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Adinical Irial was conducled to test the effectiveness ol drug uged fox treating insomnta alder subjactls Alter Ireolment wilh Iha drug, sublechs hud @ Mean Wake Im...

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Adinical Irial was conducled to test the effectiveness ol drug uged fox treating insomnta alder subjactls Alter Ireolment wilh Iha drug, sublechs hud @ Mean Wake Ime 01 91 1 mln and stndard deviallon 01 42.9 min_Asgume Ihal the 21 Faaner velves nppan dcntDM ornu Gistribuled population and construc & 9580 conhdence intervat eslmale sandard deviabon crina WanaaImale paqulabeluah bel drug Ireaimte Uoesinate9l neinei Ureatinen pfloclive?Flria Ie conhiderica intetvul uatlnalu min < (Round , w

Adinical Irial was conducled to test the effectiveness ol drug uged fox treating insomnta alder subjactls Alter Ireolment wilh Iha drug, sublechs hud @ Mean Wake Ime 01 91 1 mln and stndard deviallon 01 42.9 min_Asgume Ihal the 21 Faaner velves nppan dcntDM ornu Gistribuled population and construc & 9580 conhdence intervat eslmale sandard deviabon crina WanaaImale paqulabeluah bel drug Ireaimte Uoesinate9l neinei Ureatinen pfloclive? Flria Ie conhiderica intetvul uatlnalu min < (Round , wo decimaiplicu nacded )



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The amounts (in billions of dollars) spent on prescription drugs in the United States from 1991 through 2005 (see figure) can be approximated by the model $$ d(t)=\left\{\begin{array}{ll}{y=0.68 t^{2}-0.3 t+45,} & {1 \leq t \leq 8} \\ {y=16.7 t-45,} & {9 \leq t \leq 15}\end{array}\right. $$ where $t$ represents the year, with $t=1$ corresponding to 1991. (a) Use a graphing utility to graph the function. (b) Find the amounts spent on prescription drugs in 1997 , $2000,$ and 2004 .

All right, We've got a question here that is describing a testing of a new drug on it is tested. Um, at 10 minute intervals, the average concentration CFTR showing the table teas and measured in minutes sees measured in micrograms over milliliters. And we want to use the midpoint rule to determine integral from 0 to 100. See, of T dft. Okay, When we use the midpoint rule, we would take the Siri's eyes equal to one, and and we would have, um, see if t I multiplied by change and teeth. This is the midpoint rule here, and our n here is gonna be equal to 10. Okay, If we look at our table, we could see that we have intervals. I'm sorry. Readings collected at 0 10 2030 minutes. So r n will be 10 as it's changing 10 each time and then are changing t that actually will not be equal to 10. That's what that's what it looks like. The logical answer would be, but we have to understand how the midpoint rule works. We have a set of values from 0 to 100 and we're talking about midpoint bull. Since we have 10 intervals. We're going to need to now split these into five intervals. Would say 0 to 20. You wrote to I'm sorry. 20 to 40. 40 to 60. 60 to 80. And finally 80. 100. Okay, we have to consider these five intervals. When we're talking about midpoint rule, we're essentially splitting the amount of controls in half. Okay? And we're looking for is the midpoint of each of our five intervals. Yeah. Now here we can see that if the midpoint between zero and 20 would be 10, 20 and 40 would be 30 30 and 60 would be 50 70 you know. Okay, so are changing t here. Okay. Actually going to be equal 2 20. Good. We're saying it's changing. Went to okay. That's when we're you wanna make sure we do that correctly when we're solving for the midpoint. Well, okay, now, let's go ahead and bring this Siri's down. We know our and we've already calculated for we said that's gonna be equal to 10. Have I equals one. You have our sea of tea sub by Onda. That will be also these in, but we go ahead first, right out or change of tea won t Now let's go ahead and begin filling in thes values here. So now this is where we're gonna say. All right, We need Thio. Find the we're going to need to collect some of the mid points. Some of the mid points would be C one times t see, one time is 30 50 70 and 90. Okay, so what is this value here? See, when time it's 10, we're gonna add that to 30. Gonna add that you see a 50. Okay, I'm gonna add that to see a 70 and finally, we're gonna add that to see him. Okay. Now, when we go ahead and solve this out Excuse me. Um, you know, see, of 10 is 1.3. Also, one more clarification. Um, I want to write it out properly, So imagine it's gonna be a Siri's mhm, but this equals to this. Hey, this here. Sorry. This whole series here is equal. Okay, Now let's go and start filling in these values. See, when time is 10 is 1.3. Okay. See if 30 is 2.2. See if 50 is 25 plus, see if 70 or just 2.3. Let's see of 90 just 1.6. Okay. And when you add all these up together, it comes out to 9.9. Multiplied by 20 is gonna be equal to 198. We're told that this is in micrograms. Formularies multiplied by time, minutes. And so this will be our final answer here. And we can say that this is our final answer for when we use the midpoint rule to estimate the integral from 0 to 100 for function, See of tea. With respect to time, I hope that clarifies the question. Thank you for watching.

