in the figure, a b, and both lines are intersected by transversal t. complete the statements to prove that m<1 = m<5. a b given. m<1+m<3=180 (linear pair theorem). m<5+m<6=180 (linear pair theorem). m<1+m<3=<5+<6(alternate interior angles theorem, transitive property of equality, alternate exterior angles theorem, vertical angles theorem). m<3=m<6 ( alternate interior angles theorem, transitive property of equality, alternate exterior angles theorem, vertical angles theorem). m<1=m<5 (subtraction property of equality)

Ahigh-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. suppose that the radius r increases at the rate of 0.02 inches per second, and that r = 36 inches at time t = 0. determine the equation that models the volume v of the balloon at time t, and find the volume when t = 360 seconds. v(t) = 4π(0.02t)2; 651.44 in3 v(t) = 4π(36 + 0.02t)2; 1,694,397.14 in3 v(t) = four pi times the product of zero point zero two and t to the third power divided by three.; 4,690.37 in3 v(t) = four pi times the quantity of thirty six plus zero point zero two t to the third power divided by three.; 337,706.83 in3

Lowest fraction using common term 28/35

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).