The pattern​ 1, 8,​ 27, 64,​ 125, ... is a cubic pattern, what is the greatest number in this pattern that is less than 10 to the 4th power?

Q: A quiz consists of 3 true-or-false questions.  In how many ways can a student answer the quiz?

A: Given that there are 3 true or false questions. Each question has 2 possible outcomes. That is true…

Q: are there any even numbers greater than 2 which are prime? why or why not?

A: We will find the solution in the following step

Q: How many different 5-digit even numbers can be formed from 0, 1, 3, 4, 5, 7, and 9 if repetitions…

A: The digits used to form the 5-digit even numbers is 0, 1, 3, 4, 5, 7, and 9.

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

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Q: How many three digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible…

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Q: How many 3-digit numbers can be formed from the digits 2, 3 ,5, 6, 7 and 9, which are divisible by 5…

A: All three digit numbers which are divisible by 5 to be formed from the digits 2,3,5,6, and 7.…

Q: The first 5 terms of a number pattern are 4,9, 14, 19, 24, ... Which expression is equivalent to the…

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Q: 3. Use your result above to show that the number 1,111,111,113 is divisible by 3 while the number…

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Q: How many 4-digit numbers can be formed with the digits: 1,1,2,2, without allowing the repetition of…

A: Given digits is1,1,2,2

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 integers in {1, 2,..., 100} are not divisible by 7 or 5? (Give the exact number)

A: Find the number of integers in 1,2,...,100 which are not divisible by 7 or 5.

Q: What is the smallest positive integer that has 6, 8, and 10 as factors?

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Q: How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the…

A: To form a 3 digit number, we start we can not place 0 on hundreds position since that will make it a…

Q: ay be formed using the digits 2, 3, 4, 6 and 9 if repetitions

A: 22,23,24,26,29,32,33,34,36,39,42,43,44,46,49,62,63,64,66,69,92,93,94,96,99. In unit digit place we…

Q: What is the number of positive integers not larger than 210 and not divisible by 2, 3 or 7?…

A: Within 210, the number of integers that are divisible by 2= 210/2= 105  Within 210, the number of…

Q: suppose repetitions are not allowed. Find the number n of three-digit even nimbers that can be…

A: Given problem Given that   Suppose repetitions are not allowed. Given six digits : 2,3,5,6,7,9…

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: How many two-digit numbers can be formed from the digits 1, 2, 3, and 4 if a. no digit is repeated…

A: Given that, Digits are given 1, 2, 3 and 4 a) Two-digit numbers with no digit is repeated: Two-digit…

Q: Find the number of different ways that a family of 9 can be seated around a circular table with 9…

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Q: How to form the digits 2,9,6,4 and 3 from the greatest 5-digit odd number

A: To find the greatest 5-digit odd number

Q: What is the largest number x such that x<200 and x has exactly 4 factors?

A: Factors:    Number that are multiplied together to get a product                              Factor…

Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: How many 5- digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9, if repetitions of…

A: Givendigits = 0,1,2,3,4,5,6,7,8,9No.of digits =10

Q: How many different 5-digit numbers that are divisible by 5, can be formed from 0, 1, 3, 4, 5, 7, and…

A: Given:Total number of digits = 7 (0, 1, 3, 4, 5, 7, and 9 ) The divisibility rule for 5:The number…

Q: How many 5 digit even numbers can you form using all of the digits 1, 2, 3, 3, 5?

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

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Q: How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: What is 2% of 76

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Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: How many different 5-digit odd numbers can be formed from 0, 1, 3, 4, 5, 7, and 9 if repetitions are…

A: Given:Total number of digits = 7 (0, 1, 3, 4, 5, 7, and 9 ) The divisibility rule for 5:The number…

Q: How many 9 digit numbers are there that use each of the digits 1,2,3,4,5,6,7,8,9 exactly once?

A: To form a 9 digit number We know that each 9 digit places are must be one of the 9…

Q: How many four-digit odd numbers less than 7000 can be formed using the digits 2, 3, 5, 7, 8, and 9?

A: To determine four digits odd number less than 7000

Q: A 4-digit number is selected from the numbers (1,2,3,4,5,6} where the digits are selected withou…

A: As per given by the question, there are given the numbers {1,2,3,4,5,6} and from these number select…

Q: 4. Find the sum of positive divisor of 5,020 and also find the pair of this number so that they can…

A: We have to find the sum of all divisor of 5020 and then the amicable pair of the number.

Q: How many three-digit numbers is there such that when the middle digit is removed they become a…

A: Let the three digit number be xyz. then on removing the middle digit, the two digit number will…

Q: A 4-digit number is selected from the numbers †,2,3,4,5,6} where the digits are selected withou…

A: Available Digits : 2,3,4,5,6   a) 4 digits numbers  : For first digit 5 options available, for…

Q: How many of these numbers are even from the digits 0, 1, 2, 3, 5, 7 & 9 ?

A: Here we have to find  How many of these numbers are even from the digits 0, 1, 2, 3, 5, 7 &amp; 9 ?…

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

A:

Q: How many three-digit numbers can be formed using the digits 2,3,4,5,6,and 8, if the number is to be…

A: Given:  The provided digits are 2, 3, 4, 5, 6, and 8. The repetition of digits is not allowed. For a…

Q: How many 3 digit numbers may be formed from the digits 0,1,2,3,4, & 5 if no digit may be repeated…

A: We have to form 3 digit numbers which are less than 330 using the digits 0, 1, 2, 3, 4 and 5. Let…

Q: How many different 3-digit numbers are possible using only the digits 6,7,8,9 ? How many…

A: Given, There are 4 digit, 6,7,8,9

Q: How many twin primes are there where both primes are less than or equal to 31? Number of twin…

A: Twin prime: If there is only one composite number between two prime numbers, then that two numbers…

Q: How many different numbers which contain from four digits or fewer can be formed from the digits A,…

A: Digits can be taken with replacement   Given are 5 letters:   A,B,C,D,E AB&lt;4   and C,D,E &gt;=4…

Q: What is 20% of the least common multiple of 30, 24 and 45?

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Q: Consider 4 digit numbers with each digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} .  How many such…

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Q: A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an…

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Q: The digits 5,6,7 annd 4 are to be arranged to form a 7 digit interger. How many different integers…

A: The choices for each digit is 5, 6, 7 and 4. So each digit has 4 choices.    There are total 7…