How many positive integers between 500 and 999 inclusive are not divisible by 5?

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

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Q: How many integers between 100 and 400 contain the digot 2?

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Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

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

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

Q: 1. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?

A: A number is divisible by 5 if the last digit is either 5 or 0. We have to find the number of 5 digit…

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

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Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: Determine the number of natural numbers less than 700 that can be written using the digtits 5,6,7,9?

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Q: How many positive integers less than 850 are multiples of 8, 3, or 5? Use the Principle of…

A: Using the Principle of inclusion/Exclusion, the formula for A∪B∪C can be written as:…

Q: Consider all positive integers with 3 different digits. (Note that 0 cannot be the first digit.) (1)…

A: Iam assuming that the numbers from 0 to 99 are not valid because they are not 3 digit numbers, so it…

Q: In a set of 2 positive integers, how many ways it can be chosen in less than 50? 1.

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

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

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Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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Q: How many positive integers between 5 and 31 (a) are divisible by 3? (b) are divisible by 4? (C) are…

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Q: The number of positive integers not exceeding 1000 that are not divisible by 8 and not divisible by…

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Q: Compute the sum of all integers between 60 and 150 that are exactly divisible by 8.

A: Consider the given range of number 60 to 150

Q: 1. How many positive integers of 5-digit-number can be formed from the prime numbers starting at 1…

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

Q: 4) Find the number of positive integers not exceeding 1,000 that are not divisible by 3, 5, or 11.

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Q: How many different integers must be selected to guarantee that at least 5 of them would have the…

A: Dividing any integer by 3, can have remainder 0, 1 or 2. Therefore, possibilities for remainder are…

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: 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: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

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: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: how many four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: Find the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5.

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

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Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

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: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

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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: compute the sum of all integers between 60 and 110 that are exactly divisible by 7

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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: The sum of all positive integers less than 400 which are divisible by 5.

A: Positive integers less than 400 which are divisible by 5 are⇒n=79 5,10,15,20,...,395 The above…

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: What is the set of O of odd positive integers less than 10?

A: The odd positive integers less than 10 are 1, 3, 5, 7, 9.

Q: How many positive integers between 100 and 999 inclusive a) are divisible by 7? b) are odd? c)…

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Q: find the sum of all integers between 300 and 800 that are exactly divisible by 14

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Q: How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?

A: A number is divisible by 5, if it has a 0 or 5 in the unit digit place. Let m choices to be made…

Q: What is the value of the whole number N, if: N ofof of of 100?

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

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Q: that the set of negative integers divisible by 3 is countable

A: Set of negetivee integers divisible by 3 isS=-3n, n∈ℕf: ℕ→S   defined asf(n) = -3n,To check…

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: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

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Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: How many four-digit positive integers both start and end in even digits:

A: We need to find the number of positive integers both start and end in even digits.