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- 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2For which values of t is each set linearly independent? a S={(t,1,1),(1,t,1),(1,1,t)} b S={(t,1,1),(1,0,1),(1,1,3t)}Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.7 9.2 9.8 8.0 8.3 8.7 y 9.9 18.1 20.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.7, Σy = 82.9, Σx2 = 464.95, Σy2 = 1239.27, Σxy = 740.8, and r ≈ 0.909. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x
- Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.7 9.2 9.8 8.0 8.3 8.7 y 9.9 18.1 20.2 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.7, Σy = 82.9, Σx2 = 464.95, Σy2 = 1239.27, Σxy = 740.8, and r ≈ 0.909. (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) Suppose a small city in Oregon has a per capita income of 9.8 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.)M.D.s per 10,000 residentsLet x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.8 9.7 10.2 8.0 8.3 8.7 y 9.8 18.0 20.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.7, Σy = 82.5, Σx2 = 484.15, Σy2 = 1225.65, Σxy = 755.03, and r ≈ 0.927. Suppose a small city in Oregon has a per capita income of 9.0 thousand dollars. What is the predicted number of M.D.s per 10,000 residents? (Round your answer to two decimal places.) M.D.s per 10,000 residentsLet x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.8 9.7 10.2 8.0 8.3 8.7 y 9.8 18.0 20.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 53.7, Σy = 82.5, Σx2 = 484.15, Σy2 = 1225.65, Σxy = 755.03, and r ≈ 0.927. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage…
- Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.2 9.2 10.2 8.0 8.3 8.7 y 9.9 18.2 21.0 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.6, Σy = 83.8, Σx2 = 464.5, Σy2 = 1275.86, Σxy = 753.01, and r ≈ 0.974. (a) Draw a scatter diagram displaying the data. Flash Player version 10 or higher is required for this question. You can get Flash Player free from Adobe's website. (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x (d) Graph the…Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x 8.7 9.0 9.8 8.0 8.3 8.7 y 9.8 18.2 20.6 10.2 11.4 13.1 Complete parts (a) through (e), given Σx = 52.5, Σy = 83.3, Σx2 = 461.31, Σy2 = 1257.25, Σxy = 741.13, and r ≈ 0.878. (a) Draw a scatter diagram displaying the data. Selection Tool (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (e)…Do heavier cars really use more gasoline? Suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds), and let y be the miles per gallon (mpg). x 30 43 29 47 23 40 34 52 y 29 21 26 13 29 17 21 14 Complete parts (a) through (e), given Σx = 298, Σy = 170, Σx2 = 11,788, Σy2 = 3894, Σxy = 5927, and r ≈ −0.922. (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x = y = = + x (e) Find the value of the coefficient of determination r2. What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r2 to three decimal places. Round your answers for the percentages to one decimal place.) r2 = explained % unexplained % (f) Suppose a car weighs x = 40 (hundred pounds). What does…
- Let x be per capita income in thousands of dollars. Let y be the number of medical doctors per 10,000 residents. Six small cities in Oregon gave the following information about x and y. x:8.49.210.48.08.38.7y:9.418.920.810.211.413.1Complete parts (a) through (e), given Σx = 53, Σy = 83.8, Σx2 = 471.94, Σy2 = 1283.82, Σxy = 759.35, and r ≈ 0.924. (a) Draw a scatter diagram displaying the data (b) Verify the given sums Σx, Σy, Σx2, Σy2, Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.) Σx =Σy =Σx2 =Σy2 =Σxy =r = (c) Find x, and y. Then find the equation of the least-squares line = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.) x= y= y= _____ + ______ x (d) Graph the least-squares line. Be sure to plot the point (x, y) as a point on the line. (e) Find the value of the coefficient of determination r2. What percentage of the variation in y…t the Blood Bank, they know that O+ blood is the most common blood type and that 40%40% of the people are known to have O+ blood. Blood type A- is a very scarce blood type and only 6%6% of the people have A- blood. Half of the people have blood type A or B. Let: X=X= number of people who have blood type O+ Y=Y= number of people who have blood type A- Z=Z= number of people who have blood type A or BC. How likely are you to randomly select a consumer who cannot live without several of the products under consideration? There is a ________% chance of randomly selecting a consumer who cannot live without both google and head and shoulders. 2. There is a ________% chance of randomly selecting a consumer who cannot live without both Microsoft and head and shoulders. 3. There is a ________% chance of randomly selecting a consumer who cannot live without both Microsoft and AT&T.
