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Alake near the arctic circle is covered by a 222-meter-thick sheet of ice during the cold winter months. when spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. after 333 weeks, the sheet is only 1.251.251, point, 25 meters thick. let s(t)s(t)s, left parenthesis, t, right parenthesis denote the ice sheet's thickness sss (measured in meters) as a function of time ttt (measured in weeks).

Name each raycalculation tip: in ray "ab", a is the endpoint of the ray.

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?