A transportation engineer conducted a series of tests to demonstrate that a new cement mix for highway construction will withstand 25 years of service. She develops a wear index (WI) to assess the status of a sample after a demanding set of tests. A mix will be acceptable if its wear index has a mean value less than 20 on a scale of 0-100. Fifteen sample values of the wear index appeared to be normally distributed with a sample mean of 18.31 and a sample standard deviation of 3.09. A. Specify the appropriate null and alternative hypotheses to demonstrate that the mix does meet the target value of 20.
B. What is the rejection region for a 5% test?
C. What do you conclude for this data set?

Which set of reflections would carry trapezoid abcd onto itself? a) x-axis, y=x, y-axis, x-axis b) x-axis, y-axis, x-axis c) y=x, x-axis, x-axis d) y-axis, x-axis, y-axis, x-axis

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.)

Given abcd ac=38 and ae=3x+4 find the value of x