You have been asked to order a three-layer cake for the party. In order to feed 75 people, the bakery gave you the following two options for the size of each layer: Option 1: Option 2:

Layer 1 - 10-inch diameter Layer 1- 11-inch diameter

Layer 2 - 8-inch diameter Layer 2- 7-inch diameter

Layer 3 - 6-inch diameter Layer 3- 4-inch diameter

Each layer is shaped like a cylinder and will have a height of 4 inches. The bakery charges $0.50 per cubic inch of cake.

What is the total cost of cake Option 1?

What is the total cost of cake Option 2?

Must show work and formulas

What term makes it inconsistent y=2x - 4

Isabel graphed the following system of equations. 2x – y = 6 y = -3x + 4 she came up with the solution (2,-2). what were the 3 steps she did to get that solution? (make sure they are in the correct order)

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?