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Hat (4) Tlk #Eency deriedl AllIu nunce imrtwe mreli claseilicd m (uxrd ( Melun (2) 4nd Hea Dlancu hamahae mnilInIcHlutIcr Ol Uc Ciut Which 4e Medutur Fl Thic Wctians ucpcm Ilec Unnie olihc couldhMinCtit Jullounni WneILAL tnalfices F tath t Care (H} id (iod Can? (C) Tlx mcsulis nre hrAE mntncr Halzt ntucluce MINIn CIEILIC C {035 0.45 0.155 065 Wa IO10 [600 400 500 300 3zu 160 200 =16 ~1oo] 4740 150 Cuun_ Ecton t Lke exch At "ptntzl Froranmning uhlcs Et 2 onths? (6nrkal Using Aynalitie TVn744 atr th havethchighesl EAEo uth In OTder the Lvitial ilion consideration Ejualitn icn Hint: Take in Jeurir cu-nlL Guad Owinp Usc BACKWARD Hintzi 0) aTati | (xI) 2ok 625 63(2) = 1125 60)0 #ith 2vh



Answers

1. Determine the coefficient of linear expansion for an unknown material that
is initially 150.000cm in length when at 5?C and 150.011cm at 150?C.
2. Determine the coefficient of volume expansion for an Aluminum block
from the linear coefficient ?Al = 2.4 × 10?5
(C
?
)
?1
.
3. If 25kJ of heat is added to 1.5kg of water at 25?C what is the final
temperature of the water?
4. An 15g ice cube is added to a hot cup, (75?C), of tea that has 400ml of
liquid (assume to be water). What is the equilibrium temperature of the
tea and ice?
5. Consider a copper rod whose length is 10cm with a cross-sectional area of
1.5cm2
that has one end at 0?C and the other end at +50?C. What is the
magnitude of the heat current through the rod? The thermal conductivity
of copper; kcopper = 385.0
W
m·K

So in this question of firework was launched at some height? Right? So the graph of the projectile is given. And the equation of the projectile would be why it goes to minus five X square plus 20 X plus one here. Why is the height of the firework from the ground and access to time? Right. So we have four parts of question here. The first part is saying that uh what is the highest point that the firework would be the would reach? Right? So to find the highest point we have to find divide by the X. And we have to equate this to zero because at the highest point that slope of the cover will be whole gentle to the X axis. Right? So David by the access across digital, which means that minus 10 X plus 20 is equal to zero. So from here we get access equals to two seconds. So after two seconds the the firework will reach the maximum point right now to find the height of the maximum point, we can find the value of Y had X equals to two seconds. Light soil substitute X equals to do in the aggression. We will get minus five to his square plus 20 multiplied by two plus one. So when we simplify this will get why he goes to 21 fits. So this is the highest point that the firework will reach. Now coming to the second part, the second part is how long the firework was in the air. Right? So uh at the end the fireworks will be reaching the goal of reaching the ground. Right? So at that point the height of the firework would be judo, which means why we liquid 20 Right? So we have to equate why equals agenda. Which means that minus five X squared plus 20 X plus one is equal to zero. So some the situation will get the values of X. Right? So it is a quadratic equation. We can find the roots of the equation by minus 20 plus minus the square root of 20 square mm minus fall into minus five. Divided by to into minus five. Yeah. Right. So from here we'll get the values of X one would be 4.3 to 5 seconds, 34.3 or 49 to be more like you did. Mhm. And another value would be X equals two minus zero point Beautiful night. Since this cannot be possible, time cannot be negative. So the correct value is 4.249 So after 4.49 seconds the firework will reach around. Right? Mhm. Now coming to the sea but ah we have to find the time we've just taken to reach the highest point. Right? So two at the highest point, the slope of the cover studio that we have already found in the first part of the question. So by creating slow because we have God the value of access two seconds as in the first part. Right? So after two seconds the firework will reach the highest point. Now coming to the depart, uh we have to find the height of the firework at the initial mind where it is launched. Right? So in this uh this equation we have to find the value of Y. A. Toxic was which means that a time it was zero seconds. That is the initial point. We have to find the height of the firework. So we can we can substitute judo forex in the equation. So we'll get y equals two minus five geo plus 20 multiplied by zero plus one. So this will give the value of my years one ft late. So at uh height of one ft, the vibe work was launched, Right? So this uh this is a solution for the given question.

