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a.
Find the profit function.
b.
Find the number of units that give maximum profit.
c.
Find the maximum possible profit.
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- It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 4 5 6 y 51 44 33 26 Complete parts (a) through (e), given Σx = 16, Σy = 154, Σx2 = 78, Σy2 = 6302, Σxy = 548, and r ≈ −0.941. (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…It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 4 5 6 y 51 41 33 26 Complete parts (a) through (e), given Σx = 15, Σy = 151, Σx2 = 77, Σy2 = 6047, Σxy = 485, and r ≈ −0.958. (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…It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 51 41 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 151, Σx2 = 65, Σy2 = 6047, Σxy = 403, and r ≈ −0.9880. (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 four 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 to four 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) Find the value of the coefficient of…
- It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 49 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 152, Σx2 = 65, Σy2 = 6102, Σxy = 409, and r ≈ −0.987. (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 = = + x (d) Graph the least-squares line. Be sure to plot the point (x, y) as…It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 50 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx2 = 65, Σy2 = 6201, Σxy = 409, and r ≈ −0.991 (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 =It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 0 2 5 6 y 50 44 33 26 Complete parts (a) through (e), given Σx = 13, Σy = 153, Σx2 = 65, Σy2 = 6201, Σxy = 409, and r ≈ −0.991. (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…
- 3.It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 4 5 6 y 51 44 33 26 Complete parts (a) through (e), given Σx = 16, Σy = 154, Σx2 = 78, Σy2 = 6302, Σxy = 548, and r ≈ −0.941. (a) 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 % (b) If a team had x = 3 fouls over and above the opposing team, what does the least-squares equation forecast for y? (Round your answer to two decimal places.) %It is thought that basketball teams that make too many fouls in a game tend to lose the game even if they otherwise play well. Let x be the number of fouls more than (i.e., over and above) the opposing team. Let y be the percentage of times the team with the larger number of fouls wins the game. x 1 2 5 6 y 49 45 33 26 Complete parts (a) through (e), given Σx = 14, Σy = 153, Σx2 = 66, Σy2 = 6191, Σxy = 460, and r ≈ −0.9949. (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 four decimal places.) Σx = Σy = Σx2 = Σy2 = Σxy = r =X 1 Bar =: X 2 Bar=: X 3 Bar =: X 4 Bar =: X 5 Bar =: X 6 Bar =: X 7 Bar =: X 8 Bar =: X 9 Bar =: X 10 Bar =: R 1 Bar =: R 2 Bar =: R 3 Bar =: R 4 Bar =: R 5 Bar =: R 6 Bar =: R 7 Bar =: R 8 Bar =: R 9 Bar =: R 10 Bar =: X Double Bar=: R Double Bar =: Upper Control Limit (UCL) X Bar =: Lower Control Limit (LCL) X Bar =: Upper Control Limit (UCL) R Bar = : Lower Control Limit (LCL) R Bar = :
- A plant produces and sells semiconductor devices. The cost per one unit (also known as the unit cost) depends on the volume of production and includes a fixed part 1000 ($/device) and a variable part 2n ($/device), where n is the number of units produced per month. The price of the device, in turn, depends on the volume of production according to the law p(n)=10000−n ($/device). Determine at what volume of production the profit will be highest?Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. A bird with these tendencies is released from an island that is 3 km from the nearest point B on the shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. Points B and D are 8 km apart. (Round your answers to two decimal places.) In general, if it takes 1.3 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area?Maximize p = 2x + y subject to x + 2y ≤ 10 −x + y ≤ 5 x + y ≤ 5 x ≥ 0, y ≥ 0. p=(x, y) =