The difference between two numbers is 7. Find the two numbers if the larger number is three times the smaller.

If the ratio of sum of the first m and n terms of an ap is m2 : n2 , show that the ratio of its mth and nth terms is (2m − 1) : (2n − 1).

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) =

*15 pts* the graph of an exponential function of the form y = f(x) = ax passes through the points and the graph lies the x-axis. first line choices: (0, a) (0, 1) (0, 2) (0, -1) second line choices: (1, 0) (1, a) (1, 1) (1, -2) third line choices: above below on the