How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and 7?

Q: 3. How many 4-digit positive integers are there that are even or contain no O's?

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Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

Q: 7. How many positive integers between 100 and 999 inclusive are divisible by 78

A: We have to find the number of positive integers between 100 and 999 inclusive that are divisible by…

Q: A. If p + 2 is a prime number, prove that p? + 3 is divisible by 4.

A: Let p≠2 be a prime number.

Q: 2.3 How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: Formulae used: Total number of elements in the events E1 or E2 : n(E1∪E2)=n(E1)+n(E2)-n(E1∩E2) Total…

Q: Let i be a positive integer and A, = {..., i – 6, i – 4, i – 2, i, i + 2, i + 4, i + 6, ... }. Then…

A: We have to find intersection of Ai

Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: 10. How many positive integers between 100 and 999 inclusive a) are divisible by 7? b) are not…

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Q: The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

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Q: How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: Integers between 0 and 500 = 1, 2, 3, 4, ....., 499   Number divisible by 3 = 3, 6, 9, ...., 498…

Q: If p + 2 is a prime number, prove that p² + 3 is divisible by 4.

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Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: How many positive integers between 1000 and 9999 inclusive a)are divisible by 9? b)are even?…

A: .

Q: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

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Q: p + 2 is a prime number, prove that p2+3 is divisible by 4. (2.5

A: Prime and divisibility

Q: How many integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

Q: 5. Let a, b, c, and d be any four integers. Assume that 2 divides a, that 3 divides b, that 5…

A: If x divides y, it can be written that y=xk, where k is a constant. In other words, if y is divided…

Q: a) How many 3-digit positive integers are there with odd digits?

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Q: Consider the two-digit positive integers 10, 11, 12, ., 99. How many positive two-digit integers are…

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Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: 5. How many positive integers between 50 and 100 a) are divisible by 7? Which integers are these? b)…

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Q: If n is prime, then 2" – 1 is prime.

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Q: How many positive integers between 100 and 999 inclusive   d) are not divisible by either 3 or 4?…

A: The set: A∪B contains all the elements that are present in set A or B. The set A-B contains all the…

Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: If z ≥ 2 is an integer, show that the following numbers are composite. n! + 2, n! + 3, n! + 4, ... ,…

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Q: If a, b, c, d are distinct prime numbers with an as smallest prime then a * b * c dis None of the…

A: Given a,b,c,d are distinct prime numbers with a as smallest prime. Then, a*b*c*d=_________

Q: 1)How many integers between 1000 and 2000 are divisible by at least one of the integers 3, 5 and 7?

A: Introduction: In mathematics, integers are the sum of positive and negative numbers. Integers are…

Q: If a, b, c, d are distinct prime numbers with an as smallest prime then a *b * c dis None of the…

A: Answer

Q: Let i be a positive integer and A, = {[.., i – 6, i – 4, i – 2, i, i + 2,i + 4,1+ 6, . ). Then N 4…

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Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A: Note : According to our guidelines we can solve only first three subparts and rest can be…

Q: Show that there are infinitely many integers n such that 4(n^2)+1 is simultaneously divisible by 13…

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Q: Prove or disprove: let n be an integer. if 3 divides n^2, then 3 divides n.

A: Let us consider some cases for proving that n be an integer. if 3 divides n^2, then 3 divides n.For…

Q: Determine the number of ways a computer can randomly generate one or more such integers from 1…

A: There are 5 prime numbers between 1 to 12 . Which are 2 ,3 , 5, 7 , 11.

Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A: The positive integers between 1000 and 9999 is calculated as follows.

Q: 4.The set of integers from 1 to 10 that is divisible by 3.

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Q: If n is an integer greater than 2, then for all integers m, n does not divide m or n + m # nm.

A: c Given n∈Zand n>2. We have to prove that for all m∈Z, n/m or n+m/nm. Suppose n/m and…

Q: how many six-digit numbers can be formed so that 2 are in the place of thousandth and 5 in the place…

A: First number can not be 0. So we can pick the first number in 9 ways. (1 to 9)

Q: Let p, q, and r be primes other than 3. Show that 3 divides p2 +q2 + r2.

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Q: How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed with…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: How many integers greater than 130 but less than 640 are divisible by 7? O None of these. O 72 O 73…

A: Correct ans is = 73 Please find attachment for the details solution

Q: How many integers between 100 and 999 have distinct digits, and how many of those are even numbers?

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Q: Prove that 8 divides 9" – 1 whenever n is a natural number. For each natural number n, let P(n) be…

A: To prove that  8 divides 9^n-1 whenever n is a natural

Q: (a) How many permutations of (10] are there that EITHER alternate even and odd numbers or have even…

A: Let consider the permutations of 10 as the ordering of  the elements of 10 rather than as an…

Q: 4. How many positive natural numbers less than 1000 are neither divisible by 3 nor 5 nor 7 nor 11.

A: Let U={1,2,3,...1000} n(U)=1000 A={a∈U/ x is divisible by 3}A={3,6,9. . .…

Q: by

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Q: Let p, q, and r be primes other than 3. Show that 3 divides p2 + q2 + r2.

A: We have to prove that 3 divides p2+q2+r2, where p,q and r primes other than 3.

Q: Prove that the sum of two consecutive odd integers is divisible by 4.

A: Let the two consecutive integers be n and n+2 Then we need to prove that (n)+(n+2) is divisible by 4…

Q: A restaurant sell features a burrito bar in which a customergets to choose one of 2 different kinds…

A: As per bartleby guidelines only one question is answered please upload the other one separately…