When 32 is divided by an integer, the remainder is 4. When 51 is divided by the same integer, the remainder is 2. What is the largest integer for which this is true?

Q: what integer is closer to 6

A: given: the integer is six.

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: A number that has exactly 2 factors (1 and itself) is called a number. * O factors O prime O…

A: We have asked if a number that has exactly 2 factors (1 and itself) then what kind of number is…

Q: Find a reduction formula for ∫sinnxdx, n≥2.

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Q: Find the smallest integer greater than 100 that is divisible by 3 but leaves the remainder 1, 5 when…

A: Let x be the required number. The number is divisible by 3, so it leaves the remainder 0 when it is…

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: The student noticed that if he writes a multiplication sign between the second and third digit of…

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

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Q: does there exists   ______such that if n is divided by 5 the remainder is 2 and  if   ?

A: We have to check whether there exist n such that if n is divided by 5 then remainder is 2. Let if n…

Q: 2) The product of an even number and any other number is even.

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Q: A number is divisible by 2 if

A: A number is divisible by 2 if

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: Machine A can assemble a product in 4 hours while machine B can assemble the same product in 3…

A: Machine A and B can work in 1 hour is

Q: * If メ~NC 5e」 lo0) Find 2 PC X6) 4) P(55< x< 72) 60)

A: Given X~N50, 100

Q: Jillian observed that if the sum of its digits is subtracted from a number the result is always…

A: Given data:   Check the divisibility by three and nine.   The above general expression can be proved…

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

A:

Q: Find the largest two-digit integer that leaves the remainders 2 and 3 when divided by 5 and 7.

A: Let x be the largest two-digit number which gives the remainder 2 and 3 when divided by 5 and 7 The…

Q: A person is holding two drill bits, one is 7/16 and the other is 25/64, and wants to first drill a…

A: There are two fractions 7/16 and 25/64. To compare the person wants to make the denominators same.…

Q: A fraction is said to be _____ when the numerator and the denominator have no common factors other…

A: Here we have to fill the blank;

Q: Any n consecutive integers will include a number that is divisible by n.

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Q: Find the smallest integer greater than 100 that is divisible by 5, but leaves the remainders 1, 5…

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Q: Show that we can easily factor n when we know that n is the product of two primes, p and q, and we…

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Q: Which integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided…

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Q: What is the remainder when 10^28 is divided by 6? NOTE: 10^28 means 10 raised to the 28th power

A: Given problem Given that   The remainder when 1028 is divided by 6 is = ?

Q: The number of words of 3 consonants and 2 vowels can be made from 6 consonants and 4 vowels, if all…

A: The number of ways to select r objects from n distinct objects is given by the combination rule…

Q: A student  missed 40 problems on a physics test and received a grade of 47%. If the problems were of…

A: Given that the student missed 40 problems and received a grade of 47%.Let x be the number of…

Q: The product of any four consecutive integers is divisible by 24.

A: We will use basic knowledge of integers and congruences to solve this question.  The question says…

Q: Two numbers that add to 9 and multiply to 20 are

A: Let, x and y are two numbers. Two numbers add to 9. So, x+y=9 ......1 Two numbers multiply to 20.…

Q: John found the sum of the first 2021 positive even integers and Bob found the sum of the first 2022…

A: In this question, tne concept of sum of first positive even integers is applied.

Q: Find the positive integer which leaves the remainder 2, 3, 2  when it is divided by 7, 9 and 11…

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Q: give the least common denominator of ⅗, ⁴/10 and ½?

A: The denominators are 5, 10 and 2.

Q: 5. What is the remainder after 2x^3 +5x^2 -4x + 9 is divided by ( x + 4 ) * O 201

A: Remainder is the part of something that is left over when some other parts are completed. In…

Q: A two digits number is obtained by either multiplying sum of the digits by 8 and adding 1 or by…

A: Form the system of two equations and two unknown and solve them to get the answer.

Q: PLEASE DO THIS ASAP IM BEGGING YOU, SHOW ALL THE WORK PLEASE How many integers must you pick to be…

A: By using Pigeonhole Principle we solve the given problem as follows :

Q: On their anniversary, Mady brought a box containing n dark chocolates bars with n less than 250. The…

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Q: When a whole number is multiplied by 100, where is there a 0 in the product

A: Given:Whole number is multiplied by 100,Where is there a 0 in the product

Q: If 6.2 is multiplied by 103, what does this multiplication do to the decimal point in 6.2?

A: We have to multiply 6.2 by 103. We know property of decimal, a.b=ab10a.bc=abc102a.bcd=abcd103 And,…

Q: se one) is an integer and x1} is an integer and x21} is an integer and l<x<4}

A: a. The roaster form is given as, 1,2,3,4........ The set-builder form is written as, xx is an…

Q: Which integers are divisible by 5 but leave a remainder of 1 when divided by 3?

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Q: what is 28 over 12 in simplest form

A: We have to find the simplest form of 28 over 12.

Q: what is the soulition to 4x + 3 > -5

A: The solution is :  x ≥ - 2

Q: Find the fraction such that if 2 is subtracted from its term it becomes 4, but if 4 is added to its…

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Q: If 50% of a number is 100 and 20% of the same number is 40, find 70% of that number.

A: We have to find 70% of the number where, 50% of the number is 100 and 20% of same number is 40. Here…

Q: A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first…

A: Using the rules of Geometric progression we can solve for the statement

Q: the student noticed that if he writes a multiplication sign between the second and third digit of…

A:

Q: A person is holding two drillbits one is7/16 and the other is 25/64, and wants to first drill a hole…

A: We have to make 7/16 to 64ths    To get 64 from 16 we will multiply 16 by 4.

Q: A student imagined one number.2 is written to the right side of the number and 14 is added to the…

A: We can solve for the given question using elementry operations. We can write a number in the form…