Let f be the function defined by f(x) = −ln(x) for 0 < x ≤ 1. R is the region between the graph of f and the x-axis. 1. This question does not permit the use of a calculator.
Determine whether region R has a finite area. If so, find the area. If not, explain why.

2. This question does not permit the use of a calculator.
Determine whether the solid generated by revolving region R about the y-axis has a finite volume. If so, find the volume. If not, explain why.

Given: △acm, m∠c=90°, cp ⊥ am , ac: cm=3: 4, mp-ap=1. find am.

The mean of 10 values is 19. if further 5 values areincluded the mean becomes 20. what is the meanthese five additional values? a) 10b) 15c) 11d) 22

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?