1OO points Brainliest too! Answer in complete sentences, explain how you obtained the correct answer and make sure you correctly answer ALL FOUR of the problems. If you don't answer all four problems, answer any of them incorrectly, or don't show your work for any of them, I will flag the answer and have it removed. However, if you can correctly answer and show work for all 4 problems, you just bagged yourself 50 points! Good luck!

{Question #1} In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sinF?

Use the following information for both question 2 and question 3:
[If shoppers enter a store at an average rate of r shoppers per minute and each stays in the store for average time of T minutes, the average number of shoppers in the store, N, at any one time is given by the formula N=rT. This relationship is known as Little's law.
The owner of the Good Deals Store estimates that during business hours, an average of 3 shoppers per minute enter the store and that each of them stays an average of 15 minutes. The store owner uses Little's law to estimate that there are 45 shoppers in the store at any time.]

{Question #2} Little's law can be applied to any part of the store, such as a particular department or the checkout lines. The store owner determines that, during business hours, approximately 84 shoppers per hour make a purchase and each of these shoppers spend an average of 5 minutes in the checkout line. At any time during business hours, about how many shoppers, on average, are waiting in the checkout line to make a purchase at the Good Deals Store?

{Question #3} The owner of the Good Deals Store opens a new store across town. For the new store, the owner estimates that, during business hours, an average of 90 shoppers per hour enter the store and each of them stays an average of 12 minutes. The average number of shoppers in the new store at any time is what percent less than the average number of shoppers in the original store at any time? (Note: Ignore the percent symbol when entering your answer. For example, if the answer is 42.1%, enter 42.1)

{Question #4} If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m?

A) m+6
B) m+7
C) 2m+14
D) 3m+21