Suppose that f : x → y is a function and that a is a σ-algebra of subsets of x. show that the following collection of subsets of y is also a σ-algebra: b : = {b ⊂ y : f −1 (b) ∈ a}

Find the average speed of a rabbit that runs a distance of 22 m in a time of 1.8 s .

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) =

Ranck the following in order from least precise to most precise