4. use the probabilities from question 3 to decide whether the rain and the bus running late
are
independent or dependent events. (2 points: 1 point for the correct math, 1 point for the conclusion)

Aquadratic function f(x) has a turning point at (3,-7). what is the turning point of -f(x)?

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?

Let f(x) = 1/x^2 (a) use the definition of the derivatve to find f'(x). (b) find the equation of the tangent line at x=2