquares= x^2 +
The sum of two numbers is five. The sum of the squares of the two numbers is thirteen. Find the two numbers. (Enter your answers as a comma-separated list.)
the sum of two nonnegative numbers is 20. find the number if a. the sum of their squares is as large as possible; as small as possible b. oen number plus the square root of th eother is as large as possible; as samll as possible
Use the following formula for the sum of the cubes of the first integers to evaluate the limit in part (a). 1**3+2**3+...+n**3=((n(n+1))/2)**2 (a)lim n approaches infinity and the sum of n (top) and i=1 (bottom) with (3i/n)^3*(3/n) I don't know how to
If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b? Given that ab = 3(a + b). From this, ab/3 = a + b. Dividing through by ab yields 1/a + 1/b = 1/3.
The sum of two consecutive integers is –49. Write an equation that models this situation and find the values of the two integers.
the sum of the two numbers is five and the sum of thier squares is 37 mathematical expression
Two negative integers have a sum of -10 and a product of 24. Find the two integers.
provide one of the two positive integers whose sum is 200 and whose product is a maximum.
The product of two consecutive odd integers is 1 less than twice their sum.find the integers
The sum of three consecutive integers is negative 147.find the three integers
The sum of two numbers is 8, and the sum of their squares is 34. What is the larger number?
the ratio of two integers is 9:7. their sum is 1024. find the two integers.
A positive integer is 2 less than another. If the sum of the reciprocal of the smaller and twice the reciprocal of the larger is 5/12, then find the two integers. algebraic expression is: 1/n-2 + (2)1/n = 5/12
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
If the sum of circumferences of two circles wirh radii r1 & r2 is equal to the circumference of a circle of radius r, then what is true 1 r1+ r2 = r or sum of their squares= r2
the sum of 2 integers is 41.when 3 times the smaller is subtracted from the larger the result is 17. find 2 integers
Sum of 2 consecutive integers is 59. Write an equation that models that situation and find values of both integers
The sum of 6 consecutive integers is 171. Find the smallest of the integers
proof by mathmatical induction that the sum of the first n natural numbers is equal n(n+1)/2 It's true for n = 1. Assume that it is true for some n. Then the sum of the first n+1 natural integers can be obtained by dding the last number n+1 to n(n+1)/2.
What are the two positive integers whose sum is 200 and whose product is a maximum?
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
1. The sum of two consecutive even integers is 118. What are the integers? 2. The sum of three consecutive integers is 915. What are the integers?
The dimension of a rectangular prism are all positive integers. The volume of the prism is 2002 cubic cm. Find the minimum possible sum in cm of the length width and height.
The ratio of the areas of two squares is 32/63. After rationalizing the denominator, the ratio of their side lengths can be expressed in the simplified form (a*sqrt b)/c where a, b, and c are integers. What is the value of the sum a + b + c?
The sum of 4 consecutive integers is t. In terms of t, find the smallest of the four integers
Find the sum of the first five terms of an infinite geometric progression with a common ratio |r|
When you solve questions like "The sum of 3 consecutive integers is 147. Find the integers." do you find consecutive even integers and consecutive odd integers the same way?
A series of 288 consecutive odd integers has a non-zero sum that is a perfect fourth power. Find the smallest possible sum for this series.
The number of ways in which 63 can be expressed as a sum of two or more consecutive positive integers.
the sumof three positive numbers is 26.the second number is 3times as large as the first.if te sum of the squares of these numbers is least find the numbers
Need a formula; the product of two consecutive integers is 41 more than their sum. Find the integers.
The sum of the swuares of the first n counting numbers: 1² + 2² + 3² + 4² + 5² + 6² + ... +n² is given by the formula S = n(n+1)(2n+1) ------------ 6 Find the sum of the squares of all the counting numbers between 15 and 35. - answer is 12445; how
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. Help please!
two consecutive integers such that the sum of 3 times the frist integer and 6 times second integer is 24. Expalin the variables that you used. If I could get help in solving this ASAP, I wiould really appreicate it? Let the two consecutive integers be x
How should two nonnegative numbers be chosen so that their sum is 1 and the sum of their squares is as large as possible? As small as possible?
