Rachel can buy licorice sticks for $0.75 and cherry candies for $0.50 and has a budget of $25. if her expenses are represented by the equation 0.75x + 0.5y = 25, where x is the number of licorice sticks and y is the number of cherry candies, how many cherry candies can she buy if she wishes to spend the entire $25 on cherry candies? (note: x ≥ 0, y ≥ 0, and x and y take only integer values.)

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) =