A 32-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is two inches more than three times the length of the first piece. Find the lengths of the pieces.

Gretchen is setting up for a banquet. she has 300 chairs and needs to distribute them evenly among t tables. how many chairs should she put at each table? write your answer as an expression.

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

The random variable x is the number of occurrences of an event over an interval of ten minutes. it can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. it is known that the mean number of occurrences in ten minutes is 5.3. the appropriate probability distribution for the random variable