Concept explainers
The bar graph Shows the ratings of American Idol from season 1 (2002) through season 12 (2013).
American Idol: Each Season’s Champion and Average Number of Viewers
Source: Nielsen
a. Let x represent American Idol's season number and let y represent the average number of viewers, in millions. Use a graphing utility to draw a
b. Use the quadratic regression feature to find the quadratic function that best fits the data. Round all numbers to two decimal places.
c. Use the model in part (b) to determine the season in which American Idol had the greatest number of viewers. Round to the nearest whole number. According to the model, how many millions of viewers were there in that season? Round to one decimal place.
d. How do the results obtained from the model in part (c) compare with the data displayed by the graph?
e. Use a graphing utility to draw a scatter plot of the data and graph the quadratic function of best fit on the scatter plot. Can you see why projections based on the graph had the producers of American Idol looking for a shake-up? No shake-up was found and the show's final season aired in 2016.
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
COLLEGE ALGEBRA-MYMATHLAB
- 3. Select the polynomial that matches the description given: Zero at 4 with multiplicity 3 Zero at −1 with multiplicity 2 Zero at -10 with multiplicity 1 Zero at 5 with multiplicity 5 ○ A. P(x) = (x − 4)³(x + 1)²(x + 10)(x — 5)³ B - P(x) = (x + 4)³(x − 1)²(x − 10)(x + 5)³ ○ ° P(x) = (1 − 3)'(x + 2)(x + 1)"'" (x — 5)³ 51 P(r) = (x-4)³(x − 1)(x + 10)(x − 5 3 of 10arrow_forwardMatch the equation, graph, and description of transformation. Horizontal translation 1 unit right; vertical translation 1 unit up; vertical shrink of 1/2; reflection across the x axis Horizontal translation 1 unit left; vertical translation 1 unit down; vertical stretch of 2 Horizontal translation 2 units right; reflection across the x-axis Vertical translation 1 unit up; vertical stretch of 2; reflection across the x-axis Reflection across the x - axis; vertical translation 2 units down Horizontal translation 2 units left Horizontal translation 2 units right Vertical translation 1 unit down; vertical shrink of 1/2; reflection across the x-axis Vertical translation 2 units down Horizontal translation 1 unit left; vertical translation 2 units up; vertical stretch of 2; reflection across the x - axis f(x) = - =-½ ½ (x − 1)²+1 f(x) = x²-2 f(x) = -2(x+1)²+2 f(x)=2(x+1)²-1 f(x)=-(x-2)² f(x)=(x-2)² f(x) = f(x) = -2x²+1 f(x) = -x²-2 f(x) = (x+2)²arrow_forwardWhat is the vertex, increasing interval, decreasing interval, domain, range, root/solution/zero, and the end behavior?arrow_forward
- The augmented matrix of a linear system has been reduced by row operations to the form shown. Continue the appropriate row operations and describe the solution set of the original system. 1 -1 0 1 -2 00-4 0-6 0 0 1 - 3 3 0 001 4arrow_forwardSolve the system. X1 - 3x3 = 10 4x1 + 2x2 + 3x3 = 22 ×2 + 4x3 = -2arrow_forwardUse the quadratic formula to find the zeros of the quadratic equation. Y=3x^2+48x+180arrow_forward
- M = log The formula determines the magnitude of an earthquake, where / is the intensity of the earthquake and S is the intensity of a "standard earthquake." How many times stronger is an earthquake with a magnitude of 8 than an earthquake with a magnitude of 6? Show your work.arrow_forwardNow consider equations of the form ×-a=v = √bx + c, where a, b, and c are all positive integers and b>1. (f) Create an equation of this form that has 7 as a solution and an extraneous solution. Give the extraneous solution. (g) What must be true about the value of bx + c to ensure that there is a real number solution to the equation? Explain.arrow_forwardThe equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and c are all positive integers and b > 1. Using this equation as a model, create your own equation that has extraneous solutions. (d) Using trial and error with numbers for a, b, and c, create an equation of the form x + a = √bx + c, where a, b, and c are all positive integers and b>1 such that 7 is a solution and there is an extraneous solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.) (e) Solve the equation you created in Part 2a.arrow_forward
- A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%?arrow_forwardA boat is 15 ft away from a point perpendicular to the shoreline. A person stands at a point down the shoreline so that a 65° angle is formed between the closest point to the boat, the person, and the boat. How far is the person from the boat? Round your answer to the nearest tenth of a foot. Show your work. boat 15 ft d 65° personarrow_forward2. Find the value of x in the triangle. Round your answer to the nearest tenth of a degree. Show your work. 8 15arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell