The second side of a triangle is 4cm longer than the first, the third side is 1 less than twice the first, the perimeter is 55cm. find the lengths of all three sides.

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x)

Which of the following is a solution of z^6 = 64i? 2(cos105° + isin105°) 2(cos120° + isin120°) 2(cos135° + isin135°) 8(cos15° + isin15°)

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?