Simplify each expression. state any excluded values. show your work. 1. 2p-24/4p-48 2. b^2+8b+15/b+5 3. 5-4n/4n-5

Anthony is making a collage for his art class my picking shapes randomly. he has five squares, two triangles, two ovals, and four circles. find p( circle is chosen first)

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)

One side of a rectangle is 7 centimeters shorter than six times the other side. find the length of the longer side if we also know that the perimeter of the rectangle is 266 centimeters.