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Homework: Section 6.2: Homework assignment Scony 0l 1P comoklel Instructor-created questionHW Score: 72.7350, 8 cl 11 PisCe doneddritshor nlenurcalcucCci Hetlt_te C...

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Homework: Section 6.2: Homework assignment Scony 0l 1P comoklel Instructor-created questionHW Score: 72.7350, 8 cl 11 PisCe doneddritshor nlenurcalcucCci Hetlt_te Compk 2MhtughUkc Gaussuan eltatonGrch saeci Ihe ccreci cokteroFn cuneaerannnPaenetAqulkn *dJ} (Type Onomden Muadnin sclution sct i ( ( Kncme ac [ealnuta (6 creron; ueroIninterscaicnsLcrecconemugiotMar GnFtt Fes

Homework: Section 6.2: Homework assignment Scony 0l 1P comoklel Instructor-created question HW Score: 72.7350, 8 cl 11 Pis Ce donedd ritshor nlenurc alcuc Cci Hetlt_te Compk 2 Mhtugh Ukc Gaussuan eltaton Grch saeci Ihe ccreci coktero Fn cuneaerannn Paenet Aqulkn *d J} (Type Onomden Muadnin sclution sct i ( ( Kncme ac [ealnuta (6 creron; uero Ininter scaicns Lcrec conemugiot Mar Gn Ftt Fes



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Grading One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. (a) How many different groups of 5 problems can be chosen from the 12 problems? (b) Probability Extension Jerry did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded? (c) Silvia did 7 problems. How many different groups of 5 did she complete? What is the probability that one of the groups of 5 she completed comprised the group selected to be graded?

26 which is eight here. We need to use a combination because the order selection is not important. Anything for 12 on our beautiful five. So the combination of 25 is equal to 12 pictorial over five factorial seven Victoria, which is 12 minus line 47 92 uh, for could should be the probability that jury it chose us grew. That's completely created is equal to 1/7 9 to be good on, only one whom or five homework problems is gravy. So this is equal to open or or 1264.1 to 6%. Yes, for questions. See, um, the combination using an is equal to seven and always equal to five, which is so Victorian over five Victorian seven minus five Victorian. They got to 21 so the probability is the number devoted about the phone number. So the probability that Silva they choose good that's completely created here. The number is 21 open over 65 or 2.65

