Find the coordinates of the vertex for the parabola defined by the given quadratic function and show your work. f(x) = 2x^2 - 8x + 3
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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.)

Look at arnold's attempt to solve the equation for b: 3b = 12 b = 3 · 12 b = 36 describe the mistake that arnold made.

Let event a = you roll an even number on the first cube.let event b = you roll a 6 on the second cube.are the events independent or dependent? why?