I NEED URGENT HELP WITH #3 AND #4

The U-Move truck rental company currently has branches in four cities: Atlanta, Baltimore, Chicago, and Denver. They conduct some analysis on their records to figure out how their trucks move around. For example they find that each week, 75% of the trucks rented in Atlanta are returned to their Atlanta locations, while 10% wind up in Baltimore, 5% wind up in Chicago, and 10% wind up in Denver. Their research is summarized in table form by the following Rented in Rented in Rented in Rented in Atlanta Baltimore Chicago Denver Returned in Atlanta 75% 20% 10% 10% Returned in Baltimore 10% 65% 5% 5% Returned in Chicago 5% 10% 70% 5% Returned in Denver 10% 5% 15% 80% This can be put into a matrix as follows: .75 .2 .1 .1 .1 .65 .05 .05 T= .05 .1 .7 .05 .1 .05.15 .8 The column of the matrix indicates which cities the truck was rented from and the row indicates which city it was returned to. Atlanta is the first row and column, Baltimore the second row and column, Chicago the third row and column, and Denver the fourth. Each entry represents a percentage. Thus of all the trucks rented in Chicago, the third column, 10% are returned in Atlanta (first row), 5% in Baltimore (second row), 70% back in Chicago (third row), and 15% in Denver. (Fourth row.) 1. If the company starts a week with 500 trucks in Atlanta, 100 in Baltimore, 600 in Chicago, and 500 in Denver where will the trucks be one week later. (Assume all trucks are returned.) Think about where the numbers you are using for your calculation are coming from in the matrix T and use that to write your solution in matrix and vector form. 2. If a different week ended with 610 trucks in Atlanta, 185 in Baltimore, 320 in Chicago, and 155 in Denver what was the distribution of trucks at the start of that week? Use your matrix form from the previous problem to set up and solve this. We can also use the given information to figure out what happens over multiple weeks. If we want to know what percentage of the trucks that start in Chicago go to Baltimore the first week and Atlanta the second we can use multiplication to determine this. During the first week, 5% of the trucks in Chicago go to Baltimore. (From row 2, column 3.) Then of those trucks, 20% will go to Atlanta in the second week (from row 1, column 2.) Thus (05)(-2) = .01 or 1% of the trucks that start in Chicago will make the trip first to Baltimore, then to Atlanta. 3. How many different ways could a truck start in Atlanta and wind up in Baltimore after two weeks? (Assume cach truck is rented exactly once cach week.) Find the percentage of trucks rented in Atlanta that will follow each of those routes. What percentage of the trucks starting in Atlanta will wind up in Baltimore two weeks later? 1. Calculate 7%, and explain why the calculations for the entry in row 2 column 1 of T means the result matches the number you found in the previous part. The U-Move truck rental company currently has branches in four cities: Atlanta, Baltimore, Chicago, and Denver. They conduct some analysis on their records to figure out how their trucks move around. For example they find that each week, 75% of the trucks rented in Atlanta are returned to their Atlanta locations, while 10% wind up in Baltimore, 5% wind up in Chicago, and 10% wind up in Denver. Their research is summarized in table form by the following Rented in Rented in Rented in Rented in Atlanta Baltimore Chicago Denver Returned in Atlanta 75% 20% 10% 10% Returned in Baltimore 10% 65% 5% 5% Returned in Chicago 5% 10% 70% 5% Returned in Denver 10% 5% 15% 80% This can be put into a matrix as follows: .75 .2 .1 .1 .1 .65 .05 .05 T= .05 .1 .7 .05 .1 .05.15 .8 The column of the matrix indicates which cities the truck was rented from and the row indicates which city it was returned to. Atlanta is the first row and column, Baltimore the second row and column, Chicago the third row and column, and Denver the fourth. Each entry represents a percentage. Thus of all the trucks rented in Chicago, the third column, 10% are returned in Atlanta (first row), 5% in Baltimore (second row), 70% back in Chicago (third row), and 15% in Denver. (Fourth row.) 1. If the company starts a week with 500 trucks in Atlanta, 100 in Baltimore, 600 in Chicago, and 500 in Denver where will the trucks be one week later. (Assume all trucks are returned.) Think about where the numbers you are using for your calculation are coming from in the matrix T and use that to write your solution in matrix and vector form. 2. If a different week ended with 610 trucks in Atlanta, 185 in Baltimore, 320 in Chicago, and 155 in Denver what was the distribution of trucks at the start of that week? Use your matrix form from the previous problem to set up and solve this. We can also use the given information to figure out what happens over multiple weeks. If we want to know what percentage of the trucks that start in Chicago go to Baltimore the first week and Atlanta the second we can use multiplication to determine this. During the first week, 5% of the trucks in Chicago go to Baltimore. (From row 2, column 3.) Then of those trucks, 20% will go to Atlanta in the second week (from row 1, column 2.) Thus (05)(-2) = .01 or 1% of the trucks that start in Chicago will make the trip first to Baltimore, then to Atlanta. 3. How many different ways could a truck start in Atlanta and wind up in Baltimore after two weeks? (Assume cach truck is rented exactly once cach week.) Find the percentage of trucks rented in Atlanta that will follow each of those routes. What percentage of the trucks starting in Atlanta will wind up in Baltimore two weeks later? 1. Calculate 7%, and explain why the calculations for the entry in row 2 column 1 of T means the result matches the number you found in the previous part