For each integer n, define f_n: r rightarrow r by f_n (x) = x + n. (a) prove that for each integer n, f_n is a permutation of r, that is f_n elementof s(r). (b) prove that f_n compositefunction f_m = f_n + m and f^-1_n = f_-n (c) let g = {f_n: n elementof z}. prove that g is a subgroup of s(r). (d) prove that g is cyclic (find a generator of g).

An automobile assembly line operation has a scheduled mean completion time, μ, of 12 minutes. the standard deviation of completion times is 1.6 minutes. it is claimed that, under new management, the mean completion time has decreased. to test this claim, a random sample of 33 completion times under new management was taken. the sample had a mean of 11.2 minutes. assume that the population is normally distributed. can we support, at the 0.05 level of significance, the claim that the mean completion time has decreased under new management? assume that the standard deviation of completion times has not changed.

Zack notices that segment nm and segment pq are congruent in the image below: which step could him determine if δnmo ≅δpqr by sas? (5 points) segment mo ≅ segment qr segment on ≅ segment qp ∠ n ≅ ∠ r ∠ o ≅ ∠ q

What is the distance from zero if a quadratic function has a line of symmetry at x=-3 and a zero at 4