Using ratio pleases help i´m stuck i need #5 for one side 1-5 for the other

Given: △acm, m∠c=90°, cp ⊥ am , ac: cm=3: 4, mp-ap=1. find am.

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) =

Tom says that he needs 6 rolls to obtain each possible outcome on a 6-sided die. on the fourth roll, he rolls his second "3”. tom says that the die is loaded and that each outcome is not equally likely. is tom correct here? if you think tom is incorrect, how many rolls should tom make until he sees each number occurring about 1/6 of the time?