PLEASE HELP WILL GIVE 25 POINTS. In this task, you will practice finding the area under a nonlinear function by using rectangles. You will use graphing skills in addition to the knowledge gathered in this unit. Sketch the graph of the function y = 20x − x2, and approximate the area under the curve in the interval [0, 20] by dividing the area into the given numbers of rectangles. 1. Use five rectangles to approximate the area under the curve. 2. Use 10 rectangles to approximate the area under the curve. 3. Calculate the area under the curve using rectangles as their number becomes arbitrarily large (tends to infinity). You do not need to sketch the rectangles.

The data represents the semester exam scores of 8 students in a math course. {51,91,46,30,36,50,73,80} what is the five-number summary?

How is working backward similar to solving an equation?

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?