For the following questions, choose one of the statements and decide if the given statement is true or false, and give a brief justification for your answer. if true, you can quote a relevant definition or theorem from the textbook. if false, provide a counterexample, illustration or brief explanation of why the statement is false 1. if p(x) and q(x) are polynomials, then the differential equation y' +p(x)y'q(x)y 0 has no singular points.

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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.)

The volume of a cube-shaped shipping container is 13,824 cubic inches. find the edge length of the shipping container.