3. Consider a set of numbers B = {n E Z|1

Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

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Q: Use the roster method to write the set of integers between 0 and 12

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Q: When choosing k elements from a set of n elements, òrder may or may not matter and repetition may or…

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Q: (a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that…

A: Any number which has 0 or 5 in the unit place is divisible by 5.  Case 1: when unit digit is 0 The…

Q: . Let n =12,612,6x0,725,725 . a. If 9 | n, then x = ________ . b. If 11| n, then x = ________.

A: (a) We know 9 | n iff the sum of the digits of n is divisible by 9.     n = 126126x0725725    =>…

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: let A {a, b} and B = {4, 5, 6}. %3D

A: A=a,bB=4,5,6 To find : a A×Ab B×B

Q: a) Is (−3)! possible? Explain your answer.  b) In how many ways can you order an empty list or zero…

A: a.(-3)! is not possible only the factorial of whole numbers are possible. Main use of factorial is…

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: (b) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7 and 8 such…

A: Given Digits: 0,1,2,3,4,5,6,7 & 8

Q: 2. Create a table to list the divisors of each of the following mnumbers. (a) 30 = 2-3-5 (b) 360 =…

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Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: Given: B = (xI20 < x < 50 and x is divisible by 7 }, find n(B). a. 30 b. 20 c. 10 d. 5

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Q: 6. How many integers from 1 through 100 must you pick in order to be sure of getting one that is…

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Q: Determine whether the following statements below is true or false. 1. (1/2)2<1/2, and 123 is…

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Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: How many numbers between 1 and 100,000 can be divided by 24?

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Q: a = ? b = ? c = ? d = ? e = ?

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Q: For how many n = {1, 2, ..., 695} is n a multiple of one a multiple of one or more of 8, 3, or 7?

A: In the range of [1, 695] the number of numbers divisible by an integer k =  represents the floor…

Q: For how many n = {1, 2,…, 645} is n a multiple of one or more of 8, 7, or 3?

A: n belongs to (1,2,....645) is n a multiple of one or more of 8,7 or 3.

Q: How many integers in between 1 and 3000, inclusive are divisible by either 5 or 7?

A: Let A and B are two sets such that then number of elements in A and B are obtained as…

Q: A group of 6 people are sitting in a circle at the park for a picnic. Two seatings are considered…

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

Q: How many 3-digit numbers with digits in {1,..., 9} (repeats allowed) are divisible by 9?

A: Given digits are 1,2,3,4,5,6,7,8,9. Make three digit numbers using the given digits. To find: The…

Q: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

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Q: 25.07 is divisible by what?

A: IF ANY NUMBER HAS FACTORS MORE THAN TWO THEN IT IS CALLED A COMPOSITE NUMBER.