If two events a and b are mutually exclusive, what does the special rule of addition state? p(a or b.= p(a) + p(b) p(a and b.= p(a) + p(b) p(a and/or b.= p(a) + p(b) p(a or b.= p(a) - p(b)

The function g(x) is defined as shown. x-1, -2 g(x) = 2x+3, -1 6-x, x23

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

In each of the cases that follow, the magnitude of a vector is given along with the counterclockwise angle it makes with the +x axis. use trigonometry to find the x and y components of the vector. also, sketch each vector approximately to scale to see if your calculated answers seem reasonable. (a) 50.0 n at 60.0°, (b) 75 m/ s at 5π/ 6 rad, (c) 254 lb at 325°, (d) 69 km at 1.1π rad.