Multiple choice! the words and numbers in the brackets are the choices. a game has 3 possible outcomes: the first outcome has probability of 1/6. the result is winning $12. the second outcome has probability of 1/3. the result is winning $3. the third outcome has probability of 1/2. the result is losing $8. in the long run, you will [win, lose] $[1, 7] per game.

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.

Solve with work both bert and ernie received an increase in their weekly salaries. bert's salary increased from $520 to $520. ernie's salary went from $580 to $645. find the percent of increase for each salary. what was the larger of the two percents ?

Find the value of x for which the lines are parallel.