(differential equations) put these equations in explicit form:
ty' = ycos(t)
y' = sin(y)
mr' + rm + e^(m+r) = 0

Find the commission on a $590.00 sale if the commission is 15%.

The difference of two numbers is 40. find the numbers if 0.3 parts of one number is equal to 37.5% of the other one.

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?