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Ihe year experiments that the lab conducts Prices for 1O0 rals follow the Alab crders 100 rats: wock for each of the 52 woaks following distribulion: Prica 510,0051...

Question

Ihe year experiments that the lab conducts Prices for 1O0 rals follow the Alab crders 100 rats: wock for each of the 52 woaks following distribulion: Prica 510,00512 50$1500 Probabllity: 0.35 0,40 0.25 aumino Lhls dstributlon does not change? How much should the lab budget for next yoar $ ral Orders5850 8520 57805637

Ihe year experiments that the lab conducts Prices for 1O0 rals follow the Alab crders 100 rats: wock for each of the 52 woaks following distribulion: Prica 510,00512 50$1500 Probabllity: 0.35 0,40 0.25 aumino Lhls dstributlon does not change? How much should the lab budget for next yoar $ ral Orders 5850 8520 5780 5637



Answers

Parvez, a pharmacology student, has allocated $\$ 120$ per month to spend on paperback novels and hamburgers at his favorite burger joint. Novels cost $\$ 8$ each; hamburgers cost $\$ 6$ each. Draw his budget line. a. Draw and label a second budget line that shows what happens when the price of a hamburger rises to $\$ 10 .$ b. Draw and label a third budget line that shows what happens when the price of a hamburger rises to $\$ 10$ and Parvez's income rises to $\$ 240 .$

Given that a researcher performs an experiment to test the hypothesis that involves there the nutrients and I see in regional two types of nutrients that nice seed. And they didn't know. See if it's one group off level A ticket rates at the daily diet or precisely 30 units off Nicene so totally fit 30 units off niacin and 22,000 units off they didn't know and no see you this two types of pellets. So for this, I am making a table here. So to Elise, now this is food and food. Be so food a content 0.2 unit 0.12 units off Nicene and 100 units off regional and bi contents 0.2 units off Nancy and 50 units off. Ready? No. So now we could make, uh, he had a question that they're not going to want to live. It hits should you don't Excellent drama, April. Why grandma? Before so zero point went toe Marty plan to text so and they're open toe multiplied with y equals toe that in 1932 and then 100 unit multiplied with checks and then 50 unit, but applauded by equals toe to toe Triple Little. So now these are the two equations. Now, this one day can be considered. So here one dealer gets canceled and now we're left with this. So multiply disturbed with 25 then subtract. So by subjecting this we get, this time gets canceled. This is minus minus and minus ter. And now this time gets canceled and we left with this will be here today. This is a tree. And now this one minus seven X equals two this one way total minus $14 0 So X equals two, 200 grams or anything unit. And then why equals toe floating? The value we get? Why equals toe 40 grams off be This regard equals to that is 200 gram and because toe 14 grams

