The sum of two positive integers, x and y, is not more than 40. the difference of the two integers is at least 20. chaneece chooses x as the larger number and uses the inequalities y ≤ 40 – x and y ≤ x – 20 to determine the possible solutions. she determines that x must be between 0 and 10 and y must be between 20 and 40. determine if chaneece found the correct solution. if not, state the correct solution.

Prove that the sum of two consecutive exponents of the number 5 is divisible by 30.if two consecutive exponents are 5n and 5n + 1, then their sum can be written as 30.

Use the graph of the sine function y=2sinθ shown below

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?