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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.

Factor the following expression. 27y3 – 343 a. (3y + 7)(9y2 + 2ly + 49) b. (3y – 7)(9y2 + 2ly + 49) c. (3y – 7)(932 – 217 + 49) d. (3y + 7)(92 – 2ly + 49)

Finally, the arena decides to offer advertising space on the jerseys of the arena’s own amateur volley ball team. the arena wants the probability of being shortlisted to be 0.14. what is this as a percentage and a fraction? what is the probability of not being shortlisted? give your answer as a decimal. those shortlisted are entered into a final game of chance. there are six balls in a bag (2 blue balls, 2 green balls and 2 golden balls). to win, a company needs to take out two golden balls. the first ball is not replaced. what is the probability of any company winning advertising space on their volley ball team jerseys?