A certain statistics instructor participates in triathlons. The accompanying table lists times​ (in minutes and​ seconds) he recorded while riding a bicycle for five laps through each mile of a​ 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a​ hill? Mile_1_Minutes    Mile_1_Seconds    Mile_2_Minutes    Mile_2_Seconds    Mile_3_Minutes    Mile_3_Seconds3                               15                               3                        19                                3                             343                               24                               3                        23                                3                             313                               23                               3                        21                                3                             303                               23                               3                        18                                3                             323                               20                               3                        18                                3                             30 Find the Null hypothesis? [Nullhyothesis] Find the F statistic .[Value] Write upto 4 decimal points. Find the P-Value[Value1] What is the conclusion regarding Null Hypothesis [RejectorAccept]  

A particle is moving along a straight line and its acceleration is given by If its initial velocity is 3 ft/s, what is the velocity at t=2 seconds?

The following question is free response. You will not respond to it in Canvas. Please write your answers down on paper. You will submit your hand-written free response answer in Crowdmark. You must show full detailed work for credit on this.

Compute the left Riemann sum, using four subintervals (that is, ), for on the interval

(A): If then compute =[A]   (B): If then compute [B] (C): If then compute [C]

Free Response (16 points) Use the following definition to evaluate the integral

(A): if then compute =[A].   (B): if then compute [B].   (C): if . Then compute [C].

The area of the region enclosed by the graph of  and the line  is

A bacteria colony is cultivated in a laboratory. The number of bacteria increases at a rate of  hundred strands per day (t is time in days). Find the increase in bacteria population after 4 days, assuming that there are 1 hundred strands of bacteria at time t=0.

Find the power series representation centered at 0 for