Let n = integer; 7 divides n if and only if 7 dividesn^2 (The result(s) ought to be integer(s))

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

A: By properties we know that,

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: How many 3 digit even numbers can be created if repetition of digits is allowed

A:

Q: Express the interval shown on the number line in interval notation. -8 4 8. 10 12 -12 -10 -4 -2 () U…

A:

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 witness on a hit and run incident cannot recall the whole plate number of the car who hit an old…

A: Given that in hit and run case an old woman remembered is the plate number starts with TIP and the…

Q: Two distinct numbers are selected from the set (1,2,3,4,...,36,37) so that the sum of the remaining…

A: Given two distinct numbers are selected from the set 1,2,3,4,…,36,37 and The sum of remaining 35…

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

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

A: We have to find the number of positive integers 1,000,000 have a digit sum of 5. The number less…

Q: Show that 3 + V5 is inational number

A: Let 5^1/3 is a rational numbers. So, we can write it as 5^1/3=p/q ………….(I) according to the…

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

A:

Q: How many 5-digit even numbers can be formed using the digits 2, 4, 6, 7, 9 if no repetition is…

A: Given:

Q: All composite number can represent as product of primes numbers

A:

Q: Suppose I choose two numbers from the set {1, 2, 3,... 100}. How many have an even sum? Show all…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: The number of 3-digit numbers less than 400 that can be created if the last digit is either 4 or 5…

A: Solution  :

Q: A company has been selling 600 items every month at $ 720 each. However, for each $ 40 rebate…

A: The given data is: A company has been selling 600 items every month at $720 If a rebate of $40 is…

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

A:

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

A:

Q: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

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: What is the sum of the first 200 positive integers?

A:

Q: Show that 2 + V5 is imational number

A:

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

A:

Q: Evaluate the integral. х3 - 3х - 9 х2 - х - 6 Зх— 9

A:

Q: Find the sum of first 30 positive integers divisible by 6

A:

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

A:

Q: A hot air balloon descends at a rate of 4ft per minute for 6 minutes, then rises at a rate of 2ft…

A: Given Data: The descending rate of the balloon is: D'=-4 ft per minute The time till the balloon…

Q: Show A and Show B are two of the most popular television shows of all time. The number of episodes…

A:

Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

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

A:

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

A:

Q: What are all of the natural numbers divisible by 8 whose sum of digits is less than 10 and the…

A: Given the requirements

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

A:

Q: How 3 digit number greater than 200 can be formed a. Repetition not allowed  b. Repetition allowed

A:

Q: The distance between x and 3 on a number line is no more than 0.5.

A: Given: The distance between x and 3 on a number line is no more than 0.5

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……………….

A:

Q: Use different ways to show all possible combinations in this situation

A: Here given ,  there are three brand for cell phone  and there are 3 color for cell phone

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: Use different ways to show all possible combination in this situations

A: Here use different ways of representing a total possibilities Here use listing , table, and tree and…

Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…

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

A:

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

A:

Q: Prove that the sum of two consecutive positive odd numbers less than ten gives an even number

A: Given, The sum of two consecutive positive odd numbers less than ten gives an even number.  We have…

Q: 5 divides n -n whenever

A:

Q: How many positive integers not exceeding 100 are divisible by 5 or 7?

A:

Q: A 24-volume encyclopedia is placed on a bookshelf in numerical order. Each volume is 2 inches thick,…

A: The total volume of the encyclopedia  placed on a bookshelf =24 The thickness of each volume…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.