I'm pretty sure d) is supposed to be 3a^2 - 3b^2. where have i gone wrong?

Measures of the angle of r, 31 s (x+4) t (3x+9)

Find the magnitude, correct to two decimal places, made by each of the following with positive direction of the x axis a) y= x the answer is 45° but i don’t know how

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?