Given a set m of 1985 distinct positive integers, none of which has a prime divisor greater than 26, prove that m contains at least one subset of four distinct elements whose product is the fourth power of an integer.

What is the anwers for 9+2x=5x-3-x

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?

Side xy of triangle xyz is extended to point w, creating a linear pair with ∠wyz and ∠xyz. measure of an exterior angle what is the value of x? 64 80 100 180