Find two positive integers such that the four times loo0 and the product large as possible. the . first number and of the second of the numbers sum number is is as

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: The product of two positive integers is 30, and their sum is 17. What are the integers?

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Q: Find by direct calculation. Find by conditioning on the sum of these two numbers.

A: Travellers living in Shenzhen depart 'm' persons daily to Hong Kong West kowloon Station On a…

Q: Solve for a in

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Q: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: Find all sets of three positive consecutive even integers such that twice the sum of the two is less…

A: First take three consecutive even integer and then satisfied condition

Q: Find the smallest positive integer that leaves a remainder of 1 when divided by 2, a remainder of 2…

A: Let N be such a number N=10a+9:  N+1 = 10a+10 N=9b+8: N+1 = 9b+9 N=8c+7: N+1 = 8c+8 N=7d+6 and so on…

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits.   As 36= 4x9, so the number…

Q: When the smallest of three consecutive odd integers is added to four times the largest, it produces…

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Q: A ball is dropped from a height of 128 feet. After each bounce it will rebound to a height that is…

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Q: Find two positive integers such that the sum of the first number and five times the second number is…

A: Solution

Q: Verify that for any three consecutive integers, the sum of the smallest and largest is equal to…

A: Given: Three consecutive integers.

Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

Q: Prove that given any set of eight integers, there is a pair among them whose sum or difference is…

A: Let n1,n2,n3,n4,n5,n6,n7,n8 be the 8 integers. Let ni≡rimod12 where 0≤ri<12 Suppose, no two of…

Q: Compute A−2 two different ways and show that the results are equal.

A: Given: To Find: A−2 two different ways and show that the results are equal.

Q: Suppose two positive real numbers a and b add to 120. Find the values of a and b that maximize the…

A: Given a+b=120 .....1

Q: For each positive integer n, find the number of positive integers that are less than 210n which are…

A: ANSWER :

Q: - Find two positive even consecutive integers such that the square of the smaller integer is 10 more…

A: Consider the first even positive integer be 'x'. The second consecutive even positive integer be…

Q: Find all the odd positive integers n which satisfy ó(n) = 20. %3D

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Q: A student has scores of 78, 77.25, and 81.75 on his first three tests. He needs an average of at…

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Q: Define an odd number and show that the product of odd even numbers is also even.

A: We need to first define an odd number. And layer prove product of an odd and an even number is…

Q: Find all the odd positive integers n which satisfy 6(n) = 20.

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Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: Find three consecutive positive integers such that the product of the first and second is 32 more…

A: Explained below

Q: Use direct proof to show that product of two consecutive integers is even.

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Q: Find the largest number 8 such that if |x – 3| < 8, then |2x – 6| < ɛ, where ɛ = 0.5. Repeat and…

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Q: Find x so that x,x+2 and (x+3) are threee consecutive terms of GP

A: When a, b, c are in gp then b^2=ac.

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: A hot air balloon descends at a rate of 4ft per minute for 6 minutes, then rises at a rate of 2ft…

A: Given Data: The descending rate of the balloon is: D'=-4 ft per minute The time till the balloon…

Q: Multiply three consecutive integers together and then add the second integer to that product. Use…

A: Consider three consecutive numbers x, (x+1), (x+2). Take a product of these numbers we get,…

Q: Find three positive numbers whose sum is 24 and such that their product is as large as possible.

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Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: OFind the inlagral of : S(725(フスーヴxりー23x +4ズ)(1-4で

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 8. Find Za/2 for a = 0.04.

A: Given, α = 0.04 α/2 = 0.02 Zα/2  is value found by z value corresponding to probability 1-α /2…

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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Q: Find two positive integers such that the sum of the first number and four times the second number is…

A: Given: The sum of first number and four times the second number is 1000. The product of two numbers…

Q: Use a direct proof to show that the product of two odd numbers is odd.

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Q: Show that every odd integer is the sum of two consecutive integers

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Q: Classify each number by placing an X in any of the boxes that apply Number Natural  Whole Integer…

A: Consider the given numbers:

Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

Q: Write the number 240 as a sum of three numbers so that the sum of the products taken two at a time…

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Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

Q: Find the least natural number a with the property that the sum a + 2ā + 3a + ...+ 9a is the number…

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Q: Express the following as a single-den 4 2 x² - 16 x + 5x +4

A: Follow next step