We're gonna press enter, um, And then we get the three outputs, right? We get that f is we're gonna have equal to end somewhere numbers, and then we get P is equal to about 0.53 and it keeps going. And then the fact that because they would get the degrees of freedom DF, um, and and so on. So, um, then for part A. Um Okay, well, the null hypothesis that the three, um mean commuting manages are the same is given as well. That's gonna be our null hypothesis. H sub zero is gonna be, um, you won being equal to again. This is not a youth today, Mu. This is Mu Mu One is equal to, um, you two, which is equal to, um you three. Okay. And then our our our our alternative hypothesis for part beat will be Well, at least two of the means are different. So we say that the alternative the alternative hypothesis, uh, will be that at least a T least any two of the means. Oh, crap. At least any two of the means are different. Okay, um then for C Well, um, the degree of freedom in the numerator is too. So the degree of freedom degree of freedom in the numerator mhm is to, um, and the degree of freedom and the degree of freedom in the denominator we see is 12. Um, then we go on to part deep. So indeed, the f distribution here is used. We see again, and I calculated we see that the F distribution is used for the test of the three different means. So the F distribution AB distribution here is used, um, and then for e b test statistic. So the test statistic statistic, um, is given as 0.6 685 and the P value is 0.53 So we have for F three p value. Mm. Um, for the test is I'm still 0.53 Yeah. Okay. And then, um, Fergie while we get the graph off the distribution. So Fergie here, our our graph is gonna look, um, something like this we have. This is our It's your density. This is our ex. Um, So we come out from see this here zero to the 0.6686 which is here, and a graph is gonna look something like this. We then become a satanic here. And, um so it's Well, maybe this actually should be moved a little bit. Well, in the just the 0.6686 maybe we're right about that. Save it about here, actually. Okay. And then way Care about this area here? Um, And, um, for H, the level of significance here is, well, 0.10 So we say that I'm still in red here way. Say that the level of significance Alfa is 0.1. No, um, and our decision here will be that are novel hypothesis null hypothesis. Well, then well will be accepted. So our decision, um, is that the null hypothesis? Cool. Um, will be accepted. Okay. And what's the reason for this decision? Well, the reason would be that the p value is 0.53 which is greater than our, um, level of significance. So the reason for decision our reason is that the p value, um, which is 0.53 is greater than greater than Alfa, right. Greater than Alfa, which is our 0.130 yeah. And we can then say that the 34 The three formulas produce the same mean weight length. So we can say that, um, the three formulas produce the same mean wait.

Yeah. Alright, problem 37. So when we bought this on our calculator get this graph per day. Barbie, if at seven is 15.36 So the rat weighs 15 g parties and graphic calculator We solve for T by saying the function you go to 27 we got t equals 12.380 So it takes about 12 days to reach 27 g party When we wanna we wanna plot the derivative the graphing calculator It's gonna look like this. So if prime of tea is to go to a 0.48 plus 0.34 t on the 0.144 t squared if prime of four is you go toe 1.6096 So that's about 1.69 grams per day Party set this to go to and sell 40 Using graphic calculator, we got t equals 5.990 or 17.6207 So the ride is gaining weight at a rate of two grants part a ah t equals six days or T equals 17.6 days. Alright then part of it. We can see that the max value of F prime of tea occurs. AT T equals 11.8 and then to confirm this use, the second derivative is 0.34 minus zero point 0288 ex set the secret zero and we get X is to go to 11.8056 So the rats growing at the fastest rate at 11.8 days.