1. The first and last term of an A.P are, a and l respectively, show that the sum of nth term from the beginning and nth term from the end is a + l. 2. If mth term of an A.P be 1/n and nth term be 1/m, then show that its mnth term is 1. 3. The sum of four
The two of us ordered a pizza whose area was the same as the area of a square in which the sum of the squares of the four sides plus the sum of the squares of the two diagonals is 400. The pizza's area was A. 50 B. 100 C. 150 D. 200
i don't get this question consecutive integers are integers that differ by one. you can represent consecutive integers as x,x+1,x+2 and so on. write an equation and solve to find 3 consecutive integers whose sum is 33
Given integers R,M with M≠0, let S(R,M) denote the smallest positive integer x satisfying the congruence Rx≡1(mod M) if such an x exists. If such an x does not exist, put S(R,M)=0. Each line of this text file contains a pair of space separated integers
I am trying to find the sum of two integers. I entered the following program into the Visual Studio and it is telling me that there are errors. Can someone tell me where they are please? #include int main( void ) { int integer1; int integer2; int sum;
List the elements of the following sets: (1) {factor of 24}. (2) {Negative integers greater than _9}. (3) {Integers whose squares are less than 200 but greater than 40}. (4) {Odd positive numbers less than 30}. (Q2) Given that Y={multiples of 3 less than
The sum of 4 consecutive odd integers is -104. Find the integers with x for unknown numbers.
the sum of four consecutive integers is -72. write an equation to model this situation and find the values of the four integers
Find the smallest possible sum of six consecutive integers such that none of the integers is prime.
The sum of four consecutive odd integers is 448. Find the three integers.
An exponential sequence (GP)of positive terms and a linear sequence (AP)have the same first term.the sum of their first terms is 3,the sum of their second terms is 3 and the sum of their third terms is 6. Find the sum of their fifth terms
Let N be the sum of all positive integers q of the form q=p^k with prime p, such that for at least four different integer values of x from 1 to q, x^3−3x≡123(modq). What are the last 3 digits of N?
The sum of three numbers in g.p. is 21 and the sum of their squares is 189. Find the numbers.
Sum of two integers is -278 of one of the integers is -156,find the other.
find the sum of the series: 1. the sum from n=1 to infinity of ((-1)^n*(.2)^n)/n I simplified this to: (-.2)^n/n I know this is alternating, but how do I know what the sum is? 2. the sum from n=0 to infinity of 1/2^n Is this geometric with n^(-2)? and if
How many positive integers less than 1000000 have the sum of their digits equal to 7?
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. what is the greatest possible value of ab-cd?
How many positive integers less than 1000000 have the sum of their digits equal to 7?
Cant figure out what to do (equations) 1)Find three consecutive even integers with a sum of -30 2)Find four consecutive integers with a sum of 26
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
Five red cards numbered 1,2,3,4,5 and two black cards both numbered 5 are randomly ordered face-down into a pile. The cards are flipped over one at a time until either the sum of the numbers on the red cards is at least 10, or the sum of the numbers on the
the sum of 3 consecutive integers is the same value as twice the greatest of the integers. Find the 3 integers.
Like obtaining the sum of squares in an area in Excel =sumsq(a1:g1) I would like an algorithm/module that will give me the sum of cubes. Can anyone help me? thankyouuuuuuuuuuu!
GIven any positive integers, show that at least two must exist whose sum or difference is divisible by 10.
If positive integers x and y satisfy the equation xy−5x−10y+43=0, the sum x+y is constant. What is the value of x+y?
Hi Ms. Sue I was wondering if you could give me some advise in doing explain and unexplain variation and least-squares regression line. I know how to compute the numbers, but I am having a problem with: say there is 3.0270, 30.0463 and 33.1120. I sometimes
The sum of two numbers is 37. The sum of their squares is 756.5. Find the two numbers The answers are 12.5 and 24.5. But I keep getting 44.69 and -7.69
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)/ϕ(p)?
Let σ(n) be the sum of the positive divisors of an integer n and ϕ(n) be the number of positive integers smaller than n that are coprime to n. If p is a prime number, what is the maximum value σ(p)ϕ(p)?
