The gardener sells half of his oranges plus three more to his first buyer. the gardener then sells half of his remaining oranges plus three more to his second buyer. finally, the gardener sells half of his remaining oranges plus three more to his third buyer. the gardener is left with 13 oranges at the end of the day after the third (and final) buyer makes his purchase. based on this information, how many oranges did the gardener start out with at the beginning of the day?

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 table shown below gives the approximate enrollment at the university of michigan every fifty years. how many more students were enrolled at the university of michigan in 1950 than in 1900?

The students at jefferson middle school are raising money for a charity by selling t-shirts and hats. the number of t-shirts sold was 3 times the number of hats. the profit was $5 for each t-shirt sold and $2.50 for each hat sold. the students raised $840 for the charity. they used the system below to analyze their success and found the solution to be (144, 48). 5x+2.50y=840 x=3y how much did they earn from t-shirt sales?