You are constructing a railing to place on a ramp for your handicapped grandmother. You have been given a 12-ft rail and 5 posts to support the railing. The posts are equally spaced under the rail and the first and last posts are positioned at each end of the rail. The ramp rises at an angle of 12°.

a. What part(s) will represent the transversal(s)?
b. In order to make the posts parallel, what angles must they form with the transversal?
c. What angle would they form with the ramp?
d. Which angles would be alternate interior, alternate exterior, corresponding, and consecutive interior? Explain your reasoning.
e. What do you know about each of these angles?
f. How far apart will the posts be?

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?

On friday, there were x students at the baseball game. on monday, there were half as many students at the game as there were on friday. on wednesday, there were 32 fewer students at the game as there were on friday. which expression could represent the total number of tickets sold for all 3 games?

Fred and gene are hang gliding. fred is 700 feet above the ground and descending at 15 ft/s. gene is decending as shown in the table. interpret the rates of change and initial values of the linear functions in terms of the situations they model. show all work. freds equation is f(x)=-15x+700. ( genes is the table attached)