An undergraduate business student has purchased a laptop computer for use during exams. This laptop is perfectly reliable except for two parts: its microchip, which has a failure rate of one in every twenty hours of operation; and its battery, which has a failure rate of one in every ten hours of operation. Also, on average the battery will wear out in five hours, with a standard deviation of 30 minutes. What maximum battery life should the manufacturer specify in order to have a .1587 probability that a battery will wear out within that amount of time

We'll use reasoning and the pythagorean theroem for this.

Question One: Let's try C first. Since the leg(48) is very close to the diagonal (50), we can see if it still works. 14²+48²=50²=196+2,304=2,500; it does work Let's Try D. 27²+32²=45²=729+1,024=1,753≠2,025 So, D does not work.

Question Two: Let's look at C since we know we'll had to add 100 to 24 squared, and it's suppose to equal a number that ends in 5. 10²+24²=100+576=676≠625 So, C does not work.

Question Three: We need to look for one that DOES work. D sticks out to me because it's a popular pythagorean triple. We can still work it out. 36+64=100; So, D is the answer.