How many integers from 1 to 1000: a) Are divisible by 7? b) Are divisible by 7 but not 11? e) Are divisible by exactly one of 7 and 11? d) Are divisible by neither 7 nor 11? e) Have distinet digits? f) Have distinet digits and are even?

Q: a) Suppose in a university, each subject offered to students has a subject code consisting of four…

A: a) In a university each subject offered to students has a subject code consisting of four letters…

Q: is the set of irrational numbers closed for: a) addition and b) multiplication

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Q: Claim: For any natural number n, if 6 ∣ n, then 3 ∣ n.

A: Use the mathematical induction to show that the given statement “For any natural number n, if 6 ∣ n,…

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A: Excel is used to obtain the line and bar graph for years of education and years of experience,…

Q: 8) The number 4050 can be factored into prime divisors as: 2 x 3 x 3 x 3 x 3 x 5 x 5 a) Determine…

A: We have to solve

Q: 2. How many 3-digit numbers with no repeated didgits using 4,5,6,7,8 can be a) Less than 520 b)…

A: Number digit numbers with no repeated didgits using 4,5,6,7,8=P53=60 This is less than 520.

Q: Classify each number below as: a) a natural number b) an integer c) a rational number d) an…

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Q: ich there are no repeated digits?

A: Available digits:   0,1,2,3,4,5,6,7,8,9 Total availeble position: 3 position   1st digit  2nd…

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Q: 2. How many integers between 1 and 500 (inclusive) are a) divisible by 2? b) divisible by 7? c)…

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Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: There are total 7 digits, such that, 2, 3, 4, 5, 6, 7 and 8.

Q: Find the greatest common divisor (a, b) and integers m and n such that (a, b) = am + bn. a = 65, b…

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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: Use a Venn Diagram to solve: Out of 191 houses for sale in a specific zip code, 94 have a swimming…

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Q: How many unique codes are possibly formed from two characters, where the first character can be 2 to…

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Q: How many three-digit numbers with different digits are divisible by: a) 25 b) $4 ?$

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Q: If 6-digit positive integer is added to a 6-digit positive integer , the sum could have A) 5 digits…

A: A detailed solution is given below.

Q: Natural numbers are arranged in a triangular shape as shown below: If the pattern continues,  a)…

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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: 2. How many integers between 1 and 500 (inclusive) are a) divisible by 2? b) divisible by 7? c)…

A: Note: As per our Guidelines we can solve first three subparts. Please repost remaining parts.

Q: Using the digits 1, 2, 3, and 4, allowing for repetition:…

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Q: b) How many resulting prize numbers are possible that end with the number 1? c) How many resulting…

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Q: 98! 1. Simplify. : 100! a) 100 x 99 x 98! b) 1 100 x 99 x 98 c) 100 × 99 d) 1 100 × 99

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Q: Write R code that does the following 4 [(-3)* +5] √ 18 37 4 ind

A: The objective is to write R code to find the following expression: 724+51843

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A: We have to find number of permutations possible.

Q: 1. Find all natural number factors (divisors) of the number 42:

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Q: a) 246eight b) A3Esixteer

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Q: Suppose any digit can be repeated, how many 4-digit PINs are possible if each PIN: a) must end with…

A: As per our guidelines, we are are allowed to answer only first question . Thanks   Suppose any digit…