m-budget-rent-a-car-in-wichita-kansas-has-a-fleet-of-about-500-cars-at-three-locations-a-car-rented-

Question

[M] Budget® Rent A Car in Wichita, Kansas, has a fleet of about 500 cars, at three locations. A car rented at one location may be returned to any of the three locations. The various fractions of cars returned to the three locations are shown in the matrix below. Suppose that on Monday there are 295 cars at the airport (or rented from there), 55 cars at the east side office, and 150 cars at the west side office. What will be the approximate distribution of cars on Wednesday?
$\left[\begin{array}{ccc}{.97} & {.05} & {.10} \ {.00} & {.90} & {.05} \ {.03} & {.05} & {.85}\end{array}ight]$

Jack Chen · Accepted Answer

because so in this problem we have the initial state X zero because to ah, three by one column metrics which represent the amount off the car in each location. And we also have a transition. Metrics am on the middle. This transition metrics is given, and we are looking for eggs to because x zero is amount off the state, um, Monday and we are looking for the state, the state on Wednesday. So the statement Wednesday Muse, a traditional metrics tons the state on Tuesday and the state on Tuesday because the tradition matrix comes the state on Monday. So we have m squared times, um, x zero, the initial state A calculator he caused to on this result, that means after two days, the airport has, um, 312 different cars in the for the eastern location. He has 50 it costs and the for the Western occasion. He has won 30 because so this is

Sid Wan · Answer

can number seventy four to cost to rent a small South Korea&#x27;s thirty line orders per day or fraction off a day is the car&#x27;s picked up beach cargo and dropped off in San Luis. There is a fixed twenty seven drop off charge. Let&#x27;s see. Axe represents the cost ofthe renting the car for X days. Thinking from Scotland, Slanderous finds a following. First, we just need to find the function ofthe sea yaks. Those axes like Haman days. You rent the car. See X is a cost in total. So it&#x27;s thirty nine dollars per day. So thirty ly ex Dave plus a drop off fee toe in this other guy that&#x27;s here and say We want to find sea off two over certain. So you just plug into a nursery. So thirty Certainly I do want us race certain, But Battle twenty six, Class twenty seven, which is fifty three and B. We want Foreign Sea off eight over, and I so still your plan in number. Certainly I might apply. You are a blind man, a twenty seven, which equals some fraction of anyone so warm. Eighty five over three and see. See, Juan, you&#x27;ve got to stop lagging one twenty three like last twenty seven, which is sixty six. Andy. We got one seal, one over one and three over football. It was just thirty line, but black three. Over. I guess it&#x27;s just seven over full. Plus twenty seven and thirty line. What did bless other? Yeah, two, seventy three or four plus his guys. Okay, so three eighty you ours. And he find the cost of rangers car for four point seven days. Who clocked in just four points. All right. Okay. Guys like I do thirty line, but five, four point seven equals glass. Twenty seven, two hundred and ten point three in next one. Graft, like was C X Focus. It&#x27;s so it was the intercept twenty seven. Look, you can&#x27;t You&#x27;re no beans from zero to infinity, I guess. And slow is twenty live. So fly twenty seven. You can put a one point one is Pacific&#x27;s and is here function. Yes, it is a function explain because every ex corresponds to one well value. You see a linear function? Yes, because clearly is just once reply. What is independent, Maribel? Independent horrible acts. What is a dip in the world? Boys? See extra cost defendant. Okay, Come

Tiffany Tran · Answer

So are a rental company is charging $31.95 for one day. So that&#x27;s like a fixed price. And any mile after that, it&#x27;s gonna be 89 cents. So you want Teoh so eating my sense is gonna be your slope, and then your wine, your stuff is going to be $31 in 95 cents because this is always changing because it could be one mile to mile. So in this case, we want to figure out how much will it cost if you&#x27;re going to drive 110 miles. So what you&#x27;re gonna do is do 89 sons times 110 miles, then plus 31 95. When you do the math, it&#x27;s going to cost Utah 129 and 85 cents. Now, let&#x27;s say you&#x27;re going to travel a bit further. Okay, so you&#x27;re going to plug and 230 now. So you&#x27;re in travel 230 miles, remember? Is so gonna be $31.95 a day. So when you multiply this owl and simplify it, it will cost $236.65

