Abagel shop has onion bagels, poppy seed bagels, egg bagels, salty bagels. pumpernickel bagels, sesame seed bagels, raisin bagels, and plain bagels. how many ways are there to choose (a) six bagels? (b) a dozen bagels? (c) two dozen bagels? (d) a dozen bagels with at least one of each kind? (e) a dozen bagels with at least three egg bagels and no more than two salty bagels?

Consider the proof. given: segment ab is parallel to line de. prove: what is the missing statement in step 5?

Your friend uses c=50p to find the total cost, c, for the people, p, entering a local amusement park is the cost of admission proportional to the amount of people entering the amusement park? explain.

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?