Officials begin to release water from a full man-made lake at a rate that would empty the lake in 20 weeks, but a river that can fill the lake in 30 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.

Successful implementation of a new system is based on three independent modules. module 1 works properly with probability 0.96. for modules 2 and 3, these probabilities equal 0.95 and 0.90. compute the probability that at least one of these three modules fails to work properly.

You drop a rubber ball off the roof of a 50 meter high building onto a paved parking lot. it bounces back up with every bounce, but not quite all the way back up to you. after the first bounce it bounces back only 80 percent of the distance it was dropped from. the pattern continues, meaning after every bounce it comes up to just 80 percent of the previous maximum height. so if before the first bounce the height is 50 meters, what height does the ball reach after the fifth bounce? round your answer to one decimal place and chose the correct response from the choices below:

How can you tell when x and y are not directly proportional?