In the rectangular pyramid ABCDP, the diagonals of the base, AC and BD intersect at point O. Determine the set of points common for plane (ACP) and the plane, say u, which contains the line BD and is parallel to the lateral edge AP.

If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.

How many square centimeters of wrapping paper will be used to wrap the shoe box?

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) =