So we're gonna go through all of these bits. Um for the status question. So the first question has New York City at 750 pedestrian walk buttons at work And 2500 to deal with. If we select a random one by the probability it works for the probability it works will be the number but work. I was total number The number that work is 750. The total number is 750. Last 2500 That we get 750 over 7 50 Us 2500. And that comes out to be three 13th number two. We need to find the probability when a couple of three Children to get exactly one girl assuming that boys and girls are equally likely. Well um we need to look at all the different possibilities here. So either they have boy boy boy boy boy girl boy go go boy oh boy let me just write that. They're so boy oh boy or girl boy boy all we can have um boy girl girl girl boy girl go go boy oh girl girl girl so We can have any of these possibilities which are 123-456-78. So obviously these in some of these you still end up getting you know two boys but they're in different orders. So we need to consider all of those probabilities. So each of these probabilities are 1, 8, there's a options and each is equally likely to happen. There are 1/8 probability. Um And therefore to get um in the situations where we have one girl is this one this one and this one, so that's equal to the total probability of one girl is equal to 3/8. The other way you can do this is you know that the probability of a girl is half. So the probability of um ah the probability of getting a girl and two boys is a half cubed which isn't eight. Um And you know that there are three different ways to produce three different ways to get one girl. Either the girl as the firstborn and the girl is the second born or either the girl is the third born. So that means we just multiply by three And we get a final answer of 3/8. So you can do either either of those methods. They're both Fine question three, It asks us The probability of the horse out of here, winning the 129th Kentucky w of 1- 1, 1 out of 50. What the actual odds against al today winning the race? Well, that's pretty simple. It basically means that for every 50 races outta here winds one. So therefore odds against uh 49 to one. So for every 50 races Um he loses 49 And he wins one. And then finally for so not finally for four, when you just set the selected card randomly from a standard deck of cards, what the odds of the card being a face card? We'll face cards are Jack queen king. So that's three face cards And there are four suits. So overall four times 3 is equal to 12 face cards. There are 52 cards of the deck. So our probability of face is equal to 12/52, which is 3/13. And then finally for number five, It says in the table below 400 individuals are classified at the same blow up. The large individuals are classified according to whether they are vaccinated against influenza and whether they are attacked by influenza. Um, if one person is selected random find the probability that the person was vaccinated or attacked. They're looking for. The probability of backs plus the probability of attacked, the probability they were vaccinated is So the, the overall we have 400 individuals, the probability that they were vaccinated or attacked, it's going to be vaccinated which is 60 plus 1 90 over 400. The probability that they were attacked 60 plus 85 over 400. So that comes to be 60 plus 1 90 400 bus. The bye, That is equal to 9.9875. So overall it's a 98% chance that either one person has been vaccinated or attacked

