What is one way to check 102 divided by 6 = 17

If 1/√5+1/√5+1=p+q√r , find the values of p, q and r

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?

From the top of a tree a bird looks down on a field mouse at an angle of depression of 50°. if the field mouse is 40 meters from the base of the tree, find the vertical distance from the ground to the bird's eyes.