The foyer planned as an addition to an existing church is designed as a regular octagonal pyramid. Each side of the octagonal floor has a length of 10 ft, and its apothem measures 12 ft. If 600 ft2 of plywood is needed to cover the exterior of the foyer (that is, the lateral area of the pyramid is 600 ft2), what is the height (in feet) of the foyer?

The trapezoid is composed of a rectangle and two triangles. what is the area of the rectangle? what is the total area of the triangles? what is the area of the trapezoid? a) 48 cm2; 32 cm2; 80 cm 2 b) 48 cm2; 16 cm2; 64 cm 2 c) 128 cm2; 32 cm2; 160 cm 2 d) 128 cm2; 16 cm2; 144 cm 2

(apex) on the planet kudzu, the probability that a bird is green is 0.30. the probability that the bird is green given that the bird is female is 0.30. which statement is true?

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .