The ratio of the perimeter of triangle PQR to the perimeter of rectangle ABCD is 5 : 9. All in centimeters, Triangle (sides) PQ: (x-3) PR: (3x-5) QR: (4x+3), Rectangle (sides) AB: (2x+2) BC: (4x - 1/2) [AB is longer than BC a. Write algebraic expressions for the perimeters of triangle PQR and rectangle ABCD.
b. Write a linear equation using the algebraic expressions written in part a. Then solve for x.
c. Find the area of rectangle ABCD.

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

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?

Find the solution on the interval [0, 2pi)