This question is asking us to calculate the mean and standard deviation for each of these students and to relate this to precision and accuracy. So our formula for me is each of our sample values divided by the number of samples we conducted. Standard deviation. The formula for this is the square root of this, sum of each of our values minus the mean, that value squared for each of these, and then you divide it by the number of samples minus one. This question, it's also important to note that the density of water is one g per mil leader, So if you draw saying 150 0.150 mL of water, this is equivalent to drawing 0.150 g of water. So moving on to the calculations for each student, the participant A had values of 0.161 0.147 and 0.142 participant B. Had values of 0.158 0.156 and 0.157 participant C. Had values of 0.143 0.153 and 0.150 We can add each of these up to get the total and divide it by three because we have three samples for each participant to get our mean value. So here we have 0.161 plus 0.147 plus your 0.142 which equals 0.450 We can divide 0.450 by our three samples. And you get a mean of 0.150 g per participant B. We do the same. We add up our values get our total value which here equals 0.471 and 0.471 divided by our sample amount. And we get a mean of 0.157 g here for C. Again, same process, we get a total of 0.446 and divided by three. You get a mean of 0.149 About this is rounded from there we can calculate our standard deviations so far participant A. We have the square root of our first value is your 0.161 minus the mean of 0.150 squared. You add it to r 0.147 minus 0.150 squared and 0.14 to minus 0.15 also squared. And we divide this by end minus one. So we divided by two. When you calculate this out, you get a standard deviation value of zero 0.98 On average we do the same for participant B. Here we have 0.158 and I'll just abbreviate this 0.156 0.157 And we subtract 0.157 which was the mean from each of these values divided by two. And our standard deviation value for participant B is 0.1 We do the same for participants. See I'll abbreviated again for three to a 0.153 and 0.150 subtract the mean of 0.149 divided by two. Remember each of these values needs to be squared after subtracting the mean and you should get a standard deviation of 0.54 Standard deviation is just a basic calculation of the amount the participant is off from the mean, from each of their values. So, using this information. All right, this is an abbreviated format. We have our mean and standard deviation for each of our participants, participant A If you remember the mean was 0.150 Under standard deviation of 0.0 98 participant B 0.14 sorry 0.157 and zero and zero point 001 Lastly for participants, see army, see army was zero point 149 after rounding and 0.54 Now, in order to calculate our accuracy, what they're telling us to do is our mean value divided by our volume that we were supposed to draw and we multiply this by 100%. So here for participant A we have 0.150 divided by 0.150 times 100% equals 100% participant B. We have 0.157 divided by 0.150 And they have an accuracy value of 104.7. No the max accuracy that you want is 100%. Even if you are over 100% that is not better for participants. See we have 0.149 Fight it by 0.150 and we get an accuracy value of 99.3%. Finally they want us to evaluate the precision of each of our participants. And precision is how close their values are each time. So oftentimes when relating precision and accuracy, accuracy is how close you get to the center of the target, whereas precision is how close you get each attempt. So this would be high precision here and this would be high accuracy here. So for student A. Our accuracy was 100% in our standard deviation was 0.98 For participant be accuracy of one oh 4.7 precision of 0.1 participant C accuracy of 99.3% and precision of 0.54 If we consider we want our accuracy to be between 99 and 101% we can eliminate participant be for accuracy, so since we can eliminate participant B, we can pick our best participant based on their standard deviation and precision students see has the better standard deviation. Each of their values varies less with each attempt to draw water into the pipe. It so our best choice for hiring based on precision and accuracy students see.

Hello. So the coefficient of linear expansion given by uh the change in length invited by the original. And times are changing temperature. So, I got everything in there. So there's centimeters. This is social centimeters. So if you put in the values you're gonna get this as a coefficient of linear expansion. Okay, 40 system. Standard negative seven pair degree Celsius. All right. The relationship between uh, coefficient of volume expansion and linear. Uh So the volume because three times the linear. Okay, we're giving the linear and the question just multiply by three. I did this valley right here. Yeah. So for this question and have an amount of heat being supplied to water. So, uh just energy conservation. Okay, so the heat is going to be absorbed by the world. So you can say the heat lost sick with the heat thing. So uh yeah. And uh and of course it's going to be changing temperature for a while. So, and this is the formula And then 4200 is a constant that specifically capacity of water. Okay, so once you have this, just do the algebra to find a final temperature uh In the final temperature, it's going to be approximately 29°. Okay, For this one the ice office would have to melt. And that's the a little bit of fishing before it finally mixes with the T. Okay, so you got an ice, it's gonna melt, dad, was it milk? Not a kind of mix. Okay. So the T. Is gonna lose heat to the eyes. So once you have this expression where you just need to put in the violence, you've got uh We were given 400 mils milliliters of uh the T. And that is also 400 g. Okay, 4200. And the specific heat capacity of water, they have the temperature change. Yeah. Uh We got the mass of the ice, right? 15 g. There's the little hit the future of ice. Okay. And then uh this is when it's now mixing with the T. Okay, at this point. Right here, correct. Okay, so you put everything in and then we do the algebra and our final temperature, it's going to resist in mind. Okay, so the initial temperature of the T. Or 75. I want to miss them up. The temperature of the mixture is gonna be 69. Okay. The last question. Find the heat current, which is uhh k A changing temperature of bodies. Okay. Is the time of conductivity is the cross sectional area and it is the diameter. Okay. So the assumption is that the cross sectional area is secular. So, the area is gonna be parties credible. four, I want to find D because I have the area. Right? So, if you put an a in this, you're gonna get 1.3 cm you need to convert that to meet us. So, this is uh this is the meters. Okay, The mucus and of course now I can put in my values and my feet current There's gonna be 2,009 jewels per second. Okay? Thank you very much, Yeah.


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