The plans for a new house include a wall with two triangular windows, ABC and A ′B ′C ′. The vertices of ABC are A (−4, 1), B (−1, 1), and C (−1, 5). The vertices of A ′B ′C ′ are A ′ (−1, −5), B ′ (−1, −2), and C ′ (−5, −2). The architect wants to give a sequence of rigid motions that maps ABC to A ′B ′C ′. Select descriptions and algebraic rules for the appropriate sequence of rigid motions. Rotate ABC by ( )° around the origin, and then translate the image ( ) unit(s) down.

You are a clerk at convenience store. a customer owes 11.69 for a bag of potatoes chips. she gives you a five dollar bill. how much change should the customer receive?

(x-5)1/2+5=2 what is a possible solution?

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?