Assume f and g are continuous with f(x)greater than or equals g(x)greater than or equals0 on [a, b]. the region bounded by the graphs of f and g and the lines xequals a and xequals b is revolved about the y axis. write the integral given by the shell method that equals the volume of the resulting solid.

Afamily has five members. a mom, a dad, two sisters, & a brother. the family lines up single file. what is the probabillity that the mom is at the front of the line

How many ordered pairs of positive integers satisfy xy=32?

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?