An architect designs a theater with 18 seats in the first row, 22 in the second, 26 in the third, and so on. If the theater is to have a seating capacity of 1320, how many rows must the architect use in his design?

Q: A group of 10 friends go to a movie theater to see a newly released film. The friends consist of…

A: As per the given information 5 married couples are there and each couple must sit together Possible…

Q: A high school student needs 9 more classes to graduate.  If she has met the prerequisites for all…

A: Given information Students need 9 more classes to graduate No of class periods to fill = 5

Q: The Goal Line Gals has 35 members and the Baseball Babes has 28 members. At a joint meeting all…

A: Let's denote the set of members in the Goal Line Gals as G and the set of members in the Baseball…

Q: A pianist plans to play 6 pieces at a recital from her repertoire of 24 pieces. How many different…

A: Given data A pianist plans to play 6 pieces at a recital from her repertoire of 24 pieces

Q: Earths atmorsphere is a mixture of gases:78% nitrogen, 21% oxygen, .9% argon and .03% carbon…

A: Sum of the percent is shown on the board.The sum of the percent of the mixture of gases is found to…

Q: piano teacher is planning to take 4 of her 12 students to a concert. She wants to take 2 girls and 2…

A: Given query is to find the number of arrangement possible.

Q: Mark is working at a manufacturing company of cars and he is tasked to assemble a car. He has the…

A: Given that  Mark is working at a manufacturing company of cars and he is tasked to assemble a car.…

Q: Guests at  an escape room recreational facility are partitioned into three groups; the group doing…

A:

Q: A particular theater has 48 rows of seats. An usher monitors rows 17 through 32. He notices that the…

A: Given that, A particular theater has 48 rows of seats. An usher monitors rows 17 through 32. He…

Q: An ice cream store has 30 flavors to select from. A customer who is a connoisseur of ice cream wants…

A: We have to select three different flavors from a ice cream store which has 30 flavors. Since, here…

Q: A pianist plans to play 5 pieces at a recital from her repertoire of 22 pieces. How many different…

A: Permutation formula: nPr = n!/(n-r)!

Q: According to a salad recipe, each serving requires 3 teaspoons of vegetable oil and 21 teaspoons of…

A:

Q: windscreen by planting trees in a quarter-mile row. His daughter points out that 220 fewer trees…

A:

Q: A cereal company is deciding which box to use for their new line of cereal. The first box has a base…

A: Dimensions of first box:  length=6.5 inches, width= 2 inches, and height=10 inches. Dimensions of…

Q: How many committees are possible if the committee must have a least two men?

A: Concept:   The number of ways of achieving success that is the total number of possible outcomes is…

Q: An office needs 3200 sticky labels. If there are 80 labels each package, how many packages should…

A:

Q: A large university accepts 50​% of the students who apply. Of the students the university​ accepts,…

A:

Q: In a medical supply​ room, there are 165 packages of type O positive blood and 210 packages of type…

A: Given Information - Number of type O positive blood packages = 165 Number of type AB negative blood…

Q: ianist plans to play 6 pieces at a recital from her repertoire of 26 pieces.  How many different…

A: Total number of pieces available (n) = 26 pieces. Number of pieces (r) which a pianist needs to play…

Q: charges a fixed setup cost, plus $70 for every 100 brochures. If 700 brochures cost $515, and 1,000…

A: Suppose the fixed set up cost be x. Since the set up cost is fixed so whether we print 100, 700 or…

Q: A large auditorium has 90 rows of seats. The first row has 50 seats, and each succeeding row has 5…

A:

Q: Kobe has collected 200 football cards and 112 baseball cards. He wants to divide them into piles so…

A: Kobe has  200 football cards and 112 baseball cards and He wants to divide them into piles in such a…

Q: A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces. How many different…

A: Given : No. of repertoire pieces = 25 A pianist plans to play 4 pieces i.e n = 4

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.