Triangle \triangle ABC△ABCtriangle, A, B, C is translated 999 units to the left and 333 units up to create \triangle A'B'C'△A ′ B ′ C ′ triangle, A, prime, B, prime, C, prime. What is the length of segment \overline{A'B'} A ′ B ′ start overline, A, prime, B, prime, end overline?

Find the zero function by factoring (try to show work) h(x)=-x^2-6x-9

Jenisey has $24 to spend on seven pencils. after buying them she had $10. how much did each pencil cost.?

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?