(a) an even number (c) an odd number appears (b) a prime number appears (d) an odd prime number appears appears

Q: Prove by mathematical induction that the sum of cubes of three consequtive positive integers n is…

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Q: 3.Bobby is n years old. Cam is 5 years older than Bobby. (a) write an algebraic expression for Cam's…

A: Given: Bobby is n years old and Cam is 5 years older than Bobby. (a). To write an algebraic…

Q: Use the roster method to write the set of integers between 0 and 12

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Q: How many seven-digit numbers can be formed with the first two digits odd and the last five digits…

A: The total number of digits from 0 to 9 is 10.

Q: Using the digits 2 through 8, find the number of different 5-digit numbers such that: (a) Digits…

A: Hi thankyou for posting this question,  since you have posted multiple subparts  as per our policy…

Q: COTECE2 (л- 4)! 8. Write the following expression without using the factorial symbol. (-1)! d.…

A: 8. The answer is a.

Q: ) Find an integer having the remainders 3, 11, 15 when divided by 10, 13, 17, respec- tively.…

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Q: 692 + 685 + 678 + 671 + ... + 6

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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: What are other similar expression patterns based on n(n+1)/2

A: Solution:-

Q: (c) Create a magic multiplication table with the numbers 1, 3, 9, 27, 81, 243, 729, 2187, and 6561.…

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Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

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Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: (8) How many integers in the set [1,000] = {1, 2, ..., 1,000} are (a) divisible by 5? divisible by…

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Q: Malik currently has 39 tulips in his yard. Each year he plants 3 more. (a) Which of the following is…

A: given data  malik havs 39 tulips in his yard each year he plants 3 more  so,  p0= 39 d = 3

Q: If n is prime, then 2" – 1 is prime.

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Q: find the 100th term of 1, 3, 9,...

A: Our aim is to find the 100th term of 1 , 3 , 9,......

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

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Q: Q50 on page 159: Evaluate the following postfix expressions. a. 5 7 8 * + b. 578+ * c. 5 7 +8 * d. 1…

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Q: (1) A grocery store sells five types of fruit, called Fruit 1, the number of ways that Alice can buy…

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Q: Evaluate the expression. (-1) + (-3) +9 (- 1) +(- 3) +9 = (Type an integer.)

A: Given:     -1+-3+9

Q: Suppose I told you that 700 cannot be written as the sum of two prime numbers. Would you believe me?…

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Q: (a) Determine if the following numbers are prime: 101! + 78, 88! + 55 (b) Is 299 + 1 divisible by…

A: A prime number cannot be divided by any other number except 1 and itself. Now use this definition to…

Q: (a) 6 + 7 + 8 + 9 + ··· + 600 -- (b) 6+ 7+ 8+9+ ··· + k

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Q: For each natural aumber a, the sum 1(2) + 2(3) ++ R(n + 1) is equal ta None of the choices This…

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Q: If k is a positive integer, what is the remainder when (k+ 2)(k3 - k) is divided by 6? Stilo…

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Q: 6. Where is 50 + 5 located on a number line? a) between 7 and 8 b) between 8 and 9 c) between 9 and…

A: 50=7.075=2.23

Q: . Dan is m years old. Eric is twice as old as Dan. (a) Write an algebraic expression for eric's age…

A: We can answer all the three question as below

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

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Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…