Anumber cube labeled 1-6 is rolled out 200 times numbers 1-4 are rolled 137 times and numbers 5 or 6 are rolled the rest of the time what is the theoretical probability of rolling a 5 or 6 with the number cube .

a. 46%

b. 33.3%

c. 25%

d. 50%

Let f (x) = x e8x. find a formula for the nth derivative of f, where n is any positive integer. use x and n in your answer if needed. f (n)(x) =

Which value of m will create a system of parallel lines with no solution? y = mx - 6 8x - 4y = 12

For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius and height 2r minus the volume of two cones, each with a radius and height of r. a cross section of the sphere is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is the volume of the cylinder with radius r and height 2r is and the volume of each cone with radius r and height r is 1/3 pie r^3. so the volume of the cylinder minus the two cones is therefore, the volume of the cylinder is 4/3pie r^3 by cavalieri's principle. (fill in options are: r/2- r- 2r- an annulus- a circle -1/3pier^3- 2/3pier^3- 4/3pier^3- 5/3pier^3- 2pier^3- 4pier^3)