Noah is creating a rectangular picture frame out of wood. He wants the width of the frame to be 6 inches less than half the length. If Noah has a total of 60 inches of wood that he can use for the frame, write and solve an inequality to represent the possible measurements of the length of the frame.

Proceed as in example 3 in section 6.1 to rewrite the given expression using a single power series whose general term involves xk. ∞ n(n − 1)cnxn − 2 n = 2 − 4 ∞ ncnxn n = 1 + ∞ cnxn n = 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.

Molly shared a spool of ribbon with 12 people. each person received 3 feet of ribbon. which equation can she use to find r, the number of feet of ribbon that her spool originally had?