Consider the following vectors: ~a =   1 3 4   , ~ b =   3 3 9   , ~c =   −2 0 −6   , ~ d =   −6 −6 −18   , ~e = ~ b−proj ~a ( ~ b). For each of the following subparts, select all statements that are true. Let h·,·i and k·k denote the usual Euclidean inner product and norm, respectively. (a) (A) k~ak = 8 (B) The sine of the angle between~a and ~ b equals 48 √ 99×26 (C) ? ~ b ? ? = √ 99 (D) The cosine of the angle between~a and ~ b equals 48 √ 99×26 (E) ~a and ~ b are orthogonal (F) h~a, ~ bi < h~a,~ci < h~a, ~ di (G) ~a and~e are orthogonal

On a certain portion of an experiment, a statistical test result yielded a p-value of 0.21. what can you conclude? 2(0.21) = 0.42 < 0.5; the test is not statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 21% of the time, so the test is not statistically significant. 0.21 > 0.05; the test is statistically significant. if the null hypothesis is true, one could expect to get a test statistic at least as extreme as that observed 79% of the time, so the test is not statistically significant. p = 1 - 0.21 = 0.79 > 0.05; the test is statistically significant.