The manufacturer of the ColorSmart-5000 television set claims 95 percent of its sets last at least five years without needing a single repair. In order to test this claim, a consumer group randomly selects 420 consumers who have owned a ColorSmart-5000 television set for five years. Of these 420 consumers, 303 say their ColorSmart-5000 television sets did not need a repair, whereas 117 say their ColorSmart-5000 television sets did need at least one repair. Determine the sample size needed in order to be 99 percent confident that p, the sample proportion of ColorSmart-5000 television sets that last at least five years without a single repair, is within a margin of error of .03 of p, the population proportion of sets that last at least five years without a single repair. (Round your p answer to 5 decimal places. Round your n answer to the next whole number.)

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12

The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

Complete the worksheet. use 3.14 for π and round all decimals to the nearest hundredth. find the volume of the composite three-dimensional figure above. important terms are written in bold.1. the pyramid has a square base that is inscribed in the circular base of the cone. draw an image of the composite shape of the base. 2. if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1? 3. now that the diameter has been calculated, what is the circular area of the cone? ignore the square base of the pyramid.? 4. what is the formula for volume of a cone? 5.to calculate the volume of the cone, the height is still needed. if the cone has a lateral surface with a length of 13 units, what is the height of the cone? 6.now find the volume of the cone. do not include the empty space for the pyramid. 7.. the side length of the square base of the pyramid is 8 units long. what is the base area of the pyramid? 8.what is the formula for the volume of a pyramid9. since the cone and the pyramid share the same vertex, what is the volume of the pyramid10.using the volume of the cone and the pyramid, find the volume of the composite shape. remember, the pyramid is empty. 11,. referring to the picture in number 1, what is the area of the composite base knowing that the square is empty? 12what is the formula to find the lateral surface area of a cone? (13find the lateral surface area of the cone14what is the lateral surface area shape of the pyramid? what is the formula for its area? 15to find the lateral surface area of the pyramid the length is still needed. calculate the lateral surface length of the pyramid. 16 now that the lateral surface length is known, what is the lateral surface area of the pyramid17. using the lateral surface areas of the cone and pyramid, along with the area of the composite base, what is the total surface area?