In pottery class, ludolf made a cylindrical vase that is 32 cm tall. its base has a radius of 8 cm. he wants to paint the outside of the vase. how many square centimeters will ludolf have to paint? round to the nearest whole number. use 3.14 as an approximation for pi.

a. 6431 cm2

b. 1608 cm2

c. 1809 cm2

d. 2010 cm2

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.)