This problem. We're going to do a series of calculation using the ideal gas law PV equals NRT. If we're going to use our equal 2.08-1 that's in leader atmospheres per mole Calvin. So we're going to need to make sure that we have volume and leaders pressure and atmospheres and we'll have moles and our temperature of course will be in kelvin. Mhm. So for this 1st 1 so we've got P. D. Equals NRT. So we're giving a pressure of 1.77 ATM And we've got 4.98 l and we're looking for moles because we don't have that Put away to one And our temperature is 43.1°C.. So add to 73 .15 to that. So then we'll go ahead and solve for moles and we're gonna come out with 0.339 moles. So we can fill that into the table. And then we're gonna multiply by the molar mass of, We're using N 204. So it's going to be 92.02 g per mole. So if we multiply there we'll get 31 .2 g and can fill in that into the table as well. So on the second one, we've got our pressure and volume and some moles. Okay, so again, T. V. Equals NRT. So our pressure is 673 But it's mm of Mercury. So I'm gonna need to divide by 760 to go ahead and get that into atmospheres. Okay. Um are Volume is 488 ml. But we need that to be in leaders. So .488 leaders. Mhm. And we've got malls, So .783 moles .08- one. And one of the things we're missing here is temperature. So we'll go ahead and solve for temperature. We're going to get 6.72 Kelvin. And the other thing that we're missing here is grams. So we're gonna go ahead and take our moles, which is point 783 moles. Again, we're gonna go ahead and multiply that by our molar mass, 92 oh two g per mole. And that will give us 72 0.1 g. So those are the missing pieces of the table for part B. So in part C, we've got our pressure. Okay, They've given it to us in bar. So let's go ahead and make some conversions here, .899 Bar, If we multiply that by 100 we'll get killer Pascal's. So we've got 89.9 kpa. And then why don't we go ahead and change that atmosphere so we can plug it into our um ideal gas law, Which is one on 1 0.3. So this is going to come out to be point eight 87 ATM They've given us the mass which is 6.25 g. And we're gonna need to go ahead and change that to moles 92.02. So if we do that, we've got .0679 moles. So that's one of the things missing in the table. So we'll go ahead and circle that and our temperature is 912 degrees Celsius. So let's go ahead and change that to kelvin. So we'll get 1185 kelvin and then we can go ahead and calculate are missing volume. So PV equals NRT. We had plug in the things. We just found some 887 ATM mhm. And our volume here actually, the volume is what we're missing. Right? So we're gonna go ahead and calculate that volume And our moles is .0679 And .08- one. And our temperature 1185. So if we do out our math and we saw for our volume will get 7.45 l plug that into our table. Okay, so our last example here, we've got a volume and a temperature in Fahrenheit and some moles. So first thing, why don't we go ahead and get that Fahrenheit temperature into Celsius and then kelvin, So degrees Celsius is 5/9 of Fahrenheit, so are 39 F -32. That's how you convert from Fahrenheit to C. So we're going to get 3.88 degrees Celsius, We'll go ahead and add to 73 .15 to convert that to Calvin to 77.4 Kelvin and then plugging into piven ERT vehicles and artie uh huh We're looking for a pressure mm Oops, And we've got a volume which is 1.15 L. Mhm and we've got .166 moles was given .08- one. And that temperature we just found 277 point oh four. So calculate our pressure. We come out with 3-8 ATM there's a missing piece of our table and the last missing piece was our graham. So we're just gonna go ahead and change our malls again by multiplying by our molar mass you grams per more. And that will give us 15 0.3 g. So now we've identified all the missing pieces of the table.

Now over here in this Christian being, giving some you can see information about the Lien Hamburgo that is having 70 14, 5. So let us keep writing that down easily. Um boko Andi. It has 7% fact lucky. Now, apart from bad, if we also have £12 off ground chunk, that is 20% fact. So let us right at all. So, ground chunk. Okay, ground chunk. And it is having How much did it having 20 points in front on what is the weight of the ground feel that we are having is £12? So there is £12 of ground, which is having 20% for five Now we just have combined the sleep of hamburger off 7% fight on £12 of ground chuck off 20% facto, have a hamburger mixture. I will have important fact So the mixture shouldn't have 15% fact So now over here what? We have to find out this We have to find out the weight off the lean hamburger that is having 7% fat. That should be mixed with the ground junk off £12 having 20% fatto have a mixture that will have 15% off facts. So I guess everything is clear with all of you. Like water is given in what is being asked over here. So let us see that X pounds off. Lean hamburger fat Earlene hamburger with 7% fat content is to be mixed with £12 off ground chunk with 20% fat content. Okay, so expounds off. Lean ham poco. We have supposed to find out the weight off the lean hamburger. No. So I'm assuming that does X over here again and repeating Save expounds off lean hamburger with 7% 5 be mixed with £12 off ground chunk off, 20% fat in orderto get a mixture which will have 15 positive fat content. So what? We'll get over here simply x times 7% at IHS, we can see seven ago. 100. I'm just converted that Postant agent to a fraction over here. So now the mixture will be worth the ground chunk is the weight off the ground? Cheng is £12. So 12 times 20 upon 100. It was 20 person fact. No. So again, I'm just converted That 20% do a fraction on the mixture. The weight of the mixture will be worth simply eggs. That is the weight of the Lien Hamburgo and plus 12. 12 is what the weight of the crunch on the 5% 15 so 15 upon 100. So this will be the required equation that I've framed over here. Now we just need to solve this equation. So for that, I can just multiply by 100 on both the sides. So if you just multiply by 100 on both, the sides will get something like this. So see? 100 100 gets canceled out like this. So what I'll get is seven eggs plus 20. Thanks, 12. So that is 2 40 is equal to express 12 times 15. So I'll just open the practice as 15 x plus 12 times $15.180. Now I'll just bring the variables on one side, and then I'll soil for eggs. So let us do that quickly. So seven X minus 15 eggs. So that will give you minus eight X equal to 180 minus 2 40 That ISS minus 60. Let's cancel out this negative sign from God the size so it takes is equal to 16 60 or I can say X is equal to 60 upon eight, which is equal to 7.5. So the value of X is 7.5. Hence I can see that 7.5 pounds off lean hamburger is to be used. Thank you.