Janet Meinke · Answer

this problem deals with a number of people in each car entering the freeway at rush hour. So it&#x27;s the number of people in a car. If we think about the graph of that, Um, if it&#x27;s at rush hour, there&#x27;s probably like a lot of people. Um, there&#x27;s only one person, the car. There&#x27;s probably a little less that there&#x27;s two people in a car, three people in a car and then four people in a car, something like that. So some kind of curve And we know that the mean is equal to 1.5 and that the standard deviation, which is this distance right here, the standard deviation is equal to 0.75 Part of a asked me, could this distribution be normal? And the answer is no, it can&#x27;t be normal. And the problem is that the count of this population data takes on a whole number. Values they&#x27;re not fractions or decimals in a normal distribution can take on any real number. Okay, sir. Part B says that the capacity is 700 cars per hour, the capacity of the intersection. And so that tells me that my sample size is actually gonna be 700 and I&#x27;m looking for the probability That&#x27;s 700 cars. We&#x27;ll carry more than 1075 people. All right, So if I&#x27;m looking for 700 cars will carry more than 1075 people, I have to figure out exactly per car. How much that ISS. So if there&#x27;s 1075 people and I divide that by 700 cars, I&#x27;m gonna come up with 1.53 57 passengers per car. So I&#x27;m really looking for the probability that my sample mean is going to be greater than or equal to 1.5357 So if I draw a picture of my sampling distribution, I know the mean is going to equal to the mean of the population. So that&#x27;s gonna be 1.5. I need to first figure out the standard deviation. The sooner deviation is the populations danger deviation divided by the square root of the sample size. That&#x27;s going to be 0.75 divided by the square root of 700. And that&#x27;s gonna give me 0.283 So I have a standard deviation one student deviation on each side. This distance right here, IHS Standard deviation, Uh, 0.283 So I&#x27;m looking for the probability of 1.5357 So that&#x27;s 1.5. So that&#x27;s gonna be past this. So that&#x27;s gonna be 1.53 57 So I need to get the standard deviation for that similar fourth. The score so easy is equal to the number I&#x27;m looking for 1.5357 minus the mean just 1.5 divided by the standard deviation, which is 0.2 a three. That&#x27;s going to be 0.357 over 0.283 just going to be 1.26 So I&#x27;m looking for the probability when C is greater than or equal to 1.26 So that&#x27;s going. When I looked that up in my chart, that&#x27;s going to give me. I&#x27;m looking for this part of the graph, but when I look it up in my chart is going to give me this part of the graph. So remember the complete the total area under the distribution curve is one, so it&#x27;s gonna be one minus the probability that Z is less or equal to 1.26 So if I look up the probability of less than 1.26 see, here&#x27;s 1.26 point 896 17 I get one minus 0.89617 and that&#x27;s going to equal to 0.1 zero 383 So the probability that my sample mean is greater than or equal to 1.5357 IHS 0.10383 So that means there&#x27;s a 10% chance 700 cards. We&#x27;ll carry more than 1074 passengers.

Christine Anacker · Answer

right. So you&#x27;ve got the following data for two different locations of a dealership. They wanted to do two by three matrix ease for each month with sales. So that means we&#x27;re gonna go with two rows and three columns. So we&#x27;ll say our January matrix is equal to 400 to 50. 50 and 4 50 200 1 40 And our February matrix is equal to 3 50 130 on 3 50 300 100. That would be part a. Now they want us to do matrix addition in order to find the total sales. So for B were using matrix addition. So 400 plus 3 50 2 50 plus 100 50 plus 30 for 50 plus 3 50 200 plus 300 and 1 40 plus 10. That gives us so 50 3 50 me, um 800 500 2 40 for CNY to rid of matrix of three by one matrix about the cost. So it&#x27;s 100 for the small 150 for the medium and 200 for the big 100 are 50 and 200 would be my three by one matrix and then for parts de they want us to multiply our matrixes from parts C and part B to find our total cost made. Take that 7 50 3 50 80 800 500 2 40 Ever involved by it by 100 1 52 100 So 7 50 times. 100 plus 3 50 times 1 50 plus 80 times 200 uh, 800 times 100 500 times 1 50 and to 40 times 200. So what this is going to give us is how much, buddy? In total, they made per months at both locations. ST 50 times 1 50 plus 80 times, 200. So in January, they made a total of 143,500 and in February they made a total, um, 923,000. So they&#x27;re Rio

Tiffany Tran · Answer

So we know he receives 5% of the problem profit of any sale. So 5% 5% percent is always out of 100. So five over 100 which is reduced onto 1/20. So he get 1/20 of any sales. So we don&#x27;t know how many sales there are. So we&#x27;re gonna have s is equal to 120 X and then we know that it&#x27;s going to be a fixed him now per week, so he&#x27;ll get $375 no matter if he sells.

Problem

$[\mathbf{M}]$ Let $M$ and $\mathbf{x}_{0}$ be as…

Problem 12 Easy Difficulty

Answer

312 cars the airport, 58 cars are the east side office, and 130 cars at the west side office

Related Courses

Linear Algebra and Its Applications

Related Topics

Discussion

Top Algebra Educators

Alayna H.

Caleb E.

Maria G.

Michael J.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Alayna H.

Caleb E.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

312 cars the airport, 58 cars are the east side office, and 130 cars at the west side office

Linear Algebra and Its Applications

Alayna H.

Caleb E.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Alayna H.

Caleb E.

Maria G.

Michael J.

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications