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Given: x + y = 6. if xe (-15, -6, -1), then which of the following sets of ordered pairs are solutions? © {(-15, -21), (-6, -12), (-1, -7)} [(-15, 21), (-6, , 7)} {(-15, 21), (-6, 12), (-1, -7)}

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.

Abag contains 3 red marbles, 2 blue marbles, and 2 green marbles. one marble is picked, then another marble. assume that the selections are made with replacement. a) find the probability of picking two red marbles with replacement. b) find the probability of picking a red marble and a blue marble. assume the selections are made without replacement. c) find the probability of picking two red marbles without replacement. d) find the probability of picking a red marble and a blue marble without replacement.