A company is considering a new manufacturing process in one of its plants in an effort to save money. The company estimates that the rate of savings can be modeled by S(x)=100−x2 where x is time in years and S(x) is given in thousands of dollars per year. At the same time, the company's operating costs will increase, and the company estimates that the rate at which costs will increase can be modeled by C(x)=x2+2.75x where x is time in years and C(x) is given in thousands of dollars per year. Find the total net savings that the company should expect to realize. (Round limits of integration to 4 decimal places before integrating.)

The distance around the lake is 2 kilometers. ifelena wants to run 14 kilometers this week, howmany laps must she run around the lake

What is the solution of log2  (3x  -  7)  =  3? 4 5

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?