Determine whether or not f is a conservative vector field. if it is, find a function f such that f = -f. if it is not, enter none. f(x, y) = (2x - 4y) i + (-4x + 10y - 5) j f(x, y) = + k

Suppose that 3% of all athletes are using the endurance-enhancing hormone epo (you should be able to simply compute the percentage of all athletes that are not using epo). for our purposes, a “positive” test result is one that indicates presence of epo in an athlete’s bloodstream. the probability of a positive result, given the presence of epo is .99. the probability of a negative result, when epo is not present, is .90. what is the probability that a randomly selected athlete tests positive for epo? 0.0297

Find the magnitude, correct to two decimal places, made by each of the following with positive direction of the x axis a) y= x the answer is 45° but i don’t know how

(b) suppose that consolidated power decides to use a level of significance of α = .05, and suppose a random sample of 100 temperature readings is obtained. if the sample mean of the 100 temperature readings is x⎯⎯ = 60.990, test h0 versus ha and determine whether the power plant should be shut down and the cooling system repaired. perform the hypothesis test by using a critical value and a p-value. assume σ = 5. (round your z to 2 decimal places and p-value to 4 decimal places.)