The two way table below shows the intended careers among an incoming class of 1st year college students, divided by gender. If a male student is chosen at random, what is the probability that he intends to be a research scientist.

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.

Select the margin of error that corresponds to the sample mean that corresponds to each population: a population mean of 360, a standard deviation of 4, and a margin of error of 2.5%

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).