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The numberspcople playing tennis (In millions) thc United States from 2OO0 through 2007 approxlmated by the function T(t) 0.02330* 0.3408t3 55602 .860 22.8 U.S_ pop...

Question

The numberspcople playing tennis (In millions) thc United States from 2OO0 through 2007 approxlmated by the function T(t) 0.02330* 0.3408t3 55602 .860 22.8 U.S_ population (in millions) from 2000 through 2007 be approximated function P(t) 78t 282_ xhere represents the year; with T) (a) Find and interpret h(t) P(t)corresponding2000_h(t)h(t) represents the number h(t) represents thc numberpeople (in millions) playing tennisthe United States comparedthe numberpeople (in millions) the United States_

The numbers pcople playing tennis (In millions) thc United States from 2OO0 through 2007 approxlmated by the function T(t) 0.02330* 0.3408t3 55602 .860 22.8 U.S_ population (in millions) from 2000 through 2007 be approximated function P(t) 78t 282_ xhere represents the year; with T) (a) Find and interpret h(t) P(t) corresponding 2000_ h(t) h(t) represents the number h(t) represents thc number people (in millions) playing tennis the United States compared the number people (in millions) the United States_ pcople (in millions) the Unitcd States comparcd numbcr pcoplc (in millions) playing tennis thc United Statcs_ (b) Evaluate the functlon part (a) for h(0) million h(3) million h(6) milllon (Round your answers to four decImae places:)



Answers

The numbers of people playing tennis $T$ (in millions) in the United States from 2000 through 2007 can be approximated by the function $T(t)=0.0233 t^{4}-0.3408 t^{3}+1.556 t^{2}-1.86 t+22.8$ and the U.S. population $P$ (in millions) from 2000 through 2007 can be approximated by the function $P(t)=2.78 t+282.5,$ where $t$ represents the year, with $t=0$ corresponding to $2000 .$ (a) Find and interpret $h(t)=\frac{T(t)}{P(t)}$. (b) Evaluate the function in part (a) for $t=0,3,$ and 6 .

All right. So in this problem, TFT represents the number of tennis players in millions in the United States during a certain time period. And P A T equals a population in the United States during that time period. And so what we want to do for part a is fine age of T, which is the ratio of T A T overpay of tea. So we would just take one equation tennis player equation, and then we would divide it by the other one, the population. And we're not going to go through any attempt to simplify that. We're just going to leave it like that. So what does that mean? That would be the ratio, uh, tennis players to the population that would tell us basically as a decimal, how many people play tennis, and if we wanted to convert it to a percent by multiplying it by 100 we would have the percent of the population at plays tennis for Part B. We're going to evaluate this function for values of T 03 and six, so h of zero age of three and age of six. And of course you're just going to want to use your calculator for this. I used to the table feature on my calculator. I talked to my functions in and use the table feature and what I get is 0.807 and then point. You're a way to to and then 0.810 So if we wanted to think of it as a percent, we've got around 8% of the population playing tennis during this time period.

Uh huh. We have this function TF X Which models the number of people who have played tennis At least once in a year. And uh X represents a year since 2006. So we estimate the number of people who play tennis at least once In 2007. And then we went to estimate The participation in tennis in 2014. Okay, so for 2007 X would equal one, And in 2014 X would equal eight. So let's see, starting with the one. Mhm. This is first will be 25.5 and its million people. And then for 2014 We're going to change our explain to an eight. Mhm. And there will be 42 4 million people.

This question now you just It says if one off the test subjects is randomly selected, find the probability that the subject did not use marijuana. Find the probability of the subject that he did not use marijuana. These are the total subjects who did not actually use marijuana. These are truly negative. These are the ones who are negative and who have also tested negative. But these are the ones who are negative but who have falsely been tested positive. So 24 plus 1 54 is 1 78 1 78 by 300. This is the probability that we want. And do we think the result affect the general population rate off subjects who do not use marijuana? I think the result is somewhat low for people who do not use marijuana. By the way, this value turns out to be 0.59 something zero point Faith Night. And this is my answer

Okay. This problem, uh, talks about younger people that said they had used cannabis or marijuana. Um, so it's I'm seeing my data's over here and spread she And when you stop lit to create my graph, and then we'll write up a few sentences. Teoh, describe the distribution, um, specifics here. So the European survey used alcohol and other drugs, Actually, not just marijuana. Um, that was a 60 year olds. So, like a photograph, you gotta have a next title. You Toronto by hand. That would be like the title were wannabe access styles. Um, family member Trump's gonna paste this in here. You know what's nice about stop? Let is. There's a lot of different types of graphs you're gonna look at so again always to fall back to the dot plot because it kind of showed the most information a little bit mortar. It's a little bit more to create if you're doing it by hand. But if you're trying to analyze statistics, uh, it's very useful. And with applications, it's not so bad. So I'm showing you the other graphs there. There's a history ram, and you could also see what a box plot or stem that looks like so again for the purposes of describing things you just keep You look quickly visual of the different graphs. Um, this is good for spread and where the middle is. But I think I have to go back to my dot plot Your of the most information. So frank is an apple. It Mosley get the most information so we can draw it up nicely here. So it let's a little snapshot of our statistics me a little bit bigger. And then it's a good statistician are few sentences about this. So our summary stats shows a lot of, ah, the information we need to have. Um, let's look at this. And we're gonna say I used socks of the acronym. So I always think if you receive this written down in my class, stock stands for shape, that layers center and spread. Okay, so the shape of this graph, it's pretty uniformly distributed. Okay, so since it goes all the way along, there's the shape is uniformly distributed. There's no clear middle to another kind of spread out me o stands for out layers. There's no any clear out layers here, so, um, I'm not gonna say anything about it. My writing. But just so you know what this stands for. So the shape of the graph takes about some entrance being symmetric or skew. Look, this is all kind of spread out. So I think for uniformly distributed, it really describes that the center of the graph on the center is at about, uh, here. Let's look down our summary statistics since we have them with the medians about 18 which is about where it hit. Um, so we'll say the media is 18. So most countries, the median 18 16 year olds, reported they had used marijuana. And you always want to make a comment after center. Some comment about spread on the status pretty spread out. So a lot of temple you the inter quartile range? Um, let's just say the data. I'm going to use the overall range since this is the spread out. So it's like for all the countries it's gonna use the overall range that ranges from way down here from three all the way up to looks like 34 depending which country we're talking about, right? So that gives you good information. You can saw a little preview of different graphs. The DOT plot gives you more specific, so I use that one and you want to comment on the shape in the center and spread. And there's any unusual or out liars you seeing. You want to write about that when you're commenting on statistics crafts.


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