Xian and his cousin Kai both collect stamps. Xian has 60 stamps, and Kai has 80 stamps. The boys recently joined different stamp-collecting clubs. Xian's club will send him 12 new stamps per month. Kai's club will send him 8 new stamps per month. After how many months will Xian and Kai have the same number of stamps? How many stamps will each have?

What basic trigonometric identity would you use to verify that sin x cos x tan x =1-cos^(2)x?

Celeste wants to have her hair cut and permed and also go to lunch. she knows she will need $50. the perm cost twice as much as her haircut and she needs $5 for lunch. how much does the perm 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?