31. Assume that p and q are different prime numbers and that n divides n and q is a natural number. Argue briefly that if p divides n, then pq divides n. 32. Draw a sou Draw

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Q: Use permutations to solve. From a cooler with 6 different kinds of soda, 4 are selected for 4…

A: nPr = n!/(n-r)!

Q: . 17.MP.7 Use Structure Create a list of prime numbers from 1 to 100. · . • Write all the numbers…

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Q: One-fourth root. Show that the fourth root of 5, 5, is irrational. Trrationalsums (S)

A: ANSWER :

Q: 1. Factor 51,948 into a product of primes.

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Q: 32. Prove that 3 divides n + 2n whenever n is a positive integer.

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Q: 3. The GCF of any two distinct prime numbers is 1. (Distinct they are not the same number) means

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Q: Use permutations to solve. From a cooler with 9 different kinds of soda, 3 are selected for 3…

A: The formula of permutation is: Prn=n!n-r! This is the required answer.

Q: 3. Determine if the the number 132 is perfect, deficient or abundant. Show all work.

A: A number is said to be perfect if sum of its proper divisors is equal to the nunber.  Deficient if…

Q: 12. Lee marks sixths on a number line. He writes just before 1. What fraction does he write on the…

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Q: 3. Do a direct proof using domain knowledge: The sum of three consecutive integers is divisible by…

A: I have explained everything with in the solution. Please go through that.

Q: Is 2 • 3 • 5•7•11•13•17•19 + 1 prime or composite

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Q: 5. In the calculation of (41)eight (77)eight what is the digit in the "sixty-four's "position of the…

A: Please find attachment below

Q: 8. Use divisibility tests to decide whether the given number is divisible by 2, 3, 4, 5, 6, 8, 9,…

A: Please  comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: A palindrome is a number that reads the same forward and backward, such as 2,743,472. (a) Give a…

A: Solve the following

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A: If n elements is to be arranged  at n position out of which p and q number of elements are repeated…

Q: Factor 51, 948 into a product of primes.

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Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

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