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Aliveslock company reparts Ihat the maan weight ot group ol young stoore 1107 Ior tho woights of stcer pounds with sandang Kt Dlrcont davaltion ol 97 pounds. Based ...

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Aliveslock company reparts Ihat the maan weight ot group ol young stoore 1107 Ior tho woights of stcer pounds with sandang Kt Dlrcont davaltion ol 97 pounds. Based on the modol N(I107,97) Fnan 000 pounda? unjar 1300 pounde? batatan 1160 und 1200 pada?J%ot slaara have wolghts eboro ICOO paunds (Round ono dacmnal ploce nended

Aliveslock company reparts Ihat the maan weight ot group ol young stoore 1107 Ior tho woights of stcer pounds with sandang Kt Dlrcont davaltion ol 97 pounds. Based on the modol N(I107,97) Fnan 000 pounda? unjar 1300 pounde? batatan 1160 und 1200 pada? J%ot slaara have wolghts eboro ICOO paunds (Round ono dacmnal ploce nended



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Children's weight The Ehrenberg relation $$\ln W=\ln 2.4+(1.84) h$$ is an empirically based formula relating the height $h$ (in meters) to the average weight $W$ (in kilograms) for children 5 through 13 years old. (a) Express $W$ as a function of $h$ that does not contain In. (b) Estimate the average weight of an 8 -year-old child who is 1.5 meters tall.

All right, So, uh, for this problem, Firstly, let's verify the question. 43 13. So Q y In this case, it's ah too. I am age too, minus M helium three and the miners the immense of the proton. Sorry. In the mess off the neutral and time see squid and you can see that this video is, uh, 3.27 Meggie. And for 43 14. We have Q two equal. Ah to m age too minus M age three in the minus h sorry. Minus hold on minus the mess off. Ah, each one times he's quit and you'll see that these Valerie's four point over three mega TV and for the last 1 43 15 with Q three equal. Ah, the mess off. Ah h two plus myself H three and miners myself. Heating four in the minus one mess off. Ah, neutron time. See squid. So this video is 17.59 mega TV. Okay,

In this problem of logarithmic franson, we have given that the Ehrenberg relation that H. L. And W equals two Ln 2.4 plus 1.84 H. So this is a Ehrenberg relationship isn't empirically based formula relation Relating the height in m to the average height weight in kg for the children's 5-13 years old where H is heightened meters and W is waiting kgs. And now we have to express W as a function of edge that does not contain Ellen. So we have to express W as a function of edge. So this can be written as L. N. W minus L. N 2.4 is equals to 1.84 H. This can be written as L. N. W divided with 2.4 as equals to 1.84 H. That means the blue divided with 2.4 X equals two Into the power 1.84 H. That means W is equal to 2.4, multiplied with each of the power 1.84 H. So this is a relation between W. And H. In which laura ethnic term Ellen is not involved. And now we have to estimate And now we have to estimate the average weight of an eight year old child who is one five m tall. So the high days 1.5 m. Put this value in the formula that age here h equals to 1.5 m. So W is equal to 2.58 to the power 1.84 multiplied with 1.5. So now when we saw W is equals to approximately this is equal to 37.92 cages. So this is a solution That is the weight of the child would be 37.92 kgs.

