I. A die is rolled three times. Find each probability. Express your answers as a percent. 1.) P (three 4's) 2.) P (no 4's)
3.) P (2, then 3, then 1)
4.) P (three different even numbers)
5.) P (any number, then 5, then 3)
6.) P (even number, then odd number, then 1)​

Identify the number as a rational or irrational.explain. 127

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?

Determine the vertex form of g(x) = x2 + 2x - 1. which graph represents g(x)? -nw -3-2-1, 1 1 2 3 -3 2- 1 -3- 1 2 3 - 1 2 3