Given ∠8≅∠12 . which lines, if any, must be parallel based on the given information? justify your conclusion. a) c∥d, converse of the alternate exterior angles theorem b) a∥b, converse of the corresponding angles theorem c) a∥b, converse of the same-side interior angles theorem d) not enough information to make a conclusion

Rachel reads 1/5 of the pages of a book plus 12 pages on the first day. on the second day, she reads 1/4 of the remaining pages plus 15 pages. on the third day, she reads 1/3 of the remaining pages plus 18 pages. on the fourth day, she reads the remaining 70 pages. how many total pages are in the book?

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.)

Satchi found a used bookstore that sells pre-owned dvds and cds. dvds cost $9 each, and cds cost $7 each. satchi can spend no more than $45.