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A car rental agency only rents cars on a daily basis. Rented cars can be returned to to any of the agency's three locations; A, B, or C. The figure to the right shows the percentages of cars returned to each of the locations based on where they were picked up. Assume that all cars are rented each day and that initially 20% of the cars are at location A, 40% at location B, and 40% at location C. (a) Set up the stochastic matrix that displays these transitions. A 80% Enter your answer in each of the answer boxes. 20% (b) Estimate the percentage of cars at location A after two days. After two days, approximately % of the cars are at location A. (Round to the nearest tenth as needed.) (c) In the long run, what fraction of cars will be at location B? In the long run, the fraction of cars at location B is 10% 20% 10% 20% O B 60% 70% ?

A car rental agency only rents cars on a daily basis. Rented cars can be returned to to any of the agency's three locations; A, B, or C. The figure to the right shows the percentages of cars returned to each of the locations based on where they were picked up. Assume that all cars are rented each day and that initially 20% of the cars are at location A, 40% at location B, and 40% at location C. (a) Set up the stochastic matrix that displays these transitions. A 80% Enter your answer in each of the answer boxes. 20% (b) Estimate the percentage of cars at location A after two days. After two days, approximately % of the cars are at location A. (Round to the nearest tenth as needed.) (c) In the long run, what fraction of cars will be at location B? In the long run, the fraction of cars at location B is 10% 20% 10% 20% O B 60% 70% ?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A car rental agency only rents cars on a daily basis. Rented cars can be returned to any of the agency's three locations; A, B, or C. The figure to the right shows the percentages of cars returned to each of the locations based on where they were picked up. Assume that all cars are rented each day and that initially 20% of the cars are at location A, 40% at location B, and 40% at location C. (a) Set up the stochastic matrix that displays these transitions. A 80% Enter your answer in each of the answer boxes. 20% (b) Estimate the percentage of cars at location A after two days. After two days, approximately % of the cars are at location A. (Round to the nearest tenth as needed.) (c) In the long run, what fraction of cars will be at location B? In the long run, the fraction of cars at location B is 10% 20% 10% 20% B 10% 70% 60% ?
Transcribed Image Text:A car rental agency only rents cars on a daily basis. Rented cars can be returned to any of the agency's three locations; A, B, or C. The figure to the right shows the percentages of cars returned to each of the locations based on where they were picked up. Assume that all cars are rented each day and that initially 20% of the cars are at location A, 40% at location B, and 40% at location C. (a) Set up the stochastic matrix that displays these transitions. A 80% Enter your answer in each of the answer boxes. 20% (b) Estimate the percentage of cars at location A after two days. After two days, approximately % of the cars are at location A. (Round to the nearest tenth as needed.) (c) In the long run, what fraction of cars will be at location B? In the long run, the fraction of cars at location B is 10% 20% 10% 20% B 10% 70% 60% ?
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