Satellite Television: Two competing companies offer satellite television to a city with 100,000 households. Gold Satellite System has 25,000 subscribers and Galaxy Satellite Network has 30,000 subscribers. (The other 45,000 households do not subscribe.) The matrix shows the percent changes in satellite subscriptions each year.
(a) Find the number of subscribers each company will have in 1 year using matrix multiplication. Explain how you obtained your answer.
(b) Find the number of subscribers each company will have in 2 years using matrix multiplication. Explain how you obtained your answer.
(c) Find the number of subscribers each company will have in 3 years using matrix multiplication. Explain how you obtained your answer.
(d) What is happening to the number of subscribers to each company? What is happening to the number of nonsubscribers?
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Chapter 7 Solutions
College Algebra
- Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Cars Revenue Company (1,000s) ($ millions) Company A 11.5 120 Company B 10.0 137 Company C 9.0 98 Company D 5.5 35 Сompany E 4.2 40 Company F 3.3 32 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 合160, 140- 160 160, 160, 140- 120- 140 140- 120 120 120 100 100 100 100 80 80 80 80 60 60 60 60 ... 40- 20- 40 .. 40 ... 40 20- 20- 20- 6 10 12 2 6 8 10 12 2 6 10 12 2 14 4 14 4 14 6 8 10 12 14 Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) (b) What does the scatter diagram developed in part (a) indicate about the relationship…arrow_forwardCompanies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Cars Revenue Company (1,000s) ($ millions) Company A 11.5 120 Company B 10.0 137 Company C 9.0 102 Company D 5.5 37 Company E 4.2 38 Company F 3.3 34 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 160 T 2 160 160 T 160- 140 140 140- 140 120 120 120 120- 100 100 100- 100- 80 80 80 80- 60 60 60 60 ... 40 ... 40 40 ... 40 20 20 20 20 4 6. 8 10 12 14 6. 8 10 12 14 2 4 8 10 12 14 4 8 10 12 14 Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) Cars in Service (1,000s) (b) What does the scatter diagram developed in part (a) indicate about the relationship…arrow_forwardCompanies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Cars Revenue Company (1,000s) ($ millions) Company A 11.5 120 Company B 10.0 137 Company C 9.0 102 Company D 5.5 39 Company E 4.2 40 Company F 3.3 30 (a) Develop a scatter diagram with the number of cars in service as the independent variable. 160 T 160- 1601 140 140 140 120- E 120- 120- 100 100 100- 80 80 80 CO 60 60 60 40 40 40 20 20 20- 6 8 10 12 14 4 6 8 10 12 14 Cars in Service (1,000s). ● 4 6 8 10 12 14 Cars in Service (1,000) 4 Cars in Service (1,000) Ⓡ 0 4 6 8 10 14 O Cars in Service (1,000) (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? O There…arrow_forward
- Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars (1,000s) Revenue ($ millions) Company A 11.5 116 Company B 10 137 Company C 9 102 Company D 5.5 39 Company E 4.2 38 Company F 3.3 30 (a) Develop a scatter diagram with the number of cars in service as the independent variable. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? (c) Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal…arrow_forwardCompanies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 116 Company B 10.0 133 Company C 9.0 98 Company D 5.5 37 Company E 4.2 40 Company F 3.3 32 a.Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal places.) b. For every additional car placed in service, estimate how much annual revenue will change (in dollars). (Round your answer to the nearest integer.) Annual revenue will increase by $ , for every additional car placed in…arrow_forwardCompanies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 118 Company B 10.0 137 Company C 9.0 102 Company D 5.5 39 Company E 4.2 40 Company F 3.3 32 (a) Develop a scatter diagram with the number of cars in service as the independent variable. A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on…arrow_forward
- Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies. Company Cars(1,000s) Revenue($ millions) Company A 11.5 118 Company B 10.0 133 Company C 9.0 98 Company D 5.5 37 Company E 4.2 40 Company F 3.3 30 (a) Develop a scatter diagram with the number of cars in service as the independent variable. A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on…arrow_forward. In 2010, of a total of 67,000 rooms on the Las Vegas Strip, Caesars Entertainment managed 22,880, while MGM Resorts managed over 12,000. However, owing to the Great Recession and new hotel openings, between 2008 and 2010, MGM's hotel occupancy decreased from 92% to 89%, while its average daily room rate fell from $148 to $108. Meanwhile, CityCenter, managed by MGM Resorts, and the Cosmopolitan opened with 4,000 and 3,000 rooms respectively, and the 1,720-room Sahara closed. (Sources: Caesars Entertainment Corp., Annual Report 2010; MGM Resorts, Annual Report 2010; "Sahara's closure on May 16 will mark `the end of an era'," Las Vegas Sun, March 11, 2011.) (a) Using a suitable figure, explain how the opening of CityCenter and the Cosmopolitan affects the residual demand for an existing hotel and how it should adjust prices. (b) If MGM Resorts had not reduced its room rates, what would have been the effect on occupancy? (c) Use the Cournot model to explain…arrow_forwardA company produces handmade shawls and afghans. They spin the yarn, dye it, and then weave it. A shawl requires 1 hour of spinning, 1 hour of dyeing, and 1 hour of weaving. An afghan requires 1 hour of spinning, 2 hours of dyeing, and 4 hours of weaving. There are at most 8 hours available each day for spinning, 10 hours for dyeing, and 16 hours for weaving. Summarize the data in a table. Use the table to write a system of inequalities. Then graph the feasible region. Complete the table. Hours Hours Number Spinning Dyeing Shawls x Afghans y Maximum Number of Hours Available 8 10 Hours Weaving 16arrow_forward
- Google has changed its strategy with regard to how much and over which media it invests in advertising. The following table shows Google's marketing budget in millions of dollars for 2008 and 2011 (The Wall Street Journal, March 27, 2012). 2008 2011 Internet $26.0 $123.3 Newspaper, etc. $4.0 $20.7 Television $0.0 $69.3 a. Select a side-by-side bar chart with year as the variable on the horizontal axis.arrow_forwardA friend who lives in Los Angeles makes frequent consulting trips to Washington, D.C.;50% of the time she travels on airline #1, 30% of the time on airline #2, and the remaining 20% of the time on airline #3. For airline #1, flights are late into D.C.30% of the time and late into L.A.10% of the time. For airline #2,these percentages are 25% and 20%,whereas for airline #3 the percentages are 40% and 25%.If we learn that on a particular trip she arrived late at exactly one of the two destinations, what are the posterior probabilities of having flown on airlines #1,#2, and #3? Assume that the chance of a late arrival in L.A.is unaffected by what happens on the flight to D.C. [ Hint: From the tip of each first generation branch on a tree diagram, draw three second-generation branches labeled, respectively, 0 late,1late, and 2 late.]arrow_forwardExpress all answers as decimals rounded to 3 decimal places, if needed. Express percentages as decimals (instead of 25.6%, use .256) Cell phone users in Boise can choose between three carriers: Sprint, AT&T, and Verizon. Advertising by all three companies results in a continual shift of customers. Each year, Sprint loses 30% of customers to AT&T and 30% to Verizon. AT&T loses 20% to Sprint and 10% to Verizon. Verizon loses 25% to Sprint and 25% to AT&T. Currently, Sprint has 25% of the market, AT&T has 35%, and Verizon has 40%. Use the order Sprint (S), AT&T (A), Verizon (V) throughout this assignment. 1. State the probability vector: 2. Create the transition matrix, labeling rows and columns, and draw the transition diagram. Create your matrix with the rows ordered S, A, and V, and columns ordered S, A, and V. 3. Assume that for 5 years this trend continues. State the transition matrix after 5 years. 4. What is the market share for each company after 5 years? Sprint: AT&T: Verizon: 5.…arrow_forward