Find the solution to the linear system of differential equations {x′y′==8x−15y6x−11y { x ′ = 8x−15y y ′ = 6x−11y satisfying the initial conditions x(0)=9 x ( 0 ) = 9 and y(0)=5 y ( 0 ) = 5 .

Astore has clearance items that have been marked down by 60%. they are having a sale, advertising an additional 55% off clearance items. what percent of the original price do you end up paying?

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?

Charlie tosses five coins.what is the probability that all five coins will land tails up.