1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is repeated in any one integer is 24. O True O False

Q: 2. Perform the indicated Integer operations. -2+(-3) = -4-(-5) = 1- (-2) +2 (-3) 2 (2-4) + (-4) 2-8=…

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Q: How many integers from 1 to 700 (inclusive) are divisible by the factors of 70 greater than 1?

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Q: Suppose 35 cars start at a car race. In how many ways can the top 3 cars finish the race?

A: The information provided in the question are as follows :-There are  cars at a car race.

Q: What is the converse of: an integer has divisors other than 1 and itself, if an integer is…

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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: 2. 6n - 1 is divisible by 5 for n any positive integer

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Q: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: Prove: The sum of an odd number of odd numbers must be odd.

A: Let us prove this by induction, that if n is odd and a1,a2,. . .. .an are odd, then ∑i=1nai is odd.…

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

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: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: Texas is starting a lottery game. Play- ers use a machine that randomly selects 7 distinct numbers…

A: To calculate the probability that Texas will lose money, we need to determine the expected value of…

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: Disprove  For any integer n, n2 + 5 is not divisible by 5.

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Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: T 22 1+ ] 3 32 +ㅗ +1 + 42 + S2 1 ㅈ 6 = ? 2

A: You will find Solution  in next step

Q: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

Q: How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no…

A: The given digits are: 1, 3, 5, 7, and 9. We have to find the number of ways to write a 3-digit…

Q: Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one…

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Q: Evaluate  1/2 + 1/4 + 1/8 + 1/16 + ... + 1/1024

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Q: Assume that the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one…

A: Given, the sum of the digits of a number, n, in base 10, equals to 16. Example: n= 97 is one such…

Q: - Find every positive integer n with the property that 2" - 1 is divisible by n.

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