Cade and Tyce both tried to find the missing side of the right triangle. A right triangle is shown. The legs are labeled 6 and 9. A right angle is labeled in between them.

Cade's Work Tyce's Work
a2 + b2 = c2 a2 + b2 = c2
62 + b2 = 92 62 + 92 = c2
36 + b2 = 81 36 + 81 = c2
b2 = 45 117 = c2
√b2 = √45 √117 = √c2
b ≈ 6.71 10.82 ≈ c

Is either of them correct? Explain reasoning

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.

Heather is a cashier. she can ring up 1212 customers in 99 minutes. at this rate, how many minutes does it take her to ring up 44 customers?

How many quarts of a 50% solution of acid must be added to 20 quarts of a 20% solution of acid in order to get a 40% solution of acid?