A pizza shop delivers only one kind of pizza, which is sold for $ 10 \$10 $10 dollar sign, 10 , and costs the pizza shop $ 6 \$6 $6 dollar sign, 6 to make. The pizza shop has a delivery policy that says if the pizza takes longer than half an hour to arrive, there is no charge. Experience has shown that delivery takes longer than half an hour only 10 % 10\% 10% 10, percent of the time. Let the random variable X X X X be the pizza shop's profit for a randomly selected delivery order for one of these pizzas. Here is the probability distribution for X X X X : Late On-time X = profit X=\text{profit} X=profit X, equals, start text, p, r, o, f, i, t, end text − $ 6 -\$6 −$6 minus, dollar sign, 6 $ 4 \$4 $4 dollar sign, 4 P ( X ) P(X) P(X) P, left parenthesis, X, right parenthesis 0.10 0.10 0.10 0, point, 10 0.90 0.90 0.90 0, point, 90 Calculate the mean of X X X X . μ X = \mu_X= μ X = mu, start subscript, X, end subscript, equals dollars

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.