Suppose individual components in a system fail with probability 0.04 (that is, each function properly functions with probability 0.96). Assume each component succeeds or fails independently. a) Find the probability that in a system with 4 components, all components function properly.
b) Find the probability that at least one of the 4 components will fail.

Given the choice between receiving $1.000.000 in one month or a single penny-doubled everyday for the period of one month; which option would you choice? show your work to support your answer. (assume that 1 month=30 days)

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.

Atown has a population of 12000 and grows at 3.5% every year. what will be the population after 7 years, to the nearest whole number?