Determine whether the relation r on the set of all real numbers is reflexive, symmetric, antisymmetric, and/or transitive, where (x, y) ∈ r if and only if:

(a) x + y = 0, (b) x = ±y, (c) x − y is a rational number, (d) x = 2y, (e) xy ≥ 0, (f) xy = 0, (g) x = 1, (h) x = 1 or y = 1.

Find the greatest common factor of -30x 4 yz 3 and 75x 4 z 2.

Suppose i flip two identical coins. what is the probability that i get one head and one tail?

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?