The amounts of money Peter and Maria each charge to deliver food are described below. Peter charges a flat fee of $3.75 for each delivery plus $0.10 per mile for each mile he drives.

Maria charges a flat fee of $2.25 for each delivery plus $0.25 per mile for each mile she drives.

Peter says there are two distances for which he and Maria charge the same amount. To prove Peter is not correct, Maria graphs a line for her delivery charges and a line for Peter’s delivery charges. Each line represents the relationship between the amount (y), in dollars, each person charges for delivery, and the distance (x), in miles, each drives for the delivery.

Without showing the graph, explain how Maria’s graph of the two lines proves Peter is not correct.

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The population of a bacteria colony grows by a consistent percentage each hour and can be modeled by the function y = 500(1.16)t. what does the value 500 represent in the function?

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) =