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A big concert was held at the Bowl. Men and women had to go through separate lines to get into the concert (the women had to have their purses checked). Once everyo...

Question

A big concert was held at the Bowl. Men and women had to go through separate lines to get into the concert (the women had to have their purses checked). Once everyone was inside, total attendance at the concert had to be recorded. The turnstile counters on the female entrance showed a total count of 1542 females, but the turnstile counters on the male entrance were broken and there was no exact record of how many males attended. A sample taken from the 200 seats in Section A showed 121 females a

A big concert was held at the Bowl. Men and women had to go through separate lines to get into the concert (the women had to have their purses checked). Once everyone was inside, total attendance at the concert had to be recorded. The turnstile counters on the female entrance showed a total count of 1542 females, but the turnstile counters on the male entrance were broken and there was no exact record of how many males attended. A sample taken from the 200 seats in Section A showed 121 females and 79 males in that section. Using the numbers from Section A, estimate the total attendance at the concert. (Hint: The proportion of females at the concert should be roughly the same as the proportion of females in Section A.)



Answers

Gender Ratio The number of males per 100 females, age 65
or over, in the United States for some recent years is shown in
the following table. Source: U.S. Census Bureau.
(a) Plot the data, letting $t$ be the years since 1900 .
(b) Would a linear or quadratic function best model these
data? Explain.
(c) If your graphing calculator has a quadratic regression
feature, tind the quadratic function that best fits the data.
Graph this function on the same calculator window as the
data.
(d) Choose the lowest point in the table above as the vertex
and $(110,77.0)$ as a second point to find a quadratic func-
tion detined by $f(t)=a(t-h)^{2}+k$ that models the
data.
(e) Graph the function from part (d) on the same calculator
window as the data and function from part (c). Do the
graphs of the two functions differ by much?
(f) Predict the number of males per 100 females in 2004 using
the two functions from parts (c) and (d), and compare with
the actual figure of $71.7 .$

Everyone. Today we're solving problem number 42 from chapter to the textbook. Now, this is involved a frequency Sister Grams at describing distributions on dhe describing more about distributions, uh, driving shape of distractions than other parts, Mr. So in part, they were asked to create a frequency table. Based off numbers have been for S A T scores around the rage of 0 2400 and looking in a sample of 30 different scores and last defined frequencies based off of every interval of 200. So I start from 8 to 999 may go all the way up to the interest of 2002 to 1. Um so let's get started. I see one score my minimum value and once Forman maximum value and those two ranges. And I know that this tour is 2030 before is the deer start of six by five, which is six times five. And that's 30 um, out in between from 1002 11 99 you need. If it's worse then between 1239 986 between 1459 on different wars between 1617 unite seven different spores. I have to defense force between 1800. What? So that is how a book Freaking t now moving on to our history And we're going to basically wrap this data on our history. And where have you been seeing my Y axis and square age on my expense. By the way, just seen on my X axis. I've in decimals and I were at the bottom here it's timeto 100. And the reason I ask is that just didn't happen up space. But hope you're on your own sheet. You do on eight. Tonight. Nine corresponds to this one. Just you. So from 8 to 9.9 again, I have a frequency of one and never on history. And you want all of your bars to be the same Wait and the heights to represent the frequency vested in right. Um then from 10 to 11.9, I know how that's it. Because you want proximately the same way today. That's still see big time. That's better. You're gonna shoot at all in plastics. Oh, just breathe. No, there you have it. But between 1000 and 1103 then between 1200 of Virgin Mary Knight. Just this part of you six and six Y y axis that. See that? Obviously, this is much easier. Then I have my figure. Well, all we have time. A straight line again. I'm struggling with it with making people size wits for open guys. What? This is she that in? As best as you can. Then I have if we conceive seven between 1600. Did I do? Wow. I started off so good with my shaving and then just go. Um then finally, between 1819. 99 guys got a lot of yourself. Sometimes I have to I haven t too. All right. And finally, I'm pretty full. All right, so now, looking at this, we were asked to describe the shape of the distribution of dress drawn on our history, and hopefully guys can see looking at this, this is pretty symmetrical because this top bar right here, I'm in the middle has the highest value you get. So you have a one on both and and it just looks pretty symmetrical. It looks like very evening. Um, look, if I were to split this graph in half, I would have approximate same number on both sides. So, um, we don't say like it's approximately same luxury. Well, I mean, you could, but the more proper terminology in statistics is going to be rightfully so much so I want to use that word. And it's not just a metric adjective symmetrical Rafi go again. That's describing the sheet are the things we want to mention our center, the centre's office Legally, comedians obviously gonna be strange. Why not out liars? Which unity party? Because it asks us to describe other parts of our discretion So we could say, um, in terms of out lies, there are no outlines. There's nothing really outlandish in this you'd really want, right? No apparent out liars, no, again. The median range between 4999. Remember, the median is where the 50th percentile. But you split your data points in half on the least to the greatest. Actually, you could find the actual one. I don't have the numbers, and but oh, every TV numbers you find. So you know that there's fortune on both ends and then you're left with 15 and 16 numbers, so you would add the 15 city school began from descending to say something that 15 scoring at 16 school you advent by Martine that would get your actually rockets. It means for range is gonna be between 1450. And your immediate square itself will fall. Yeah, to find that's for what you're going to do is find the 15th and 16th turn interview that reinforce first, organize it from these two greatest value by 15 16 numbers in that Easter greeting status. At that just organized. I have those two numbers that on. And then finally, you know that most scores appear in what range? Eyes off you notice from our history and from the frequency. The largest weapon T and the tallest spire in history has the range bones starting at we sport a 1400 going all the way to 50 because they asked us to use that I'm with the 200. Sign that danger and there you have it. If you guys injured as well, please, like one next to it. I hope you'll have the next day. Thank you for watching

