Is 2 • 3 • 5•7•11•13•17•19 + 1 prime or composite

Q: If n is a prime number greater than 3, what is the remainder when n² is divided by 12?

A: The objective of this question is to find the remainder when the square of a prime number greater…

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: Compute: 35] [30] : -1 5 20

A: According to the question,

Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: IF 1+ 1 then 22 3 1+ ] 32 +ㅗ 42 + +ㅗ S2 a 17 ? 6

A: The given problem is to evaluate the given series sum of the given series 1+1/32+1/52+... with given…

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: I am a fraction less than 1.My numerator is divisble by 3 and my denominator is a prime number. The…

A: We have to find a fraction that is less than 1. Whose numerator is divisible by 3 and denominator is…

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: 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: Calculate 19992 – 19982 + 19972 – 1996² +... -22 + 12.

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

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Q: Which number line shows the solutions to n > -2? + 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 +++ 1 2 3 4 5 6 -6…

A: Given: To identify the line which shows n>-2

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

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Q: If the first even integer is 4, then what will be next three consecutive even integers ? O 5, 14, 10…

A: In the question it is asked to represent next three consecutive even integers after even integer 4.

Q: 2.x4 + x3 x4 xp-

A: Given query is to find the value of the integral.

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: Prove log, + log, 20 log, 8 = o

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Q: What is 150 +150+150+150+150+150+150+150+150

A:

Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: Given P is a prime number >2, will 7P ever be prime? Why or why not?

A: Step 1:No, 7P will never be prime if P is a prime number greater than 2.Here's why:- For 7P to be…

Q: How many integers between 100 and 999 inclusive are multiples of 13?

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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: 2) (-17) + (-22) + (-27) + (-32)..., A) -224 B) -448 C) -217 D) -218

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Q: Why is 1 is not a prime number?

A: Prime Number :- A number can be defibe as prime number it it divisible by by itself and by 1. So by…

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: 2)5

A: The integration is given as: ∫0∞x7e-x6dx

Q: What are the even integers between -9 and 5?

A: An integer k is said to be even if it can be written as k = 2n where n is an integer.The integers…

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: Show that there are no prime triples other than 3, 5, 7.

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Q: If n(A ∪ B) =113, n(B) =62, and n(A ∩ B) =44, what is n(A)? (Enter answer as a whole number)

A: Given,1136244We have to find Using formula,

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: If P is a prime number >2, will P+7 ever be prime? Why or why not?

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Q: How to convince someone that the number 10 is not prime.

A: