What is the exact value of sin(v+w), given sin v = -3/5, cos w = 10/11, v is an angle in Quadrant III, and w is an angle in Quadrant IV?

Is it true that product of 3 consecutive natural numbers is always divisible by 6? justifyyour answer

Find solution of the linear equation y = 2/3x + 1/3

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?