So for this one, we're just wanting to find a system of equations. We don't even have to do any actual math here. We just have to set up the equations. So let's see. So it says that ticket to sit on the bench are seventy five dollars, So then we can call it seventy five seventy five b and then for the lawn it's going to be forty dollars. That's going to be forty. So then we're gonna This is the equation that's going to represent the amount of money, and we know that the total amount of money is going to be nineteen thousand two hundred and fifty. And just as a reminder, we know that we can set it up this way because when doing systems the equations, you want to separate the two situations. In this case, it's the money and the tickets, and then we want to have in a form where it's something. Plus something is equal to the total. So for the total number of tickets, they told told us that there were three hundred fifty total and then that some of that is going to be. However, many tickets for the bunch plus, however, many tickets for the lawn Okay, so then that equation system of equations is maybe d. So that's our current cancer. So again, we don't even have to solve it. We just have to set it up correctly, using this format and by separating the two different things that we have.

Charges on Ah, ticket, son. Funnest it! I'm gonna be in the axe. Just the ticket, son for a journal, Billy. Why? And for the adorable. Is that so? We hand off just a question from his farm. X y does is that we go to 11 75. And now we have the ah, 28. And then we have no amount of, uh uh during the thanks. Plus, Jen, did you pawn fi? Well, all right. On August 19 eyes that Miko gente a Townsend. When 1215 Um, put a question here we have, uh, Andre Benson tries a money. A doe is a train ticket. So we have, uh we have the centrist, but thou will be doubled the ticket, so I don't have it means that it could to Ah, you are. So we have the system in question. One Jew and three. So it was served assistant question here. We should get the answer. Equal Jew. Ah, the axe will echo Thio. The student will be 500 ticket for a student And why it will be for the Children. And do you identify and that we're equal? You know, father, and that's a sedition

Okay, let axe equal the number of student tickets. What? Why? Equals the number of children tickets and then left Zi, pull the number of adult tickets. Okay, we know that all the tickets together is experts y policy. And this is 1175 because they saw 1025 tickets total now substituting and the prices they've given. As you can see, $20 for student tickets substitute. In that information, you get 20 acts plus 22.5. Why? Plus 29 equals Giving Z equals two. Why? Okay, it's gonna be important for later. No, we know that we have ex post wide plus two y equals +1175 betweens expose three. Why equals 11 75. This means that acts equals 11 75 minus three. What now? Substitute in two. The original equation 20. 20 acts and you should end up with if we know the axe is 1025 Minuses. Three. Why would substitute end to the original equation? As the as that is, the value acts this should give us why equals 225. Okay, now we have one variable. You have two more variables to do. You know that Z equals to why? I underline that earlier. The two times 1 25 is going to be 4 50 So for 50 equals e. Okay, now solving for X X equals 1175 minus three. Why? But now we have the value of y so he can simply plug in and they get X equals 500. So the answer is 500 student, 225 children and then 450 adult tickets.


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