After his electricity went out, mr. choi took out two candles. both were the same length, but the label on candle a said it would burn for 4 hours while the label on candle b said it would burn for 5 hours. mr. choi lit both candles at the same time and let them burn until the electricity was restored. he discovered that what remained of one candle was exactly four times the length of what was left of the other. how long were the candles burning?

What value of x is in the solution set of –5x – 15 > 10 + 20x?

The accompanying table shows the numbers of male and female students in a particular country who received bachelor's degrees in business in a recent year. complete parts (a) and (b) below. business degrees nonbusiness degrees total male 189131 634650 823781 female 169539 885329 1054868 total 358670 1519979 1878649 (a) find the probability that a randomly selected student is male, given that the student received a business degree. the probability that a randomly selected student is male, given that the student received a business degree, is nothing. (round to three decimal places as needed.) (b) find the probability that a randomly selected student received a business degree, given that the student is female. the probability that a randomly selected student received a business degree, given that the student is female, is nothing. (round to three decimal places as needed.)

The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of the productwhen it is sold at a unit price of x dollars.-0.5x^2 + 22x - 224what is represented by the zero(s) of the expression? a.the profit when the unit price is equal to 0b.the unit price(s) when the profit is equal to 0c.the profit when the unit price is greatestd.the unit price(s) when profit is greatest