The triangular prism has a base area of 666 square units and a volume of 636363 cubic units. The pentagon-based prism has the same base area and height, but its shortest edge is 222 units long instead of 333 units long. What is the volume of the pentagon-based prism?

The half-life of a certain material is 0.002 second. approximately how much of a 14-gram sample will be left after 0.004 second? a. 12 grams b. 3.5 grams c. 0.06 gram d. 7 grams

As a project for math class, two students devised a game in which 3 black marbles and 2 red marbles are put into a bag. first the players must decide who is playing black marbles and who is playing red marbles. then each player takes a turn at drawing a marble, noting the color, replacing the marble in the bag, and then drawing a second marble and noting the color before returning it to the bag. the point scheme for the game is detailed in the table below. point values for marble game black marble points red marble points both black: +2 points both red: +4 points different colors: –1 point different colors: –1 point both red: 0 points both black: 0 points

The weights of soy patties sold by a diner are normally distributed. a random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. at the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is < 4 ounces. what is the correct conclusion at the 0.05 level of significance?