Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

Q: The set of all odd numbers between 100 and 110 that are a multiple of 3

A: We need to find the set of all odd numbers between 100 and 110 that are a multiple of 3.List of all…

Q: plz solve q4

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Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: Show that 8(-n--8()

A: By properties we know that,

Q: Find the least positive integer that yields the remainders 1, 3, and 5 when divided by 5, 7, and 9,…

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Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

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: When four positive integers are added three at a time the sums are 1551, 1659, 1720 and 1736. The…

A: when four positive integers are added three at a time the sums are 1551, 1659 ,1720 and 1736. we…

Q: A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each…

A: Given:     The sequence is:     1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,... To get this number, we have to…

Q: Prove the formula for the sum of the first positive integers:

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Q: Consider all positive integers that are mueiples of 20 and that are less than or equal to 300. What…

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Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

Q: Prove that the summation of three odd integers is odd.

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Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

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: How many integers 2 ≤ n ≤ 65 have no prime divisor less than or equal to ¹/³?

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Q: Find the sum of the positive even integers up to and including 50.

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

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Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: 6.) Find the sum of the first 50 positive integers ending in 6.

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Q: "Every positive integer can be written as the sum of the square of 3 positive integers." prove…

A: Given: "Every positive integer can be written as the sum of the square of 3 positive integers." To…

Q: If the sum of any two integers is even, then so is their difference.

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: Find the sum of all even integers from 10 to 500

A: Sum of all even integers from 10 to 500 .

Q: that if 3 divides the sum of the digits of n, then 3|n

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Q: Show that (n + 1)! > 2"+3, for n > 5.

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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: Which numbers in Z17 are relatively prime to 17? Enter your answer as a comma separated list of…

A: The objective of the question is determine all al relatively prime to 17 in Z17 .

Q: Use a direct proof to show that the sum of two odd integers(k and l) is even.

A: The number n is even if it is expressed as  n=2m , where m is an integer. The number n is odd if it…

Q: Find the least natural number a with the property that the sum a + 2a + 3a + .. + 9a is the number…

A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: Find the average of the first 50 natural numbers is……………….

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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: Determine the smallest integer that can be expressed as a sum of two primes in three different ways.

A: The number is 22 and all others smallest integer can not be written as sum of two primes in three…

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: be run under the building. If these two blocks must always be next to each other, how many s can the…

A: Given Here we have 7 blocks ,but we  have to keep 2 perticular blocks together. So we have to…

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: Show that every odd integer is the difference between two consecutive perfect squares.

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Q: Find the sum of the first 80 positive even intergers.

A: Sum of the arithmetic progression with for n terms where a1 is the first term and an is the last…

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

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Q: 5 divides n -n whenever

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Q: the sum of any positive integers that is less than 30

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Q: Find for the sum of the first 50 negative even integers.

A: Negative even integers :-    -2,-4,-6,-8, ....... This is AP series with a=-2, d=-2

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.