As you should remember from Calculus, every cubic polynomial with real coefficients has a real root. Express that statement using ∀, ∃ quantifiers and other math symbols but without using any words.

Use the normal approximation to the binomial distribution to answer this question. fifteen percent of all students at a large university are absent on mondays. if a random sample of 12 names is called on a monday, what is the probability that four students are absent?

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:

Every weekday, mr. jones bikes from his home to his job. sometimes he rides along two roads, the long route that is shown by the solid lines. other times, he takes the shortcut shown by the dashed line. how many fewer kilometers does mr. jones bike when he takes the shortcut instead of the long route?