A figure is located at (2, 0), (2, −2), and (6, 0) on a coordinate plane. What kind of 3-D shape would be created if the figure was rotated around the x-axis? Provide an explanation and proof of your answer to receive full credit. Include the dimensions of the 3-D shape in your explanation.

An eight-sided die, which may or may not be a fair die, has four colors on it; you have been tossing the die for an hour and have recorded the color rolled for each toss. what is the probability you will roll a brown on your next toss of the die? express your answer as a simplified fraction or a decimal rounded to four decimal places.

Given the points a(-2, 1) and b(8, 6), find the coordinates of the point c on directed line segment ab, that partitions ab in the ration 2: 3.

What is the ratio for the surface areas of the cones shown below, given that they are similar and that the ratio of their radil and altitudes is 4: 3? 23