On a coordinate plane, square P Q R S is shown. Point P is at (4, 2), point Q is at (8, 5), point R is at (5, 9), and point S is at (1, 6).Which statement proves that the diagonals of square PQRS are perpendicular bisectors of each other?The length of SP, PQ, RQ, and SR are each 5.The slope of SP and RQ is Negative four-thirds and the slope of SR and PQ is Three-fourths. The length of SQ and RP are both StartRoot 50 EndRoot. The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.

Multiply −2x(6x^4−7x^2+x−5) express the answer in standard form. enter your answer in the box.

Chandler was a caretaker at the state zoo. he noticed that the number of animals adopted by the zoo increased at a constant rate every year since 2010. which of the following graphs shows the slowest rate at which the animals in the zoo were adopted?

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.)