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Listed below are the numbers of deaths resulting from motor vehicle crashes. Let x represent the​ year, with 1975 coded as x=​1, 1980 coded as x=​6, 1985 coded as x=​11, and so on. Construct a scatterplot and identify the mathematical model that best fits the given data. Use the best model to find the projected number of deaths for the year 2030. x_(year)    y_(deaths)1975    445141980    510681985    438221990    446061995    418202000    419292005    434652010    32717 Write the nonlinear equation.[Equation] Find the projected death.[ProjectedDeathin2030]  

An investigator analyzed the leading digits from 762 checks issued by seven suspect companies. The frequencies were found to be 224​, 129​, 80​, 67​, 75​, 57​, 46​, 36​, and 48​, and those digits correspond to the leading digits of​ 1, 2,​ 3, 4,​ 5, 6,​ 7, 8, and​ 9, respectively. If the observed frequencies are substantially different from the frequencies expected with​ Benford’s law shown​ below, the check amounts appear to result from fraud. Use a 0.01significance level to test for​ goodness-of-fit with​ Benford’s law.  Leading_Digit    Actual_Frequency    Benford’s_Law:1                              224                           30.10%2                             129                            17.60%3                               80                            12.50%4                               67                              9.70%5                               75                              7.90%6                               57                              6.70%7                               46                              5.80%8                               36                              5.10%9                               48                              4.60% Write upto 3 decimal points Find the test statistic[TestStatistic] Find the P-Value[Pvalue]

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

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

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