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Up the systemeouations5o1vEby Using nuere MatricecAce Trucking Company of the productsnrder tortnr?e productsand C} fr Celivery_ The rable givesYolumecubic feet, the weightpcunds and the value Tor insurancedclarsRachProductProductproductUnit volume (cu #) Weight (Ib)Vale800OQQeachinucCarry0d0 CU #ang400insured5542,000_Many UnitsBacn prcductComnedtProduct PraducrunitsunitsPradudunilsthe insure_ valu? Ingrezsel$72,000, find the new delivery_ SCnerePraducrunitsPraduCrunitsProductunilNeed Help?Ruad

up the system eouations 5o1vE by Using nuere Matricec Ace Trucking Company of the products nrder tortnr?e products and C} fr Celivery_ The rable gives Yolume cubic feet, the weight pcunds and the value Tor insurance dclars Rach Product Product product Unit volume (cu #) Weight (Ib) Vale 800 OQQ eachinuc Carry 0d0 CU #ang 400 insured 5542,000_ Many Units Bacn prcduct Comnedt Product Praducr units units Pradud unils the insure_ valu? Ingrezsel $72,000, find the new delivery_ SCnere Praducr units PraduCr units Product unil Need Help? Ruad It



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SHIPPING Golden State Manufacturing wants to increase the size of the boxes it uses to ship its products. The new volume $N$ is equal to the old volume $V$ times the scale factor $F$ cubed, or $N=V \cdot F^{3} .$ What is the scale factor if the old volume was 8 cubic feet and the new volume is 216 cubic feet?

Three kinds of humidifiers a bedroom humidifier, a living room, humidifier and a whole house treatment the fire. And they want to figure out how many of each they should load onto their van if they weigh 10, 20 and £60 and the van holds £440 and they take up a cubic feet, a key recre 28 cubic feet and the bank can hold 248 cubic feet. Okay, so first we can write equations or inequalities. Doesn't matter if you work in the same way. Oh, first, I'd better tell you what the variables they're going to be. Let's let X be the number of bedroom humidifiers and why will be the number of living room and you will be the number of whole house. Sure, I'll take you. Okay, so then our equations will be the first one will be the weight, and the second one will be the volume. So 10 X plus 20 y plus 60 Z has to be less than or equal to 440. And then, um, they were 88 and 88 and 28 eight x plus eight y plus 28 Z has to be less than or equal to 248. Okay, so now we have lots of ways to solve this. I'm gonna go ahead and use matrix methods is much easier. Less writing. Okay, notice also that we have three variables and we only have two equations. So that means we're not gonna be able to get one. Answer Exactly. One answer, but more than one. So 10 2060 for 40 eight, eight. 28 2. 48. Okay, so the first thing I'm gonna do is get at one here in the 11 place by dividing everything in that row by 10. You get 1 to 6. 44. You could have done that right off the bat without writing it down the way it waas. And next, I'm gonna get a zero right here. But what I just did on that one Waas want 10th row one in row one to place. Now I'm going to dio Negative eight times Row one, plus road to and put it in Rhode Tooth place. Negative eight row one plus wrote to in row twos place. Okay, so I'm leaving the first row one times Negative. Eight plus 80 Two times negative. Eight plus eight. That's negative. Eight, six times negative. Eight plus 28. So negative. 48 plus 28. That's negative. 20 44 times negative. Eight 352. And I'm gonna add to 48 to it. So I'm really subtracting negative. 104. All right, now I'm gonna do negative. Negative. 18 Yeah. Um, negative rate negative. 1/8 row two in row twos place. I should have done that before I did the ad. It would have been much easier right there. Negative 1/8. Row two in row twos. Place 01 This gives me 10, 8 or 28 which is 10 force, which is five halfs ah, 104. Divided by eight. That's 1 13. All right, I'm going to do one more thing. I'm gonna back go back and get rid of that two up there. That's a six, not a zero. I'm gonna do negative a negative, too. Wrote to plus row one in Row one's place to get one negative. Two times one plus two negative. Two times five halves plus six Gives me one negative two times 13 gives me negative. 26 plus 44 gives me 18. All right, so now what I have is both x and y in terms of Z. So the first one is X plus Z is 18 and second one is y plus five half z is 13. Yeah. Okay, So the first one tells me that neither X or Z could be bigger than 18, so that's not very useful. But the next one tells me that why and why has to be less than 13 and five have Z has to be less than 13. So that means Z can't be. Let's see, five halves, the less than or equal to 13. So the less than or equal to 26 over to, uh, watch 26/5. So Z has to be less than five. And not only that, but it needs to be even okay, because if we put an odd number in there, that will make any sense, Okay? Because then we'll be bringing half parts of Z or half parts of why. So Z has to be even and less than five. I just make a charge here, so my first choice will be four. So if CS four than X plus 4. 18 so x is 14 and why? Plus 10 inches 13. So we could bring 14 of the 1st 13 of the second one for the third one. Okay, um, Z could be two NFC was to then X would be 16. And why would be because he was, too. Why would be eight? So we could bring 16 of the 1st 1 18 of the 2nd 12 of the third one or Zika V. Zero and X could be 18. And why could be 13? Okay, so there's your different choices of answers. 14 home or 14 bedroom, three living room and for whole home and then etcetera, etcetera. All right.

