. Suppose that f is a continuous function and that −24 ≤ f 00(x) ≤ 3 for 0 ≤ x ≤ 1. If the Midpoint Rule of order n, namely Mn, is used to approximate R 1 0 f(x) dx, how large must n be to guarantee that the absolute error in using Mn ≈ R 1 0 f(x) dx is less than 1/100?

Look at the following graph of the given equation. determine whether the equation is a function. explain why or why not.

Adesigner charges a one time fee of $200 plus $40 an hour for each project. write an expression to represent how much money the designer will make for a project

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?