A cone and a sphere have equal radii lengths, but the cone's volume is three times as large. If the volume of the sphere is 4500πft^3 what is the surface area of the cone? Please round your answer to the nearest tenth. Show work if applicable.

What is the ratio for the surface areas of rectangle prisims shown below given that they are similar and that the ratio of their edge lengths is 7: 3

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?

If set d is not the empty set but is a subset of set e, then which of the following is true? d ∩ e = d d ∩ e = e d ∩ e = ∅