Amarket research firms conducts studies regarding the success of new products. the company is not always perfect in predicting the success. suppose that there is a 50% chance that any new product would be successful (and a 50% chance that it would fail). in the past, for all new products that ultimately were successful, 80% were predicted to be successful (and the other 20% were inaccurately predicted to be failures). also, for all new products that were ultimately failures, 70% were predicted to be failures (and the other 30% were inaccurately predicted to be successes). for any randomly selected new product, what is the probability that the market research firm would predict that it would be a success?

Assume that y varies inversely with x. if y=1.6 when x=0.5 find x when y=3.2

When you flip a biased coin the probability of getting a tail is 0.6. how many times would you expect to get tails if you flip the coin 320 times?

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)