Find: The sum of all positive integers less than 400 which are not divisible by 5.

Q: nd a sixth integer between 1 and

A: a)  A player in the power ball lottery picks five different between 1 and 69  ways to choose first…

Q: Determine how many eight-digit positive integers you can make if the integers must include at least…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: (a) Find the number of integers between 32 and 395 that are divisible by 6. (b) Find their sum.

A: (a) The first term of the integers between 32 and 395 is a1=36 which are divisible by 6   and the…

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

A:

Q: R.1. Show that among 14 distinct integers, there must be two that have the same remainder when…

A: In order to prove this statement pigeonhole principle has to be applied. According to pigeonhole…

Q: Find the number of positive integers not exceeding 1000 that are not divisible by 2 or 3 but…

A: The positive integers not exceeding 1000 that are not divisible by 2 or 3 but divisible by 5 are 5,…

Q: Show that if n is any integer, then 3 divides n3 − n

A: To prove:  if n is any integer, then 3 divides n3 − n. Concept used: Here we shall use the identity:…

Q: Determine whether the statement is true or false, "3 is an even integer and 3 is less than 5."

A:

Q: In a sports league of x teams in which each team plays every other team twice, the total number N of…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the product of all positive integers from n down through 1 for n = 5.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4.

A:

Q: A theater hall has n rows of seats. The first row has 25 seats, the second row has 33 seats, and the…

A:

Q: How many integers will there be on the number line between the numbers 2.09 and 15.3?

A: There will be 13 integers between 2.09 and 15.3 on the number line.

Q: very third grade class has acert

A: The solution is given below

Q: Set C is the set of positive two-digit even numbers less than 56 that are divisible by 5.

A:

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: What is the sum of the first 150 positive integers?

A:

Q: (b) Determine whether 6|(n³-n), for each integer n ≥ 0.

A: 13) b We prove that n3-n is divisible by 6 by using mathematical induction   Basis step: For n=0…

Q: (a) How many positive integers divide 10!.

A: Since  you have posted a multiple  question according to guildlines I will solve first   question…

Q: Use direct proof to show that product of two consecutive integers is even.

A:

Q: Find the smallest number greater than 200 with 14 positive divisors

A:

Q: How many committees are possible if the committee must have a least two men?

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: Find the order of 2 2; in C

A: Order is 8

Q: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

A:

Q: How many seats are there in all 28 rows?

A:

Q: Find the total number of integers 'n' such that 2 ≤ n ≤ 2000 and H.C.F. of n and 36 is 1.

A:

Q: Find N

A: Here we have; ∠P=(x+9)∘ and ∠Q=(2x+3)∘ We have to find ∠N=?

Q: Solve by mathematical induction For all integersn> 3, 4(4" – 16) 4 + 4* +4 + .. ……+4" =

A: Solution: The objective is to prove that the given statement using mathematical induction.

Q: Find the sum of all the integers from 1 to 1000. Select one: a. 505,000 b. 5,000,000 C. 500,500 d.…

A: We have find out sum

Q: The first ten rows of seating in a certain section of a stadium have 30 seats, 32 seats, 34 seats,…

A: Given: he first ten rows of seating in a certain section of a stadium have 30 seats, 32 seats, 34…

Q: Suppose 58 cars start at a car race. In how many ways can the top 3 cars finish the​ race?

A: We have to find no of  ways can the top 3 cars finish the​ race...

Q: How many zeroes are at the end of 1000!/(500!500!)?

A: Calculate number of zeroes in 1000! and then subtract it from the number of zeroes in (500!500!).

Q: Q7. How many positive integers not exceeding 100 are divisible either by 6 or by 10?

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: A theater has 30 seats in the first row, 32 seats in the second row, in- creasing by 2 seats each row…

A: Total number of rows = 26Increment in each row = 2So, starting from the first row, we have 30 seats,…

Q: Determine the is a non-negative integer

A: The number of non-negative integer solution to the vectors…

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: Explain how to find n! if n is a positive integer.

A: Given that the term n!.

Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

Q: R.2. Show that among 29 distinct integers, there must be a set of 5 integers all of which have the…

A:

Q: Find the number of positive integers not exceeding 120 that are divisible by 3 or 4

A:

Q: How many integers must you pick in order to be sure that at least two of them have the same…

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Q: Find the sum of the integers from −20 to 256.

A: It is required to calculate the sum of integers from -20 to 256 that is:

Q: How many zeros are there at the end of 1001?

A: This question is related to Number Theory

Q: Find the number of positive integers ≤ 1000 that are not divisible by 5, 13, or 31?

A: .  Symbol of Greatest Integer Function  To Find: Number of positive integers ≤ 1000 that are not…

Q: Let n be the positive integer n=36!/26! Determine the remainder when n is divided by 13.

A: We will find out the required value.

Q: How many zeroes are at the end of 25! (= 25 factorial)?

A: The given number is 25!.  Now, we need to find the number of zeros at the end of 25!.

Q: 5 divides n -n whenever

A:

Q: Find the sum of the integers between301 and 400 inclusive that are multiples of 4.

A: