How many positive integers less than 1,000,000 have a digit sum of 5?

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

A: 2, 4, 6, 8, 10,....... This is an arithmetic sequence with  a1=first term=2d=common difference=4-2=2…

Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

Q: How many zeros does 25! end with?

A: A number will have trailing zeros when 5 and at least one even number are factors of it.   Also, the…

Q: Find 1 + 2 + 3 + 4 + ......... + 100, the sum of the first 100 natural numbers.

A: Given: The expression 1+2+3+...+100, To find: The sum of the expression.

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

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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: 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: 10. Find the sum of the coefficients of (2x– 3)°. c. -6560 d. -5120 а. -5660 b. -6780

A:

Q: What is the smallest integer n for which 25n>512?

A: The provided expression is as follow:

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: How many numbers between 1 and 1000 are divisible by 12 or 15, or both 12 and 15?

A: We need to find how many numbers between 1 and 1000 are divisible by 12 or 15, or both 12 and 15. To…

Q: Which integers leave a remainder of 1 when divided by 2 and also leave a remainder of 1 when divided…

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Q: Find the sum of the first 20 positive even integers.

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Q: How many positive numbers less than 300 are divisible by 7 but not 5?

A: We need to find positive numbers less than 300 that are divisible by 7 but not by 5. First count the…

Q: What is the sum of the first 100 nonnegative integers?

A:

Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…

Q: What is the smallest sum possible sum of 25 consecutive positive integers which s a perfect square?

A: Let's take the 25 consecutive positive numbers as an Arithmetic Progression with first term a.…

Q: How many four-digit odd numbers less than 6000 can be formed using the digits 2, 4, 6, 7, 8, and 9?

A: Consider the given situation in the problem, we have four groups in which we have to make choice to…

Q: Show that every odd integer is the sum of two consecutive integers

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Q: Find the total number of positive integers < 100 that are either odd or the square of an integer.

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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

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.