a) n(n+1)(n+2)is divisible by 6 b) n(n+1)(n+2)(n+3) is divisible by 24 c) 5" -3" is divisible by 2

Q: (1) What is gcd(31212021 + 3, 31212021 - 3)? I am aware of 3121 is a prime number, and 2021 is…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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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: 4) Prove that the product of any three consecutive integers is divisible by 6.

A: We have to show that product of any three consecutive integers is divisible by 6

Q: ity by 11 by alternately adding and subtracti left, beginning with the units digit-that is, units…

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Q: If N =30 -1. Is N is divisible by 125?

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Q: Prove that for all integers, n , n^3-n is divisible by 3.

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Q: 10) Prove that if 21 = 2, then 2 23. What is mZ1? Explain. 3.

A: The given figure is

Q: 9.) Is 9" + 3 is divisible by 4? PROVE IT!

A: Given : 9n+3 is divisible by 4. To Prove: The given statement is true for n=k+1. Consider Tn=9n+3.…

Q: Suppose 51 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

A: Solution: From the given information, number of cars start at a car race is 51.

Q: divisible by 3 for

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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: How many integers between 1 and 1000 are divisible by 3, 5, 11, or 13?

A: We have to find the total  integers between 1 and 1000 are divisible by 3, 5, 11, or 13. First find…

Q: 2) How many integers between 1 and 200, including both 1 and 200 are divisible by 4 or 5? 3) How…

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Q: How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by…

A: # As per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

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: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: what two consective odd integers have a product of 63?

A: Find two odd integers.

Q: Suppose each license plate in a certain state has two digits, followed by two letters, followed by…

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Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: what are ALL the six-digit numbers of the form 47_8_6 that are divisible by 24?

A: The six-digit number has form 47__8__6

Q: How many 5-digit numbers can be formed using the numbers 0, 1, 2, ….9, such that: Repetition is…

A: There are 10 digit available from 0 to 9. To construct a 5 digit number , the first digit always…

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

A: Just use inclusion-exclusion principle for three sets.

Q: Suppose each license plate In a certain state has three letters followed by three digits. The…

A:

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9 which are divisible by 7…

A: Given:   Digits: 2 , 3 , 5 , 6 , 7 and 9 3-digit code  which divisible by 7 with no repetition of…

Q: How to find σ if σ2 =(1657324)?

A: In general, the terms σ2 and σ will be defined as:  σ2-population varianceσ-population standard…

Q: What is the greatest common divisor of 24 and 44? n If n is a natural number such that gcd(800, n) =…

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Q: A nursery employee wishes to plant 7 aplle trees, 5 pear trees, and 10 apricot trees in one row.…

A: Given a nursery employee wishes to plant 7 apple trees, 5 pear trees, and 10 apricot trees in one…

Q: 8. Show that 4 29! +5! is divisible by 31.

A: We have to prove that 4.29!+5! is divisible by 31.

Q: Prove that 9? −1 is divisible by 8,for all n ≥ 1

A:

Q: 5. Find the number of positive integers less than 700 that are divisible by 3 but not divisible by…

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Q: How many positive integers not exceeding 3000 are divisible by exactly two of 4, 10, 12? (Steps…

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Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5…

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Q: Let A denote the set of all 4 digit numbers that are divisible by 3, and B denote the set of all 4…

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Q: Suppose 26 cars start at a car race. In how many ways can the top 3 cars finish the race? ..... The…

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Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: 2. Show that 1184 – 534 is divisible by 7. -

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Q: How many three-digit odd integers can be formed using the digits 0, 1, 4, 5, 6, 7, and 9 only once?

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: How many 3-digit numbers can be formed from the digits 2,3,5,6, and 9, which are divisible by 5, if…

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Q: How many different 3-digit numbers are possible using only the digits 6,7,8,9 ? How many…

A: Given, There are 4 digit, 6,7,8,9

Q: If  n×k divisible by 4, then n is divisible by 4 or k is divisible by 4. Which of the following is…

A:

Q: 3. There are seven students who always compare their CS test grades. They discovered that either the…

A: It is given that there are seven students who always compare their CS test grades. They discovered…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

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Q: How many positive integers less than 2ˆ{20} are not divisible by 7, 11 or 13. Use…

A: The solution is given below

Q: 4503 is divisible by 2,3,,5,6,9or 10

A: 4503 is divisible by 2, 3, 5, 6, 9 or 10.

Q: What does the divisibility rule of 4 and 8 have in common ?

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Q: Show that 42n -1 is divisible by 5 for n>0

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Q: Fill in the blank so that the resulting statement is true.

A: Given: 3285-40-670 To get result the easiest way to evaluate 3285-40-670 is to expand about the…

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…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.