The domain for all variables in the expressions below is the set of real numbers. Determine whether each statement is true or false (i) ∀x ∃y (x + y ≥ 0)

(ii) ∃x ∀y (x · y > 0)

Four airplanes carrying a total of 400 passengersarrive at the detroit airport. the airplanes carry, respectively,50, 80, 110, and 160 passengers.a) one of the 400 passengers is selected uniformly at random.let x denote the number of passengers that were on theairplane carrying the randomly selected passenger. find var(x)for x as given in the problemb) one of the 4 airplane drivers is also selected uniformly atrandom. let y denote the number of passengers on the chosen driver’s airplane. find var(y) for y as given in the problem

Will mark determine whether the conjecture is true or false. give a counterexample for any false conjecture. given: points r, s, and t conjecture: r, s, and t are coplanar. a) false; the points do not have to be in a straight line. b) true c) false; the points to not have to form right angles. d) false; one point may not be between the other two.

The moats separating people from the animals are 5 m wide for lions and 4 m wide for the elephants. if the lion’s moat is 4 m deep, how deep should the elephants’ moat be?