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Leo was curious about the distance his guests travel to visit the resort: When registering at the front desk the registrant writes down his/her home address on a gu...

Question

Leo was curious about the distance his guests travel to visit the resort: When registering at the front desk the registrant writes down his/her home address on a guest card. For 2017, guests arrived from the following areas: US Hawaii and Alaska 5000 US West Coast 25000 US Mountain West 22500 US Midwest: 30000 US South: 15000 US East: 20000 International: 1200013. In the space below, draw or paste (Excel) histogram that portrays Alice' $ findings_ Use in increments of 2500 in your bins This

Leo was curious about the distance his guests travel to visit the resort: When registering at the front desk the registrant writes down his/her home address on a guest card. For 2017, guests arrived from the following areas: US Hawaii and Alaska 5000 US West Coast 25000 US Mountain West 22500 US Midwest: 30000 US South: 15000 US East: 20000 International: 12000 13. In the space below, draw or paste (Excel) histogram that portrays Alice' $ findings_ Use in increments of 2500 in your bins This problem is worth 10 points:



Answers

Solve each application.
Three food shelters have monthly food costs $F$ in dollars, number $N$ of people served per month, and monthly charitable receipts $R$ in dollars, as shown in the table.
$$\begin{array}{c|c|c} \hline \begin{array}{c} \text { Food } \\ \text { costs }(F) \end{array} & \begin{array}{c} \text { Number } \\ \text { Served }(N) \end{array} & \begin{array}{c} \text { Charitable } \\ \text { Receipts }(R) \end{array} \\ \hline 1300 & 1800 & 5000 \\ 5300 & 3200 & 12,000 \\ 6500 & 4500 & 13,000 \end{array}$$
(GRAPH NOT COPY)
A. Model these data by using
B. Predict food costs for a shelter that serves 3500 people and receives charitable receipts of $\$ 12,500 .$ Round your answer to the nearest hundred dollars.

Okay, so we're given a function for the cost of supplying bins. Toe p percent of the population on the cost is in dollars. So for a we want to find 15% of the population. So we're just gonna substitute 25,000 times 15 divided by 100 minus 15. 25,000 times 15 is 375,000. Have to divide that by 85. And we got 4411 point. Um, so it's 764 So I'm going to stop it. 76 So $4411 and 76 cents for 15% of the population. Be. We want to do the same thing for 50 now for 25,000 times 50 divided by 100 minus 50. So 25,000 times 50 gets us. Okay, 1,250,000 on divide that by 50. Mhm. It's We get 25,000 dollars for see, we want to do for 90% of the population. So 25,000 times 90 divided by ah, 100 minus 90. Okay, so 25,000 times 90 iss 2,250,000. We want to divide that by 10. Now, just get rid of a zero. So we are left with $225,000. Um, last, but at least they want us to grab this function, using some kind of graphing utility and being sure to choose an appropriate viewing window. You have to explain that. So I'm using does Mouse. So I typed N y equals 25,000 p divided by 100 minus p. And then I just drag my screen toe, find a window that I like. Um, so this is the window that I like. I definitely want to make sure that we have 0 to 100 showing as well as the majority of the curve. If I was to zoom in too much more, I don't really see too much of that curve. I don't see it past 80 uh, to even so I just shrink it so I can see more of it. Okay, but I don't need to go. So what does that look like? My Y values are, um, increasing by 200,000 to see most of this. And I stop just a little bit after ah 100. That 110 or so because I do see a little piece of the graph beyond 100 poking out. So while that might be interesting for us to see graphically, it's not necessarily important for our example, because, uh, they gave to us on an interval from 0 to 100 not including 100. We could see why we're not including 100 because the graph doesn't exist at 100. Um, there's an ass until here. And if we look back at the question, we would end up dividing by 100 so that would have worked out.

