There are 32 teams participating in a single-elimination soccer tournament, in which only the winning teams from each round progress to the next round of the tournament. the graph shows the number of teams, f(x), that are still in the tournament after x rounds have been completed. determine the domain and range of this function. a. d = [0, 5] and r = [0, 32] b. d = {0, 1, 2, 3, 4, 5} and r = {1, 2, 4, 8, 16, 32} c. d = {0, 1, 2, 3, 4, 5, 6, 7} and r = {0.5, 0.25, 1, 2, 4, 8, 16, 32} d. d = {1, 2, 4, 8, 16, 32} and r = {0, 1, 2, 3, 4, 5}

The graph of the quadratic function shown on the left is y = –0.7(x + 3)(x – 4). the roots, or zeros, of the function are . determine the solutions to the related equation 0 = –0.7(x + 3)(x – 4). the solutions to the equation are x =

If 20% of a number is 35, what is 50% of that number?

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.