Carlos downloaded a pattern from the Internet for making a table with an irregular polygon-shaped top. The instructions on the pattern say that the scale factor is the sides of the pattern are shown on the diagram below. What is the length of the longest side of the finished tabletop?

What are the possible rational zeros of [tex]f(x) = x^4+2x^3-3x^2-4x+18[/tex]

1. are the triangles similar and if so why? what is the value of x? show your work.

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.)