Sketch the following to answer the question. kite qrst has a short diagonal of qs and a long diagonal of rt. the diagonals intersect at point p. side qr = 10m and diagonal qs = 12m. find the length of segment rp.

Given that ot =5, xt=12, and ox= 13 is xy tangent to circle o at t? explain.

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.)

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.