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Explain why the function is discontinuous at the given number a. (select all that apply.) f(x) = 1 x + 1 a = −1 f(−1) is undefined. lim x→−1+ f(x) and lim x→−1− f(x) exist, but are not equal. lim x→−1 f(x) does not exist. f(−1) and lim x→−1 f(x) exist, but are not equal. none of the above

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.)

David and alton are training for a race. they spend 35 minutes stretching and then go on a 5 mile practice run. david runs at a pace of 7 min/mile. alton runs at a pace of 8 min/mile. write an equation for each runner that shows the total length of their workout. then solve each equation showing your work