There is a mathematical relationship between on infants wait and total body surface Area B s A given by the function A of w equals 4.688 times w race to the exploring to your point 8168 minus Europe 10154 times they seem a little rhythm of help you where w is the infants? Weight in grams and a WCBS a in square centimeters. He brought a We're going to calculate a of 4000 That is the total body surface area you say for an infant that weighs 4000 Gramps, that is four kilograms in part B. We're going calculated derivative of a at 4000. I interpret the result any parts he we're going to show the graph of fatal blue on A Did you mean 0.2000? 10,000 for W and the range of syrup through 67 for eight. Some part a. First we're going to calculate a 0 4000 and that simply replacing w equals 4000 in the formula off A of W. So this sequel to four point 688 times W that he's 4000 praise to the zero point 8168 minus 0.15 four times lower them based 10 off 4000. And to have these values a year began to use a computer or a calculator, and we have them so on. Obtained separatism illegal too. 2000 509 e. Tie a point to 264 square centimeters. So this is a B a safe for an infant. Who's way these 4000 Gramps you party? We're going to calculate the derivative of A at 4000. And for that burgundy calculate first, the general derivative of pay at any W. And we have to. There is a constant get out of the derivative 4.6 80 and that times the derivative available you to the 0.48168 minus Europe 10154 times lower than base 10 of W in that expression is the it's ah, it's a power of often expression that depends on the variable W and the exponents. We have also the variable W. So we know that this is equal to the same function. W to zero point age 168 China syrup. I'd, Cyril warned, 54 times the decimal logarithms off, don't you? In that times the exponents that he's syrah point 8168 minus here a point 0154 times slower them based 10 of W times the derivative off the vase that is there, the derivative respect to W off W and all that the body by the base w plus in that delivery them off the base, they'll believe times dear pretty healthy exponents. That is the derivative respect to W Off your a 0.8168 minus Europe 10154 times. Yeah, this human delivery them off w So the C's and here close is square bracket. And this is Theo expression. We get to cattle it now This is equal to four 0.688 times W to the zero point 8168 minus. See your Opens hero 154 times and they seem delivery them of W times. Here he servitia physical to want. So we get that the first term and said it. Square bracket is syrup 0.8 Juan 68 minus syrup on 0154 times they seem a little rhythm of W, divided by W plus Pless. The National Arboretum of W Times. The Syrian motive Here This one is equal to the relative off the first term, which is hero because it's a constant minus the relative off the second term here, which is the ghost and zero point 0154 times the derivative respect to W off the decimal algorithm of W. And now we know that this sequel to 4.6 88 times still you to the zero point 8168 in a syrup on zero on 54 times delivery them based on a W and that supplied by Cira 0.8168 minus zero 0.154 times slower than based and w oldies pressure. Anybody by W And now we can see here. There is m Blust sign here, but it there's a minus in here, so it becomes minus the ghosts and syrah 0.1 54 time. See, not a little rhythm of W. And now we know that these derivative here is one over w times in as a leverage them off the base of the slavery that the least natural rhythm of 10. So this is one over. Don't believe times de make some space here. Here. Oh, it is here. Okay, So was saying Went over the only times the night Delivery them off the face of thes Lower them here, but he still good and we close here Square bracket. So this is equal to 14.688 times w to the syrup on 8168 minus syrup 10154 times the delivery of W times 0.8168 Minus syrup on Syria 154 times Delivery them based in a Bellevue divided by W minus syrup Sincere of 154 times he natural rhythm of W and that divided by the lead times Natural rhythm of 10. And this is a vinyl expression for a hurry. Here it's the final expression for a cough derivative off w. And now we want, even though it is at 4000. And so this is equal to replacing W By 4000 they had this secret to four 0.6 eight age times 4000 raised to the syrup point 8168 minus syrup 0.0. So your 0.0 154 times three decimal luxury them off 4000 times. Syrah 0.8168 minus syrup 0.154 times suggesting my logarithms off. 4000 invited by 4000 minus minus syrup on 015 four times the natural logarithms off 4000. He bought it by 4000 times in natural algorithm off 10. And so we use a calculator here, too. Find his expression is separate similarly equal to syrah Point for five 71 and these must be express and sitting me to square pair girl. So the interpretation of the result ease the DBS say increases because he's changing In the positive sense, though, is increasing. The BS increases off about zero point poor five 71 So is the rate of change in fact, centimeters, squares or square centimeters when ah, the weight of the infant With the order infant Wait, he's increasing, going or in Greece is off longer from 4000 grams to 4000. Lawn Gramps. It's important to remark that the changing one grand firm comes starting at 4000 grabs and if t away changes in one gram from 4000 grams to 4001 grams. Then the BSO increases but off about 4.0 point 457 Juan sitting me a square and then in part C, we're going to show the graph of the function A of W or B. You say, in terms of weight own, ah, 2000 and seven for the weight and 0 6000 for the value of A. So we have here the graph, the function. So here we have told you. And here we have a off W or a B s A. So we have in an increasing behavior of thief function, starting that somewhere around, uh, between what's happening to something. Yeah, um, getting up to nearly 5000. So we have calculated the the rivet ive of the function at thes point, and we have also calculated the value of a function which waas for about 2005 190. So does things well, you here. And if we draw the tension lined at this point, then we're gonna have Corliss uh, the slope of this. That tension is gonna be a derivative of the 0.4000 which have which has being calculated before, which which was syrup going for 571

We're told in this question that babies that are born after a 32-35 weeks, just they, excuse me, gestation gestation period on average way 2600 g with a standard deviation of 670 g. And then babies who are born essentially full term at 40 weeks way 3500 g with a standard deviation of 475 g. So they weigh more but have less variation in their weights. We're told them that we have a baby who was born at 34 weeks, so falls into that first time period and wait 2400 g. And then we had a baby who was born at full term weighs 3300 g. So each of them way less than the respective average for their time period. But we want to know which baby weighs less in putting into perspective the different again, gestation periods that they had. So this is where we want to use the idea of Z scores. It allows us to take data that comes from that's represented by different parameters and compare them to see which baby does technically way less. Not just in terms of its weight, that's pretty obvious, but in terms of the average for that time period in which it was born. So first we'll look at calculating the Z score for the baby that was born at 34 weeks. Our formula for Z score is your observed value minus your mean divided by your standard deviation. And so for this particular problem, that's going to mean that we're taking the $2400. Excuse me, 2400 g. We're subtracting the mean that corresponds to 34 weeks, so that's 2600. And we're going to divide that by the standard deviation of 670. We're going to have a negative Z score. Which makes sense because our weight is less than the mean. So in our numerator we have negative 200 Divided by 670. To get a Z score of approximately negative 0.30 by round to the nearest 100. It's negative 0.30 So it's just 3/10. This baby was just three tents of a standard deviation below the mean. We want to compare that with our baby that was born at full term. So again, if I apply the Z score formula, I'm going to take 30 300 g And subtract 30 500. Again we're going to have negative 200 But this one is being divided by 475. So We can see they both weighed 200 g less than average for their gestation period. But we kind of want to know which one of them. Is that more unusual? Um and and kind of a greater less weight, if that hopefully makes sense? So now negative 200 divided by 475 gives us a Z score of negative 0.42 If you think of your normal curve, and we kind of take a look at each of these, I'm gonna look at them even though they wouldn't be on the same normal curve, because they have different means and standard deviations. If we just think of the idea that the mean would be in the middle, our baby that was born premature Would have been about here, let's say at negative 0.30 standard deviations away from the mean, and our Baby that was born full term would be there. And I'm gonna right above here at negative 0.42, it was slightly more to the left of the mean, meaning that that baby technically weighed less in respect to babies of its same gestation period at birth. So to answer the question, the Baby born at 40 weeks weighed less when compared to, oh sorry, again it weighed less when compared to um average babies at 40 weeks. Because it's Z score was more to the left.


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