On this problem we are dealing with trailer loads and we were wanting to find the meat. Remember your mean which is normally representatives mu it's the same as your expected value and is able to some of the excess the probability of that. So that's what we're going to make use of here. It's some of the excess times of probability. That's yeah. Yeah. Yeah. Let's go and make our probability distribution for this. That's well that's and p that We're doing one of them 30 of the time And the one that we do 30 of the time is with the 30 ft trailer. And so it's eight x 10 x 38 times 10 times 30 gives us 20 430 of the time we were using a trailer With the 2400 cubic foot capacity. Now the other 70 of the time It's eight x 10 by 40 Which is 30 200 and so that's what we're using the other 70 of the time. Yeah. So to find the expected value, This is 2400 Times .30 X tons of probability that Plus 30 200 Times the probability of 30 200, which is 70%. That's what we're going to take this and evaluated 2400 times 24000.30 Those 3200 times .70. This gives us 2960 so that is the mean volume.

It is your dad. A truck is carrying toward this ex cubic feet off cargo, which consider of washing machine and a refrigerator on the coast off. One washing machine is given us $300 on a ship in 36 cubic feet of court garden. Now the coast off one refrigerator is given us $900. On it is you've been 45 cubic feet of Khartoum, and the total coast off the cargo is giving us $51,000 so we have to find a number off washing machine and a number of refrigerator. So let the number of washing machine B X on the number off a refrigerator. Beware so they can write the great Jinnah's Statistics X Plus 45 way, as he calls to 300 artistic centre cubic feet. Because there is 26 cubic foot of garden for washing machine toe, 26 times X plus 45 cubic feet, fall refrigerated is given, so 45 y is equal to the total that this talk to 600 cubic feet. Finally, next year, equation weaken right in terms off money, which is a 304 washing machines, $20 or 300 X plus in 900 away IT records too. The total cost, which is 51,000. So we have a plane. These two equation We can simplify the first equation. Onda. We can write Wigan divide the first equation by nine So we get The question is for X plus five is equals to 400. Let this be as first equation and we can divide the second equation by 300. So looking right X plus three y is equal to 1 70 So let this be as equation About two now will be using Cramer's rule to find the value of X and y. We know that from cameras from the value of X is the ex baby in the valley off is divi body So first of all, they will calibrate the value of B So these were called to the detriment value off for 153 average in the coefficient of X in the first column coefficient of right in the second column. So we get the value of D S seven. Now we look over the value over DX, so the actual because it's to the detriment off 401 70 53 average in the averages. Will you in the first color and the value of the coefficient off by in the second column. So we'll get developed off a DX as 350 Now we'll calculate the value off a delay. So D rival be calls to the detriment value off 41 401 70 average in the coefficient of X in the first column on our religious value in the second Golam. So we'll get the value off a divi as 280. So finally we can say that the value of X is to be expected. So the Excel restrictive to divide by seven which comes out to be S 50 on the value of I comes out to be S 40. So finally begin right number off washing machine is 50 on a number. Off the refrigerator is 40

Here in this problem, it is given that truck is scaring to step off. Thanks. The 1st 1 is washing machine on the next one is a refrigerator on it is given the coast off. One washing machine is $300 on the coast off. One refrigerator is $900 on the course. The total ghost of the cargo is 51,000 Dolo. Next, they are saying that the washing machine is shipped in Tartus. Six cubic feet off card cartoon Onda three uterus shipping 45 cubic feet off cartoon. No, the capacity off cargo is 3600 cubic feet and V after, does the value off the how many washing machine and refrigerator is being carried by the truck. So let us assume that there are exposing machine. And there are why a refrigerator? So you can write the equation as a 300 X place 900 way ID equals 2 51,000 on. We can rewrite this equation by dividing this equation with 300. So we'll get X place. Three way is it cools to 1 70 So does it. If US equation now, the next equation weaken right is 36 x plus 45 y is equal to 3600 now when will dry? Evan would divide this equation by nine. Get for X plus five. Why is it called? So for under? So there's a second ago unit. We have up change. Now we have to use a clamor stool to find the value of X and Y. So let me write this equation here. The to record in that we have got that is explicit. Three Way is equal to 1 70 on forex Bless. Five Way is equal to 400. Now we know that from the Kraemer Soon X is given by D X, divided by d and vice. Equals should be right of everybody. So far, so four will calculate the value off D so Daisy could do the betterment of value. 1435 Average The provision of ex hair in the first column condition of I in this second column so we'll get definitely off de as seven. No well, right. The actually issued negative ST you to be dead one because five into one is five minus trialists. Negatives were not soon now, like a good value of BX. So the extra week will to the detriment of value. So it's 1 70 here, 400 on 35 average in the averages value here on the coefficient off. Why in the second column? So we'll get there early of the excess and negative 3 50 now vehicle readily off B y, which will be equal to the detriment of value off one full 1 7400 of Linux coefficient of X in the first column on this averages value in the second column, so you get the value of D Y as negative authority. So finally, beginning a good pick we can can we can calculate X equals two. Do I buy a D? So negative 3 50 divided by negative seven will be glued to 50. Similarly, revival Big worlds to 40. So finally we can conclude that washing machine in the truck is, ah, 50 on the number off refrigerator, and the drugs for in the truck is 40. So this is the final answer


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