A college professor wants to survey a sample of students taking his course. Here are some details about his course:He teaches555 sections of the course. There are250250250 total students across those sections. There are505050 graduate students and200200200 undergraduate students taking the course. Each section has about505050 students (some graduate and some undergraduate).The professor wants to take a sample of303030 students for a survey. He suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account.

Someone answer asap for ! a discount store’s prices are 25% lower than department store prices. the function c(x) = 0.75x can be used to determine the cost c, in dollars, of an item, where x is the department store price, in dollars. if the item has not sold in one month, the discount store takes an additional 20% off the discounted price and an additional $5 off the total purchase. the function d(y) = 0.80y - 5 can be used to find d, the cost, in dollars, of an item that has not been sold for a month, where y is the discount store price, in dollars. create a function d(c(x)) that represents the final price of an item when a costumer buys an item that has been in the discount store for a month. d(c(x)) =

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?

Use the irregular polygon below. show all work. a. find the perimeter. b. find the area. the angles of the irregular polygon is 2, 8, 8, and 4.