Suppose a set of 8 numbers are selected from the set {1, 2, …, 13, 14}. Show that two of the selected numbers must sum to 15.

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)

Which statements are true for the functions g(x)= x^2 and h(x) = -x^2? check all that apply

Mike was going to sell all of his stamp collection to buy a video game. after selling half of them he changed his mind. he then bought ten more. how many did he start with if he now has 27?