Find the distance between the points e(3, 7) and f(6, 5). the exact distance between the two points is .

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?

How many heads would you expect if you flipped a coin twice? first, fill in the table below with the correct probabilities. hint: the sample space for flipping a coin twice is {hh, ht, th, tt}. a = b = c = f

Find the length of the radius of a circle with the center at -7+2i and a point in the circle at 33+11i