And this problem we're going to use the concept of combination. Now in the problem it is said that there is a professor who grades homework by randomly choosing five out of 12 homework problems to grade. Now the first question asked, how many different groups of five problems can be chosen from 12 problems? Now, since the order does not matter in this case, since there is no arrangement and only a selection of five questions from 12 questions needs to be made. So the concept of combination will be used so we can find the answer by finding the value of C. There are 12 homework problems to see 12 coma and there are five home or problems with the randomly selected. So we need to find the number of combinations of five or more problems being selected from 12 or more problems. So that is equal to C. 12 coma five. Now, since C m comma R s equals two. N. Factorial by R factorial times N minus R factorial. C 12 comma five will be equals to 12 factorial by five factorial. 12 -5 Factorial. So this is equal to 12 factorial by five factorial and 12 -57. So that is equals to seven factorial. Now The value of 12 factorial is quite large to calculate. So instead of directly calculating it we can rewrite well bacterial as 12 times 11 Times 10 times 9, 10. 8 times seven factorial. And then the denominator we have five factorial and seven factorial. So the seven factorial can be cancelled from the numerator and the denominator. So this will be 12 times 11 times 10 times nine times 8 Divided by five factorial which is equals to 120. Now we can simplify this 12 and 1 20 can be reduced and then this 10 and 10 can be cancelled. So we are just left with 11 times nine times eight And the value of 11 times nine times 8 is 7 92. So there are 792 different groups of five problems that can be chosen from the 12 problems. Now the next problem asks that if there is a boy who did five problems, only five problems of an assignment. And what is the probability that the problems he did comprised the group that is selected to be graded. Now there is a total of 792 different groups. So the total number of outcomes will be seven 92. And out of that, the boy only completed five problems. So that is, he completed just one group of five problems. So that means that the favorable outcomes, the number of favorable outcomes is one and the probability required, probability is 1x792. This can be converted to percentage by multiplying it. 500. So it's one by 7 92 times 100%. So one by 7 92 times 100 is Approximately equals to 0.126. So this is approximately equals to 0.126 percent. Yeah. And the last problem, we have a girl who read seven problems and how many different groups of five did she complete? So we will once again use combination and out of seven problems. We have to find the number of groups of five. So this will be C 75 and that will be equals to seven factorial by five factorial Divided by 7 -5 factorial. So that means seven factorial by five factorial times two factorial. Now the value of seven factorial is equals 25,040. The value of five factorial is equal to 120. And the value of two factorial is equals to two. So 5040 divided by 120 divided by two is equals to 21. So the girl completed, there are 21 different groups of five that she managed to complete. And what is the probability that one of these groups is selected? Once again, there are 792 to allow outcomes because that's the number of different groups that are possible and she completed 21 of these groups. So the probability is 21 divided by 792. And this can be written in percentage farm as 21 x 792 times 100 percent. So 21 x 792 times 100 is approximately equals 2.65. So this is approximately equal to 2.65%. The probability that one of the groups of this girl, the one of the groups that the girl completed comprised the group selected to be graded is approximately 2.65%.


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