As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.