Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point? Enter your answer as a single number (no variable or units). If necessary, round your answer to the nearest tenth (one decimal place).

Find a number such that if you add 8 and divide the result by 4 you will get the same answer as if you subtracted 3 from the original number and divided by 2

Do social recommendations increase ad effectiveness? a study of online video viewers compared viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. the results are given below. correctly recalled the brandarrival 409153browsing20484b. conduct the hypothesis test, using the 0.025 level of significance. what is the value of the test statistic? χ2stat=what is the p-value? p-value=is this value significant atα=0.025?

Abag contains 4 red, 7 blue and 5 yellow marbles. event a is defined as drawing a yellow marble on the first draw and event b is defined as drawing a blue marble on the second draw. if two marbles are drawn from the bag, one after the other and not replaced, what is p(b|a) expressed in simplest form? a. 7/16 b. 7/15 c. 14/16 d. 14/15