Hi. My name is Avi in here to solve problems 67 from Chapter 10. Systems of equations and inequalities of section One Systems of Lanier equations in two variables. So let's quickly read the questionnaire here. Nutrition. A researcher forms experiment to test a hypothesis that involves the nutrients nice and and retinal. She feeds one group of laboratory rats a daily diet precise of precisely 32 units and nice and 22,000 units of retinal was quickly Note that down. So 32 units of nice and and 22,000 units of Rhett Retinal Okay, she uses two types of commercial pellet boots. Food A contains 0.12 unit of nice and 100 units of retinal per gram. Food be contains point to unit of lice in and 50 units of retinal program. How many grams of each food is she? Does she feed this group of rats each day? So to note this down food, eh? Contains point 0.12 units and nice and and 100 units of retinal. Who would be contains 0.2 units of nice and and 50 minutes. Oh, right. No. And this is all in one gram. of each of the foods. And the question is, how many grams of each food basically, uh, does she feed the rats to get 32 units of nice And and I'm sorry, 22,000 units of retinal. So to solve this first, let's give each of them variables. So it's give food a nice and just get food, eh? X so X will count the number of grams food a used So number of gramps food, eh? And then we'll have why be the number of grams for food? Be stuff. Looking at this, we can already set up a system of equations based on the information given to us. So since we know that there is point 12 units of nice and in one gram food, eh, we can go ahead and set that equal to 0.12 X because that's the number of grams, actually number of grams of food aid. So we can add that 2.12 side point 20. Why, which is the number of grams of food be and we can set that all equal to 32 32 units of nice and basically what this means is this 0.12 comes from the food A up here there are points, 12 units of nice and in one gram. If we use the X value here, which is the multiplier of how many grams Ah, food A. There are going to be 32 units of Nice and that this researcher gives to the rats and the same thing for food be There are 320.20 units of nice and and why is the number of Grant Conversely, we can set up another set of equations using retinal. So since we know that there is one 100 units of retinal in food a in one gram, we can go ahead and add that to the 50 units of retinal in one gram of food. Be and we know that we add these together we should reach 22 1000 units of retinal in total. No, What we're trying to do here is self for X and y to find out how many grams of each food is a researcher using To do this, we can do this substitution method to send these two equations. So we confined axe and why? To do that, I'm gonna go ahead and select this equation and plug it in Thio here, do that. We have to solve for one of the variables. First, I'll pick. Why? So let me quickly create a new page on right the equations. One more time. So point well x plus point 20 Why should equal 32 units of Nice And? And the other equation was 100 units of retinal. Ah, food. Eh, Plus 50 units of retinal from food be should equal 22 1000 units of retinal in total. It's no. I said we were gonna do the substitution method, and I said I was going to like this equation to plug into here. So first we have to solve for variable. So 100 bucks, Because 50 why equals 22,000. I'm gonna go ahead and subtract 100 X on both sides to isolate one term. So now we have 50. Why? Because 22 1000 minus 100 X. Now I want Oh, I wantto I sleep Why, right? So I don't know, get rid of anything I have on the other side. So owner divide both sides by 50. So we have why by itself. So then we can get why equals 22,000. Divided by 50 is 440 and ah, 100 divided by 50 is too. So we're left with minus two X. Now we have an equation for why, right? Why it goes 440 minus two X. Now, you just plug this back in to this equation up here, up here. Sorry to solve for X. So I'm gonna go ahead and do that right now. We'll create a new page. So I have more space to work with the equation for Why was why equals 400 40 minus two x. And the other equation we had was 0.12 x waas point to your Why was 32. Now I'm gonna take this why? And plug it in for this. Why? Down here we are substituting this. Why? With 420 minus two x. Since we know why equals that. So you got a 0.12 ax plus point 20. Our substituting the Y. You're gonna go ahead and replace the Y with the known X value in terms of X R E minus two X right. That's the why that should always go 32. I would go ahead and a most of play. Point. 12 x plus 0.2 times for 40 is 88 and 0.2 times negative. Two exes negative 0.4 x that equals 32 first. That's combined like terms so 0.12 x minus point for X will yield. Negative point to eight x plus Hey, hey. Cols 32. We wanna isolate Axel. Subtract 88 On both sides. We have negative 0.28 X equals negative. The e six, right? Yes, 56 get 56 and we want to get back on a sulfur X. So we divide both sides by negative 0.28 and we get X equals 200. So now we know that there's gonna be 200 grams of food aid that the researcher uses, but we're not done with the question because we all stop the song for Why, which is how much? How many grams of booby fishies. So now we just plug in this X value. Since we have our equation up here, we can go ahead is easily solved for why? Why equals 440 minus two X. We're gonna go ahead and replace that X with 200 Since we know what X is why it goes for 40 minus two times 200 400 and why equals 40? So there we go. We have solved the question. So in conclusion, this could be each conclusion we know that or hunt sort of woman 200 grams of food, eh is used and 40 grams food be is is used to make sure this actually works and makes sense. I'm gonna go ahead and plug this back in to one of the equations, plug it back into this equation that we got 100 X plus 50 y equals 22 1000. Let's begin X, which was 200 why? Which is 40. So we should get 22,000 if we do this plug and 200 plus 50 times 40 still 100 times. 2000 is 20,000 than 50 times 40 2000. And 20,000 plus 2000 is in fact 22,000. So 22,000 does indeed equal 22,000. So therefore, this is correct Food A is 200 grams to underground's foodies used and 40 grams of food be issues thing


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