In this question are doing B well cooks in send renters, so I must first completely insane. The difference between windows in in minutos wasn't too, is it? A good and faithful was 0.4 seats pursue their open 78? Was it you? 0.26 wasn't here. 0.3 was to no. 0.17 Was it too? 0.1 and then I think it's who? 0.6 The Marcellus. What a difference. Syrup wind right? Well 0.46 0.178 They're open to six. 0.30 zero Brent 17 0.1 and zero wind 06 ringing from did always to pay your salon. Sorry, it's why to three, you know but 67 eight Descend Bring positive. 7 46 What is to eight was to pull Was to five. Was three. Was it one and negative to then states united. But this is for test age notes. New human does is equal to the animal toes. Did human does what the animals h one the human does Is Morgan the animals? Sure it's it's more. Hey, everyone dish realistically. But then you seven k so find the critical value and is accorded to age, and our for for the one until test is zero. Planned 05 in critical video is 1/4 to 6. It didn't find its estimated. An intell first publicized a. Some offerings. So what is your drink? Some. It's a question. Seven plus six last eight less for that's life. That's three. That's why she's a qualitative dating for then the and Nick. It's here. Drink. So is the quiet too negative, too? Didn't find a much less for this sums the bunch of us for Nicki to, So there's a quiet. Sure it's true, and you consider IDs the negative. Bring some is the lowest. So the treaties is, uh, tested video and comparing it's estimated the crisp elevator. Since our test video, which is to is less there they critical building, which is six. We reject and confident there is enough evidence. Two separatist lee came. Did the human those coast more did Intimate does is enough evidence slip woods being print? They're commandos. Khost. Well, then they any murders And one reason is that some people my notes afford to pay a lot. Sof money. Oh, dear. It's medication. And it's sorry it for night, but a full okay. And Oh, Mom. Uh, yeah, it's medication.

Were asked to answer a question about prescription drugs using functions. He pulled the 3% p of prescriptions filled with generic drugs. The United States from 2000 and four in 2010 can be approximated by a model because a piecewise function, Donald says that PFT is equal to 4.5 70 plus 27.3 40 greater than or equal to four in less than equal to seven and is equal to 3.352 plus 37.6 40 greater than or equal to eight and less than or equal to 10, Where t represents the year with T equals four correspondents 2000 and four Press Jesus model to find a percentage of prescriptions filled with generic drugs. And each year from 2000 and four through 2010 were given a figure Exercise 69 showing the percent of prescriptions filled Well, we're going to treat T as a discrete variable. We're only going to calculate pft energy values of teeth. So first of all, we calculate p of four and I'll actually collect this information in the table so we'll have our year mhm, and we'll have the row pft and then a right percentage below that. Okay, we have four rows now for the columns. We have our years 2000 and four through 2010. I'll abbreviate these with go for Oh, five. Who's six seven? The weight nine and 10 and the corresponding times t Well, these are t those four, 56789 and 10. Then we use our formula to calculate pft for each by U T. So, for example, for t equals four you plug in because four is greater than or equal to four and less than or equal to seven. We plug teeth was four into the first formula. So we get 4.57 times four plus 27.3. This simplifies to 45.58 Likewise, five is greater than or equal to four in less than equal to seven. We plug in teeth was five to be first formula. The five is equal to 50.15 Likewise, six is greater than or equal to four less than seven plug into the first formula. He gets 54.72 seven is greater than or equal four less than equal to seven. Plug it into the first formula you get 59.29 eight is greater than or equal to eight and less than equal to 10. We called this into the second formula, and we get 64.4 nine is also greater than or equal to eight and less than or equal to 10. Plug this. In the second formula, we get 67.75 and 10 is greater than or equal to eight and less than or equal to 10. Put this into his second formula. We get 71.1. Finally, I convert these values of peak percentages, so let me get 45.58% 50.15% 54.72% 59.29 percent, 64.4% 67.75% and 71.1 percent

This question. Not doing the wilcox in sand wrong. Just so from us best completes the table difference between you is and Ghana. Was it here? One win. Tasteful. Close to 1.2. Was it too? One go into. Was it soon? 1779 Was it too? 1.96? Was it too? 1.67? Was it you? Zero point then one. Was it here? 1 28 8 Then naked Sue 0.26 Nick and Soup 0.2 in there, uh, being more stressful difference. It's one win eight school 1.2 one playing to 1.7 night, 1.96 1.67 0.91 1.88 There are went to six and zero Oakland zero to it didn't rain from the lowest video. It's where three position four in five of the same. So it's folk went by no point, but then six seven a nine. The ST Ring presences age wasn't Your Hotpoint fight was to focus five, cause you serve in 1 to 10. Close to six 13 Certain positive nine negative to negative one in States. The novel hypothesis is, what a test h nuts Your prize is off. Prescription drugs in the United States thinks are equal to the prices in Canada. The prices Oh Shane in the okay, quote the prices in and hor it drugs. So in Canada, a chica fronts. Sorry, so you cannot ah, Daschle artistically. But in used him K friendly, crisp, elevated and is the coach of 10. I don't finds a quote. Zero point you don't find Let's go to video. It's little there, then president to find the intestine radio and it's true complicity. Some offerings close. It's too. Bring some is a quote soon AIDS does four point by that's what right does. Seven. Thus sin. That's six Last three. Yes, nine is a question 52 Then the nay kids who bring some isn't quote. Teoh. Make it 22 us. One. His quotes to tickets of three been a much less cool, naked, simpering. Some history since the my address for negative Bring Sung is the lowest. It is a lot ist baby within calm bay. It tested, baited with the Chris called Vega. Since the test, villages three is less than Chris Carter villages live in We're E J and contro Dead's. There is enough evidence which supports the claim that it drugs sort in Canada that you there is enough. It didn't thanks. So in Karada a cheap


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