The product of a binomial and a trinomial is x 3 + 3 x 2 ? x + 2 x 2 + 6 x ? 2. which expression is equivalent to this product after it has been fully simplified?

Write an explicit formula that represents the sequence defined by the following recursive formula:

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?

Of the 304 people who attended a school play, 5/8 were students. how many of the people who attended were students.