Emily has a collection of plastic containers shaped like cylinders and cones. Emily has two identical cylinders and six identical cones. The combined volume of the cylinders is equal to the combined volume of the cones. The diameters of the cylinders and cones are 412 inches and the heights of the cylinders are 7 inches. What is the height of each cone?

Solve the equation by completing the square. x^2+2x=17

The rectangle shown has a perimeter of 108 cm and the given area. its length is 6 more than five times its width. write and solve a system of equations to find the dimensions of the rectangle.

Atest of sobriety involves measuring the subject's motor skills. a sample of 31 randomly selected sober subjects take the test and produce a mean score of 64.4 with a standard deviation of 2. a claim is made that the true mean score for all sober subjects is equal to 65. for each part below, enter only a numeric value in the answer box. for example, do not type "z =" or "t =" before your answers. round each of your answers to 3 places after the decimal point. (a) calculate the value of the test statistic used in this test. test statistic's value = (b) use your calculator to find the p-value of this test. p-value = (c) use your calculator to find the critical value(s) used to test this claim at the 0.2 significance level. if there are two critical values, then list them both with a comma between them. critical value(s) =