Assume that all four-digit integers (numbers from and including 1000 to and including 9999) are written up. How many times has the number 1 been written down? How many times has the digit 3 been written down?

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

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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: How many positive integers less than 10000 are there which contain at least one 7 or at least one 9…

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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: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: Name all integers from -100 to 100 that are congruent to -1 modulo 25!

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Q: Is the set of all of the integers between 12 and 99 finite or infinite?

A: Given : The set of all of the integers between 12 and 99

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: of the first 150 positive integers?

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Q: The set of numbers whose decimal representations are neither terminating nor repeating is called the…

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

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Q: i need the last one, thank you

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Q: Prove that the sum of any five consecutive positive integers is always a multiple of five.

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Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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Q: Let Sbe the set of all (nonnegative) 4-digit integer. How many integers from start with 1 and end…

A: let S be the set of all 4-digit integer. how many integers from start 1 and end with 9

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

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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: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: prove that the one's digit of any integer,n, is the remainder when one divides n by 10.

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

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

A: Note : According to our guidelines we can solve only first three subparts and rest can be…

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: Determine the number of ways a computer can randomly generate one or more such integers from 1…

A: There are 5 prime numbers between 1 to 12 . Which are 2 ,3 , 5, 7 , 11.

Q: Show that if n is an odd integer then []

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Q: How many 98-element subsets does [100] have? (Here [100] is the set consisting of the first 100…

A: Given: Let us consider n be the number of elements in the set and r be the elements-subsets. Then, n…

Q: If n is a positive integer, is there always a prime between n and 2n?

A: given that n is a positive integer. we have to show that there is always a prime number between n…

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain?

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Q: Find out how many distinct three-digit numbers can be formed using al the digits of 1, 2, and 3. * O…

A: To find  Number of distinct three digit numbers can be formed using all the digits 1,2 and 3.

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

A: Permutation and combination concepts will be used to filter out all the 3 scenarios in getting…

Q: Let S be the set of all (nonnegative) 4-digit integers. How many integers does S contain? Enter your…

A: Disclaimer: Since you have asked multiple questions we will solve the first question for you. If you…

Q: a. On each of four consecutive plays in a football​ game, a team lost 8 yards. If lost yardage is…

A: On each of  four consecutive Plays in football gane team lost 8 yards

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: from the list 0, 14, 2/3 , π, √7, -11/14 , 2.34, -19, 55/8, -√17, 3.2 ̅1, and -2.6, identify each of…

A: Given: Given List : 0, 14, 2/3 , π, √7, -11/14 , 2.34, -19, 55/8, -√17, 3.2 ̅1, and -2.6.…

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: How many integers between 100 and 999 have distinct digits, and how many of those are even numbers?

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Q: Show that the set of odd numbers is countable.

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Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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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: Assuming every integer is either even or odd, How would I show that for any integer, the difference…

A: Assume that every integer is either even or odd. Let the integer considered say x is even. Then by…

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: How large a subset of the integers from 1 to 50 must be chosen to guarantee that one of the numbers…

A: We have to determine How large a subset of integers from 1 to 50 must be chosen to guarantee that…

Q: Let be a prime number (integer). Show that p2 + 5 cannot be a prime number.

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

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

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Q: Prove that the sum of two consecutive odd integers is divisible by 4.

A: Let the two consecutive integers be n and n+2 Then we need to prove that (n)+(n+2) is divisible by 4…

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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