Your friend is purchasing an umbrella with a slant height of 4 feet. there are a variety of such umbrellas to choose from. a. a red umbrella is shaped like a regular pentagonal pyramid with a side length of 3 feet. find the lateral surface area of the red umbrella. b. a yellow umbrella is shaped like a regular hexagonal pyramid with a side length of 2.5 feet. find the lateral surface area of the yellow umbrella. c. a blue umbrella is shaped like a regular octagonal pyramid with a side length of 1.9 feet. find the lateral surface area of the blue umbrella. d. based on lateral surface areas, would you suggest that your friend pick the umbrella that is her favorite color? explain.

Apsychology student wishes to investigate differences in political opinions between business majors and political science majors at her college. she randomly selects 100 students from the 260 business majors and 100 students from the 180 political science majors. does this sampling plan result in a simple random sample? why or why not? no, because each group of 200 students in the sample does not have the same chance of being selected. yes, because each group of 200 students in the sample has the same chance of being selected. no, because each individual student does not have an equal chance of being selected. yes, because each individual student has the same chance of being selected.

Use the four functions below for this question. compare and contrast these four functions using complete sentences focus on the slope and y- intercept first, and then on any additional properties of each function

Thee blue triangle has rotated from quadrant i to quadrant iii about the origin. describe the effects of the rotation on the coordinates of the blue triangle.