Suppose that you have a map on which 1 inch represents 30 miles. You trace a state on the map, out out your tracing, and draw this tracing onto card stock. Using a scale, you determine that a full
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- 9. Solve the System of Ordinary Differential Equations Using Matrix Methods Turn to page 57 for the system of ODES. Solve the system using matrix methods, such as eigenvalue decomposition or diagonalization. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show a clear, step-by-step solution.arrow_forwardA study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05 significance level for both parts. a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? OA. Ho PP2 H₁: P1 P2 OC. Ho H₁₂ H₁: P₁arrow_forward3. Solve the Differential Equation Using the Method of Characteristics Go to page 51 for a partial differential equation problem. Use the method of characteristics to solve the given equation. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2ql5dbpVLCS/view? usp=sharing] Include all detailed steps in your solution.arrow_forward8. Determine the Fourier Series Expansion of the Function Refer to page 56 of the document for the Fourier series problem. Compute the Fourier series expansion of the given periodic function. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include all steps involved in the calculation.arrow_forwardFind the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports. Is the prediction worthwhile? Use a significance level of 0.05. Lemon Imports 235 264 356 Crash Fatality Rate 16 15.9 15.6 476 518 15.3 D 15.1 Find the equation of the regression line. + (Round the y-intercept to three decimal places as needed. Round the slope to four decimal places as needed.) The best predicted crash fatality rate for a year in which there are 475 metric tons of lemon imports is fatalities per 100,000 population. (Round to one decimal place as needed.) Is the prediction worthwhile? OA. Since there appears to be an outlier, the prediction is not appropriate. OB. Since all of the requirements for finding the equation of the regression line are met, the…arrow_forwardA study of seat belt users and nonusers yielded the randomly selected sample data summarized in the accompanying table. Use a 0.05 significance level to test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data? Click the icon to view the data table. Determine the null and alternative hypotheses. OA. Ho: The amount of smoking is dependent upon seat belt use. H₁: The amount of smoking is not dependent upon seat belt use. OB. Ho: Heavy smokers an H₁: Heavy smokers an OC. Ho: The amount of sm H₁: The amount of sm OD. Ho Heavy smokers an H₁: Heavy smokers ar Determine the test statistic. x²= (Round to three decin More Info Number of Cigarettes Smoked per Day 0 1-14 15-34 35 and over Wear Seat Belts 193 20 42 9 Don't Wear Seat Belts 159 10 41 9 Determine the P-value of the t P-Value =…arrow_forwardAssume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.3 kg and a standard deviation of o=5.5 kg. Complete parts (a) through (c) below. a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.) b. If 9 male college students are randomly selected, find the probability that their mean weight gain during freshman year is between 0 kg and 3 kg. The probability is (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size. OB. Since the weight gain exceeds 30, the distribution of sample means is a normal distribution for any sample size. OC. Since the original…arrow_forward4. Find the Eigenvalues and Eigenvectors of the Symmetric Matrix The symmetric matrix problem is provided on page 52 of the document. Compute the eigenvalues and eigenvectors using the characteristic polynomial method. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxp RyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show each step clearly in your solution.arrow_forwardFind the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. Click to view page 1 of the table. Click to view page 2 of the table. The area of the shaded region is ☐ (Round to four decimal places as needed.) 95 125arrow_forwardSimpson’s Rule with n = 4 subintervals to estimate the integral of the squre root of x dx with upper bounds of 9 and lower bounds of 1 is 14.2302 but exactly 18. Use the Error Bound to find the bound for the error.arrow_forwardThe accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a scatterplot, find the value of the linear correlation coefficient r, and of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.05. Click the icon to view the ages of the award winners. Best Actresses and Best Actors Construct a scatterplot. Choose the correct graph below. OA. Best Actor (years) 70- 17 OB. Best Actresses and Best Actors OC. 20- 20 70 Best Actress 27 30 30 62 33 32 46 30 58 23 45 51 Best Actress (years) Best Actor 43 37 37 44 47 47 56 49 40 56 46 34 The linear correlation coefficie (Round to three decimal place Determine the null and alterna Print Done Ho P H₁ P (Type integers or decimals. Do not round.) The test statistic is t= (Round to two decimal places as needed.) The P-value is (Round to…arrow_forwardA data set includes data from student evaluations of courses. The summary statistics are n = 93, x=3.83, s = 0.68. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? OA. Ho μ*4.00 H₁ =4.00 OC. Ho p=4.00 H₁:p>4.00 Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. ☐ (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Ho. There is OB. Ho H=4.00 H₁ #4.00 OD. Ho p=4.00 Η μ < 4.00 evidence to conclude that the mean of the population of student course evaluations is equal to 4.00 correct.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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