Asurvey of people on pizza preferences indicated that 55 percent preferred pepperoni only, 30 percent preferred mushroom only, and 15 percent preferred something other than pepperoni and mushroom. suppose one person who was surveyed will be selected at random. let p represent the event that the selected person preferred pepperoni, and let m represent the event that the selected person preferred mushroom. are p and m mutually exclusive events for the people in this survey? (a) yes, because the joint probability of p and m is greater than 0. (b) yes, because the joint probability of p and m is greater than 1.(c)yes, because the joint probability of p and m is equal to 0. (d) no, because the joint probability of p and m is equal to 1. (e) no, because the joint probability of p and m is equal to 0.

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.