Given Segment AC with point B contained on the segment, as shown below. Write a complete two-column proof for following information:

Given: Segment AB = x + 16, Segment BC = 4x + 11

Segment AC = 77

Prove: AB = 26

Astudent drew a circle and two secant segment. he concluded that if pq ~= ps, then qr ~= st. do you agree with the student’s conclusion? why or why not?

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) =

In a class of 77, there are 44 students who play soccer. if the teacher chooses 33 students, what is the probability that none of the three of them play soccer?