Concept explainers
Wind Energy The table shows the annual amounts of U.S. consumption W (in trillion Btu) of wind energy for the years 2008 through 2013. (Source: U.S. Energy Information Administration)
Year | 2008 | 2009 | 2010 | |||
Consumption | 546 | 721 | 923 | |||
Year | 2011 | 2012 | 2013 | |||
Consumption | 1168 | 1340 | 1595 |
Spreadsheet at LarsonAppliedCalculus.com
A mathematical model for the data is given by
(a) Use a graph and a table to compare the actual consumptions with the model.
(b) Use the model to predict the consumption in 2019.
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
CALCULUS: APPLIED APPROACH LOW COST MA
- Using your graphing calculator, make a scatter plot of the data from the table. Then graph your model from Question 2 along with the data. How well does your model fit the data? What could you do to try to improve your model?arrow_forwardResearchers initiated a long-term study of the population of American black bears. One aspect of the study was to develop a model that could be used to predict a bear's weight (since it is not practical to weigh bears in the field). One variable thought to be related to weight is the length of the bear. The accompanying data represent the lengths and weights of 12 American black bears. Complete parts (a) through (d) below. Click the icon to view the data table. Click the icon to view the critical values table. ..... (a) Which variable is the explanatory variable based on the goals of the research? O A. The number of bears B. The weight of the bear O C. The length of the bear (b) Draw a scatter diagram of the data. Choose the correct graph below. O A. O B. O C. D. A Weight (kg) 180- AWeight (kg) 180- ALength (cm) 180- A Weight (kg) 180- 40- 100 40- 100 Length (cm) 40- 100 40- 100 200 200 200 200 Length (cm) Weight (kg) Length (cm) (c) Determine the linear correlation coefficient between…arrow_forwardThe table below show data that has been collected from different fields from various farms in a certain valley. The table contains the grams of Raspberries tested and the amount of their Vitamin C content in mg. Find a linear model that express Vitamin C content as a function of the weight of the Raspberries. grams5565758595105115Vitamin Ccontent in mg11.916.321.225.829.833.639.5 A) Find the regression equation: y= x+Round your answers to 3 decimal places B) Answer the following questions using your un-rounded regression equation. If we test 145 grams of raspberries what is the expected Vitamin C content? mg(round to the nearest tenth)arrow_forward
- examples of graphic presentation of dataarrow_forwardPlease help mearrow_forward(c) Th Data Table Total Length (cm) 138.0 135.0 130.0 120.5 149.0 141.0 141.0 150.0 166.0 151.5 129.5 150.0 Print Weight (kg) 110 60 90 60 85 105 95 85 155 140 105 110 Done 0 X Critical Values for the Correlation Coefficient 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 0371 X not practical to v parts (a) througharrow_forward
- My UHart | University of Hartford The owner of Showtime Movie Theaters, Inc., would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow. Weekly Gross Revenue ($1,000s) Television Advertising ($1,000s) Newspaper Advertising ($1,000s) 96 5.0 1.5 90 2.0 2.0 95 4.0 1.5 92 2.5 2.5 95 3.0 3.3 94 3.5 2.3 94 2.5 4.2 94 3.0 2.5 The owner then used multiple regression analysis to predict gross revenue (y), in thousands of dollars, as a function of television advertising (x,), in thousands of dollars, and newspaper advertising (x,), in thousands of dollars. The estimated regression equation was = 83.2 + 2.29x, + 1.30x2. (a) What is the gross revenue (in dollars) expected for a week when $3,000 is spent on television advertising (x, = 3) and $3,300 is spent on newspaper advertising (x, = 3.3)? (Round your answer to the nearest dollar.) %$4 (b) Provide a 95% confidence interval (in dollars) for the mean revenue of all…arrow_forwardThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. X 11.3 y 13.3 10.9 9.9 8.4 6.8 3.9 2.8 2.4 2.5 7 6.7 6.4 6.3 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation ŷ = 0.79x + 4.32. Use this equation to answer the following. Answer = 12.829 0.9 5 A) How many murders per 100,000 residents can be expected in a state with 10.1 thousand automatic weapons? Answer = 6.123 x Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 2.7 thousand automatic weapons? x Round to 3 decimal places.arrow_forwardJust need help with part 2 and 3 please and thank you!arrow_forward
- The following table lists heights (in inches) and weights (in pounds) for 9 supermodels:Height (in.)_x__|__71____70.5____71____72____70____70____66.5____70____71_Weight (lb) y | 125 119 128 128 119 127 105 123 115 Plot the scatter diagram for the paired data.b) Assuming a 5% level of significance, use hypothesis testing and the linear correlationcoefficient (r) to determine if there is a linear correlation. α = 0.05 c) Find the equation of the regression line and plot it on your scatter diagram using an x of 68and an x of 71. d) Determine the residual value for an x of 70.5 and explain its meaning. e) Determine the coefficient of determination and explain its meaning.arrow_forwardFuel efficiency can make a big difference in the operating cost of your car. The following table gives the fuel economy for selected 1995 two-seater cars along with the average annual fuel cost to operate the car. Make and Model of Car Estimated mpg (city) Annual fuel cost Chevy Corvette 17 900 Dodge Viper 13 1266 Honda Del Sol 29 562 Honda NSX 18 1012 Mazda MX-5 Miata 22 751 Mercedes Benz SL 320 17 1012 Nissan 300 ZX 18 1012 Suzuki X-90 2WD 25 693 Source: Consumers’ Research Magazine, Nov. 1995 v.78 Would you expect that there would be a relationship between these two quantities? Explain. YES or NO (circle one) Why? If the relationship was linear, would you expect it to be a positive or negative correlation? POSITIVEorNEGATIVE (circle one) Why? Name the independent and dependent variables. independent variable (x): _________________________ dependent…arrow_forwardan you tell how old a lobster is by its size? This question was investigated by the authors of a paper that appeared in the Biological Bulletin (August 2007). Researchers measured carapace (the exterior shell) length of 27 laboratory-raised lobsters of known age. The data on x = carapace length (in mm) and y = age (in years) in the following table were read from a graph that appeared in the paper. Age CarapaceLength Age CarapaceLength Age CarapaceLength 1.00 63.32 1.82 118.25 2.93 147.82 1.00 67.50 2.18 108.24 2.92 140.17 1.00 69.58 2.18 109.64 2.92 135.73 1.00 74.41 2.17 117.99 2.92 121.81 1.42 80.32 2.17 123.81 3.17 141.30 1.42 81.80 2.33 138.47 3.41 151.73 1.42 84.59 2.50 133.95 3.42 145.78 1.82 105.07 2.51 124.25 3.75 147.21 1.82 106.16 2.50 123.51 4.08 152.04 (a) Construct a scatterplot of these data, and then find the equation of the least squares regression line that describes the relationship between y = age and x = carapace length. A scatterplot…arrow_forward
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtTrigonometry (MindTap Course List)TrigonometryISBN:9781305652224Author:Charles P. McKeague, Mark D. TurnerPublisher:Cengage Learning