Triangle ABC is rotated 45° counterclockwise about vertex A to obtain triangle XYZ. If the m∠ABC is equal to 30°, what is the m∠XYZ? 15°

30°

45°

75°

Arecipe calls for 32 fluid ounces of heavy cream.how many 1 pint containers of heavy cream are needed to make the recipe?

Laura read 1/8 of a comic book in 2 days. she reads the same number of pages every day. what part of the book does she read in a week

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?