1. The largest of five consecutive integers is twice the smallest. Find the smallest integer. 2. When the sum of three consecutive integers is divided by 9 the result is 7. Find the three integers. 3. If each of three consecutive integers is divided by 3,
Let S be the sum of all values of r such that the coefficient of the x^2 term in the expansion of (x−3)(rx+2)^3 is −6 . If S=a/b, where a and b are coprime positive integers, what is the value of a+b
The difference of two integers is 6. The sum of twice the smaller and the larger is 72. Find the integers. The sum of 3 times a larger integer and 2 my answer the lager integer is 192 and the smaller integer is 72
A Quadratic Word Problem. The difference between two positive numbers is 3. The sum of the squares of the numbers is 89. Find the numbers.
In a sequence of four positive numbers, the first three are in geometric progression and the last three are in arithmetic progression. The first number is 12 and the last number is 452. The sum of the two middle numbers can be written as ab where a and b
Clara measured the diameter of the circle. How many centimeters is the diamter? Clue:The measure of the diameter is between 6 x 0.15 and 9 x 0.15. Clue:The units digit and the hundreths digit are the same Clue:If the diameter was 100 times longer, its
the following two lines indicate another way to derive the formula for the sum of the first n integers by rearranging the terms in the sum. Fill in the details. 1+2+3+...+n=(1+n)+(2+(n-1))+(3+(n-2))+... =(1+n)+(1+n)+(1+n)+...
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
One positive integer is three moee than twice another and their sum is greater than 65 but less than 75. What pairs of integers satisfy this conditions?
400 draws are made at random with replacement from 5 tickets that are marked -2, -1, 0, 1, and 2 respectively. Find the expected value of: 1. the number of times positive numbers appear 2. the sum of all the numbers drawn 3. the sum of the positive numbers
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can
the number 2008 can be written as a sum of consecutive integers such that the number of terms in the sum is twice the number of factors of 2008. Find the smallest of three consecutive integers.
The ratio of three positive integers is 2:4:5 and their least common multiple is 300. What is the sum of the smallest and the largest of the three numbers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
How many integers 1≤N≤1000 can be written both as the sum of 26 consecutive integers and as the sum of 13 consecutive integers?
The sum of 3 consecutive odd integers is 57.Find the integers
Find the sum of all integers c, such that for some integers a and b satisfying a
Let S be the sum of all the possible values of sin x that satisfy the following equation: 5-2cos^2(x)-7sin(x) = 0 S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?
Let a,b,c be complex numbers satisfying a+b+c=abc=1 and (ab+bc+ac)/3=(1/a^2)+(1/b^2)+(1c^2) The sum of absolute values of all possible ab+bc+ac can be written as (√n)/m, where n and m are positive coprime integers. What is n+m?
1. (Given the simple interest formula, I = Prt, solve for t) 2.(Consecutive integers are integers that follow each other in order (for example 5, 6, and 7). The sum of three consecutive integers is 417. Let n be the first one. Write an equation that will
suppose a,b,c and d are different positive integers whose sum is 100, and a-c=5. What is the greatest possible value of ab-cd?
Two even integers are represented by 2n and 2n+2. Explain how you can find the value of those integers if their sum is 14. Name the integers.
suppose that a, b, c ,and d are positive integers whose sum is 100 and a-c=5.What is the greatest possible value of ab-cd answers
given any seven positive integers, show that at least two must exist whose sum or difference is divisible by 10.
Given a positive integer n, let S(n) denote the digit sum of n. Consider the sequence of numbers given by n₁ = S(n) nk = S(nk−1)k≥2 For how many positive integers n ≤ 2013 does the sequence {nk} contain the number 9?
c and d are positive consecutive odd integers whose sum is 240. If c > d, then 1/square root of c=? Help?
Part (a): Find the sum a+(a+1)+(a+2)+.....+(a+n-1) in terms of a and n Part (b): Find all pairs of positive integers (a,n) such that n>= 2 and a+a+1)+(a+2)+....+(a+n-1)=100.
What iz d. sum ov all 3digit positive integers exist dat when divided by 7 leave a remainder ov 5
The sum of four consecutive integers is decreased by 30, the result is the fourth integer. Find the four integers.
The squares of a 2×60 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can

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The sum of 11 consecutive positive integers is 2002. What is the greatest of these 11 integers? *************************************** I truly appreciate the time and effort that you all give answering our questions and taking the time to explain how to
Find two numbers whose sum is 10 for which the sum of their squares is a minimum.
