A rectangular table seats 14 ​people: 1 person on each end and 6 on each of the longer sides.​ Thus, two tables placed end to end seat 26 people.   ​(a) How many people can be seated if n tables are placed in a line end to​ end?

Q: In your head, determine (2.1075 + 2)100 mod 3 and (10100 +1)99 mod 3.

A:

Q: For this problem, assume there are 9 adjacent seats in a row. How many different ways can 9 people…

A: 9! = 9*8*7*6*5*4*3*2*1 = 362880

Q: A professor has 180 students in her classes at the beginning of the semester, but 18 students…

A: At the beginning of the semester the professor has 180 students in her classes. But 18 students…

Q: 3.) A chef cooks 2 of a pound of pasta. She plans to serve - of a pound to each customer. How 12…

A:

Q: Mr. H has a collection of 500 vessels. In how many ways can he name his favorite and second favorite…

A:

Q: A class consists of 12 students ​(six boys and six ​girls) and one teacher. In how many ways can the…

A: Here there is a class consists of 12 students where there is 6 boys and 6 girls and 1 teacher We…

Q: Apolice department in a small city consists of 10 officers. If the department policy is to have 5 of…

A:

Q: Assume that the pond contains 90 fish: 68 blue, 21 orange, and 1 white. A contestant pays $0.65 to…

A: Total number of fishes = 90 Contestant pays $0.65 for catching one fish and receives $0.20 if fish…

Q: Assume that the pond contains 90 fish: 76 orange, 13 blue, and 1 green. A contestant pays $0.55 to…

A:

Q: How many ways can 4 people sit in a row of 7 chairs? The number of ways 4 people can sit in a row of…

A: Given: number of chair (n)=7 number of people (x)=4

Q: A farmer was asked how many chickens he had sold at market that day. His reply was: "I've had four…

A:

Q: Four married couples have bought 8 seats in the same row for a concert. In how many different ways…

A: Four married couples have bought 8 seats in the same row for a concert. There are two possibilities…

Q: Marsha has three times as many one-dollar bills as she does five-dollar bills. She has a total of…

A: let  Marsha has 5 dollar bill= x Marsha has 1 dollar bills= 3x total= $32

Q: You have 10 houses in a row on a one side of a street, going from left to right. You are to paint…

A: Number of houses = 10

Q: There are 5 boys and 5 girls at a party. In how many ways can they be seated in a row if they must…

A:

Q: or this problem, assume that 13 exhibits entered the science fair, and that we want to assign 5…

A: Given Data :  Number of exhibits are 13 in a science fair                        Number of Prizes…

Q: At an awards ceremony, ten women and eight men are each to receive an award and are to be presented…

A: Women=10Men=8Total=18

Q: John has 9 boxes of apples. Each box holds 12 apples. If 6 of the boxes are full, and 3 of the boxes…

A:

Q: A four-person committee is to be selected from an organization’s membership of 12 people.  How many…

A:

Q: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. How many…

A: In a large family, 20 have parrots, 15 have rabbits, and 5 have both. One own a pet dog. We need to…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.