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Listed below are amounts of court income and salaries paid to the town justices for a certain town. All amounts are in thousands of dollars. Find the​ indicated prediction interval. There is sufficient evidence to support a claim of a linear​ correlation, so it is reasonable to use the regression equation when making predictions. For the prediction​ interval, use a 99​% confidence level with a court income of ​$800​,000.   Court_Income    Justice_Salary64                        29412                     491553                   901144                   51272                     47252                     61102                     20157                     3026                       22   Lower Bound[LB] < y < Upper Bound[UB] - Approximate upto 2 decimal places  

Conduct the hypothesis test and provide the test statistic and the critical​ value, and state the conclusion. A person purchased a slot machine and tested it by playing it 1,117 times. There are 10 different categories of​ outcomes, including no​ win, win​ jackpot, win with three​ bells, and so on. When testing the claim that the observed outcomes agree with the expected​ frequencies, the author obtained a test statistic ofχ2=11.516. Use a 0.025 significance level to test the claim that the actual outcomes agree with the expected frequencies. Does the slot machine appear to be functioning as​ expected? Find the test statistic[TS]? Find the critical value?[CV] Do you accept/reject?[acceptorreject] Write upto 3 decimal points

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