The midpoints of the sides of a series of a square of side 1 are joined to form a new sqaure. This procedure is repeated for each new square. a) find the sum of the areas all the squares b) find the sum of the perimeters of all the aquares
The sum of the reciprocals of two consecutive even integers is 11/60. Find the integers....... 1/n + 1/(n+2) = 11/60 what is the question? the question is, "What is the value of the integers? I will be happy to critique your work. We don't do it for
Show that the sum of the squares of any five consecutive integers is divisible by 5. I think I should do something with n+(n+1)+(n+2)+(n+3)+(n+4), but I have no idea where to go to from here. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The product of 2 positive integers is 1000. What is the smallest possible sum of these 2 integers?
Two consecutive positive integers have the property that one integer times twice the other equals 612. What is the sum of these two integers?
If the sum of the five consecutive integers is 80, what is the value of sum of the least of these integers and the median of these integers? Can you explain it?
two fair six-sided dice are rolled and the sum of the dots on the top faces is recorded. a) complete the table, showing the number of ways each sum can occur sum: 1 2 3 4 5 6 7 8 9 10 11 12 ways:1 2 3 b)use the table to find the probability of the
the product of two consecutive positive even integers is 14 more than their sum .set up an equation that can be used to find the two numbers and solve it
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
Function f(x) is positive, decreasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the left sum, right sum, and trapezoidal rule approximations for the value of
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
The sum of three consecutive integers is a multiple of 89 and is a value between 600 and 900. What is the sum of the first three integers? Thank you! :-)
Find 5 consecutive whole numbers if it is known that the sum of the squares of the first 3 numbers is equal to the sum of the squares of the last 2 numbers.
The positive difference of the cubes of two consecutive positive integers is 111 less than five times the product of the two consecutive integers. What is the sum of the two consecutive integers?
Don chooses a positive integer less than 11 which he calls a and an integer b such that 11
The sum of four consecutive even integers is the same as the least of the integers. Find the integers. I'm not sure how to solve it and put it in an equation!
5. The sum of 7 unequal positive integers is 61. What is the largest possible value that any of those integers can have? A.55 B.40 C.39 D.13 E.9 please show work
What is the sum of the first 60 positive integers?
Two integers have a sum of 11. The sum of the greater integer squared and 30 times the smaller integer is 205. What are the two integers?
the sum of the square of two consecutive positive integers is 265.what are the integers?
The product of 2 numbers is 24,and the sum of their squares are 52.Find their sum.
The mean of seven positive integers is 16. When the smallest of these seven integers is removed, the sum of the remaining six integers is 108. What is the value of the integer that was removed?
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
2.B 2.The sum of two integers is ____ positive. A.always B.sometimes C.never
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Four different positive integers sum to one hundred twenty-five. If you increase one of these numbers by four, decrease the second by four, the multuply the third by four, and divide the last by four, you will produce four equivalent numbers. What are the
1.Find an A.P. such that the sum of the first three terms is one half the sum of the next four terms,the first term being 12. 2.In an A.P.,the sum of the first three terms is 18,and the sum of the squares of these terms is 126.Find the terms.
The sum of the positive odd integers less than 50
Two non-negative numbers are chosen such that their sum is 30. Find the numbers if the sum of their squares is to be a maximum. Explanation to solve this would help !
Which statement about the sum of two additive inverses is true? Select all that apply. A. The sum is 1. B. The sum is zero. C. The sum must be a positive number. D. The sum must be a negative number. E. The addends are the same number with opposite signs.
Find four consecutive odd integers so that five times the sum of the first and third integers excceeds four times the sum of the second and last integers by 14.
Two positive integers are in ratio 1:3. If their sum is added to their product, the result is 224. Find the integers. On my own, I came up with the formula 224 = x + 3 x + 3x^2 but it's not really working out. Could someone please help me?
Find the sum of all positive integers less than 1000 ending in 3 or 7. What is the answer?
Find the sum of all integers m that are less than 1000 and equal to n!+1−−−−−√ for some positive integer n.
the product of three consecutive positive integers is 35,904. what is the sum of the three integers?
if f (x) is a polynomial of degree 3 whose roots are p,q,r. FIND f (3) if sum of cubes of roots is 0 and sum of squares of roots and sum of roots are unit digit of 3^2018 and 5^50666666666 respectively?
The sum of three consecutive positive integers is 315. Find the numbers. ( Hint: x, x+1, x + 2 )
Find four numbers in AP whose sum is 20 and sum of whose squares is 120.