So what if the Caro's that in the persons aged household incomes with last 50 5500? Um, just in the equation for that is 500 Cape Waas 4099 90 90 109 100 Eli in quest of 55,000. So care here is 10.2 and add up the overnight rates. We have some big is equals two off p I. It was just this 4.3 percent that's for specially, and that should be the same logic. Just pocket the data again. The same kpk. But now this p K equals Sue. 85,000 Silver K for this part will be 16.2 On begins summed over, We have 26.25% If a posse we're gonna use a calculator fitting The draft, which is a linear function, terms the exponential function. So we have three parameters A, B and C respect anything and plug in the data by using the regression or Wortham that from the ever catch. You later confirmed that advance is equal to three on 2135 some set for three where he's leading function times. The exponential of naked was urban was five times 643 That's it

Hadn't started by organizing this data so that it is in, uh, order from least a greatest. So by looking at the graph, you can see we have one employee that drove zero six that drove 100. So I gotta write 106 times. Three or five, six. 123456 Perfect. Next, we have 10 employees. You drove 200 miles. So going to write. 210 times. Three for five, six, seven, eight, nine, 10. Which my work. 123456789 10. Perfect. All right. Next, we have 300 employees that drive 16 miles. So right. 300 or excusing, You have 16 points that drove 300 miles. Not the other way around. So 12345 six, seven Eat nine. Turn 11 12 13 14 15 16. Okay, let me talk. 123456789 10 11 12 13 14 15 16. Perfect. Next we have 10 employees that drove 400 miles. One to three for five, six, seven eat nine, 23456789 10. Then we have six employees that drove 500 miles. Three or five six. And then, lastly, we have one employee that drove 600 miles. All right, so if we add this up not all these numbers, but the amount of employees. So we had one plus six plus turn, plus 16 plus turn, plus six plus one. And then we divide this by two. We will get the place where we need to look, so we just add all these up real quick. One plus six plus turn plus 16 plus 10 plus six plus one is just going to be 50 then divided by two is just gonna be 25. So in the 25th data point, that is where the median is going to be. So we have 123456789 10 11 12 13 14 15 16 17 18 1922 1 22 23 to 4. 25. So 300 is going to be our median

Have Winona who's going to the zoo and she pays $100 for a lifetime membership. And that makes her have to pay for each time she goes in, she has to pay a dollar. So we want to find what the average cost is in terms of her number of visits. Well she has to pay $100 plus for every visit she makes, she'll pay a dollar. So if it had been $3 we would go three X. But this is how much money she'll spend for X visits. But then we wanted on an average, so we need to take the total cost which is on top divided by the number of visits. So that's her cost on the average. So if she visits 100 times, you know she only visits once, then she's going to have $101 as her average cost. So again, if I were looking at like a little grab of this um When X. Is very small, then her cost is very high because she's paying $100 right at the onset. But if she goes 100 times to visit 100 plus 100 Divided by 100 200, divided by 100. Her average cost is just going to be $2 a visit. So it starts out it's very expensive. But as she keeps going it becomes lower, lower and lower. And so if you want to grab this, I mean, you can do it where you have um, the 10 visits or you could go up by fifties. Say you had if she were, We can't have, we can't have zero because that would be division by zero. So there is an assume towed right here on this function. Oh, and by the way, another way to write this function that would be kind of slick is to think of this as 100 over X plus one. So if we do it that way, we can see that if she goes for 50 visits and if I put a 50 in here, that's going to be $3. If she goes 100 visits, we know that that's $2. If she goes, um, 150 visits, 150 in here, we have 100 Divided by 150 is going to be .6 repeating. So that's going to end up being a dollar, uh, 67. If we go up to 200 visits, we can see if we put 200 in there, it's going to be an average of a dollar 50. And so if we went through and graph this and say this is the average cost on this access. And we had this as uh, say 50. Right. Oops, I'm sorry. Have three right here. And so we know that this is 50 If this is 100 If this is 150 If this is 200, we know that this is at three. This is at Duke, here's at two here, is that a dollar 67 approximately. And this is at 1.5. We can see we are reaching an assam tope and we find out that c as X gets bigger and bigger and bigger. So we would really say the limit of this function as X gets bigger and bigger. We can see that when X gets bigger and bigger, this fraction is going to zero. So we'll end up approaching a dollar, won't ever be there, but it will be very close to a dollar on the average, as X gets larger and larger.


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