Find the sum of the series 1 + 2 + 4 + 5 + 7 + 8 + 10 + 11 + ... + 299, which is the sum of the integers from 0 to 300, omitting the multiples of 3.
The sum of the integers from 40 to 60, inclusive, is 1050. what is the sum of the integers from 60 to 80 inclusive? Please help me find the pattern and how to use it instead of adding 60+61+62+63..... etc.
1)find the sum of the odd integers from 25 to 75 2)find the sum of the first 20 terms in the series 10+5+2.5+1.25... . please show the steps to solve the problem^_^
How do you do. Please Explain Sum of X Sum of Squares Sum of X squared
Find the last three digits of the sum of all positive integers n
Function f(x) is positive, increasing and concave up on the closed interval [a, b]. The interval [a, b] is partitioned into 4 equal intervals and these are used to compute the upper sum, lower sum, and trapezoidal rule approximations for the value of
1.)The product of 14 and n is -28. Write the algebraic equation. 2.)Four times a certain number is the same as the number increased by 78 3.)A blue bike is $14 less than a red bike. The sum of their prices is $300. How much is the red bike 4.)Alex is six
(b) the digits of a positive integer having three digits are in A.P and their sum is 15. The number obtained by reversing the digits is 594 less than the original number. Find the number. (c) if a,b,c are in A.P, prove that (i) (ab)^-1, 1/ac, 1/bc are also
Calculate S20 if the sum of the squares of the first integers is given by Sn=n(n-1)(2n+1)/6
What is the difference between the sum of the first 200 positive multiples of three and the sum of the first 200 positive even integers?
Find the sum of all primes a
Find the sum of all positive integers b such that b^2 =a^3 +1 , where a is a prime number
Find the sum of all positive integers b such that b^2=a^3+1, where a is a prime number.
Can someone please explain to me how I can get the solution for this question. Use the top-down modular approach and pseudocode to design a suitable program to help you solve this problem. Whenever appropriate,validate the input data. Find the sum of the
URGENT HELP!Squares into Primes Some primes can be expressed as the sum of two squares, as in 13=2^2+3^2; some can't:7=/=a^2+b^2. Other primes can be c^2+2e^2 like 11=3^2+2*1^2; still others are f^2+3 g^2, like 31=2^2+ 3* 3^2. Find all the primes less than
Tell whether the sum between the two integers is always, sometimes, or never positive. Two Positive Integers: Sometimes One Positive and one negative integer: Always Is it right?
X X2 1 1 2 4 3. 9 5 25 8. 64 10 100 It asks me to do the Sum of X Sum of Squares Sum of X squared Can you please help me on this. I don't get it
This is a reply to the question posted here //www.jiskha.com/display.cgi?id=1178989522 As I explained there, you can find the parameters by defining: x1 = Sin(0.49 t) x2 = Cos(0.49 t) and treat this as an ordinary linear regression problem. If we
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3. Details and assumptions The digit sum of a number is the sum of all its digits. For example, 1123 has a digit sum of
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a + b.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The product of two consecutive positive integers is 11 more than their sum. What the integers? Please help.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b.
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as \frac{a}{b} where a and b are coprime positive integers. Find a + b
How many numbers from 1 to 1000 inclusive can be expressed as the sum of k >= 2 consecutive positive integers for some value of k ? Sorry to post question from Brilliant, I got 997 integers, but it's wrong. If you think you can answer ...
find three consecutive even intergers for which the sum of the first two integers is greater than 9 more than the third integer, and the sum of the first and third integers is less than 17 more than the second integer
The difference of two positive integers was multiplied by their sum. If possible, find two numbers such that the result is equal to 212.
There are six ways to write 5 as an ordered sum of three positive integers: 3+1+1, 1+3+1, 1+1+3, 2+2+1, 2+1+2, 1+2+2. A) What is the number of ways to write "n" as an ordered sum of "r" integers? B) What is the number of ways to write "n" as an ordered sum
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
Prove that a number 10^(3n+1) , where n is a positive integer, cannot be represented as the sum of two cubes of positive integers. thanx
The sides of the outside square in the figure are 8 inches long. The corners of the next smaller square are at the midpoints of the outside square, and so on. a.) find the sum of the perimeters of the first three squares. Imagine that the process of
Three consecutive odd intergers are such that the sum of the squares of the first two integers is 54 more than 20 times the third integer. Determine the three integers. Please help and show all work thank you SHOW WORK SO I UNDERSTAND HOW TO DO IT THANK
Let x,y be complex numbers satisfying x+y=a xy=b, where a and b are positive integers from 1 to 100 inclusive. What is the sum of all possible distinct values of a such that x^3+y^3 is a positive prime number?
Call a positive integer N ≥ 2 “special” if for every k such that 2 ≤ k ≤ N, N can be expressed as a sum of k positive integers that are relatively prime to N (although not necessarily relatively prime to each other). How many special integers are
A. Four times one odd integer is 14 less than three times the next even integer. Find the integers. B. The average of four consecutive odd integers is 16. Find the largest integer. C. When the sum of three consecutive integers is divided by 9 the result is
I need help solving this problem, I have followed the sequence forward and backwards but can't seem to find the solution. I believe it's the pigeon hole theorem. Here's the problem; Let A be any set of twenty integers chosen from the arithmetic progression
Write a loop that will continuously prompt the user for integers to sum, -1 to exit. Sum these values and display the sum to the console. Here is what I have so far, but I feel like I am missing something: public class Sum1 { public static void main
The model below uses three squares to form a right triangle. 29 cm,,,...21 cm,,,....20 cm,,,....,,, The model shows that... A. The square of 20 equals the sum of the squares of 29 and 31. B. The square of 29 equals the sum of the squares of 20 and 21.
For all positive integers n, let f3(n) be the representation of n in base 3, considered as a number in base 10. For example, since 5 in base 3 is 123, so f3(5)=12. What is the sum of all positive integers n such that f3(n)=8⋅n?
1. solve: x^3 =4x 2. solve: (x-3)^2 = -4 3. solve: (6 +5i) ^2 4.Two integers have a sum of -4 The sum of their squares is 40. What are the two integers?
if the sum of the positive integers x and y is 12 then x can be equal to all of the following except 5y 4y 3y 2y y
CounterExamples and Inductive Reasoning and Conjectures? Make a Conjecture for Each Scenario. Show your Work - the sum of the first 100 positive even numbers, - the sum of an even and odd number. - the product of two odd numbers. FInd One CounterExample to
Explain how to find the sum positive three plus negative eight using chips, a number line, or the rules for adding integers. Give the answer with your explanation.
The difference between 2 positive numbers, x and y where x > y, is 7 and the sum of their squares is 137. By forming 2 equations in x and y, find the product of these 2 numbers.
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Which two integers have a positive quotient and a negative sum? a. -9 and -3 b. -6 and 2 c. 5 and 1 d. 8 and -4
For all x greater than 2, let *x be defined as the sum of the positive integers less than x. What is the value of *16 - *13?
Explain how to find the sum positive five plus negative nineusing chips, a number line, or the rules for adding integers. Give the answer with your explanation
Find the sum of all 3-digit positive numbers N that satisfy the condition that the digit sum of N is 3 times the digit sum of N+3.
Joe picks 2 distinct numbers from the set of the first 14 positive integers S = \{1,2,3,\ldots,14\}. The probability that the sum of the 2 numbers is divisible by 3 can be expressed as \frac{a}{b}, where a and b are coprime positive integers. What is the
Find the sum of all positive integers less than 1000 ending in 3 or 7.
The sum of two different positive integers is 123. The larger integer is four more than six times the smaller one. What are the two integers?
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
Find all sets of two consecutive positive odd integers whose sum is less than or equal to 18.
The four values x, y, x−y and x+y are all positive prime integers. What is the sum of all the four integers?
show that the sum of the squares of the lengths of the medians of triangle equals three-fourths the sum of the squares of the lengths of the sides.(hint:place the triangle so that its vertices are at points(-a,0),(b0)and (0,c))
Two positive numbers have the property that their product is 2 and their sum is as small as possible. Find their sum.
Let's denote the three numbers by a1, a2, and a3. Consider the third degree polynomial: p(x) = (1 + a1 x)(1 + a2 x)(1 + a3 x) Take the logarithm: Log[p(x)] = Log(1 + a1 x) + Log(1 + a2 x) + Log(1 + a3 x) Expand in powers of x by using that: Log(1 + x) = x