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(h) Suppose it is claimed that the mean distance for an object traveling at km/s is 0.8 Mpc Would you reject this claim? (You have only one attempt) Fail to reject ...

Question

(h) Suppose it is claimed that the mean distance for an object traveling at km/s is 0.8 Mpc Would you reject this claim? (You have only one attempt) Fail to reject this claimReject this claim(i) Compute 95% prediction interval for the mean distance when velocity Lower: Mpc and Upper: Mpckm/s_ (Use 3 decimal places)Based on your prediction interval, is it plausible that an object traveling at km/s is on Earth (0 Mpc away)? (You have only one attempt) PlausibleImplausible

(h) Suppose it is claimed that the mean distance for an object traveling at km/s is 0.8 Mpc Would you reject this claim? (You have only one attempt) Fail to reject this claim Reject this claim (i) Compute 95% prediction interval for the mean distance when velocity Lower: Mpc and Upper: Mpc km/s_ (Use 3 decimal places) Based on your prediction interval, is it plausible that an object traveling at km/s is on Earth (0 Mpc away)? (You have only one attempt) Plausible Implausible



Answers

Suppose you observe two galaxies: one at a distance of $10.7 \mathrm{Mpc}$ with a recessional velocity of $580 \mathrm{km} / \mathrm{s}$, and another at a distance of 337 Mpc with a radial velocity of 25,400 $\mathrm{km} / \mathrm{s}$. a. Calculate the Hubble constant ( $H_{0}$ ) for each of these two observations. b. Which of the two calculations would you consider to be more trustworthy? Why? c. Estimate the peculiar velocity of the closer galaxy. d. If the more distant galaxy had this same peculiar velocity, how would your calculated value of the Hubble constant change?

In this exercise, we have a project tile that's launched on Earth. Okay, here is the surface and we know that in order to make all the calculations that chapter 3.5 did we have to consider that the force of gravity is always pointing hours to this interruption. And this amounts to disregard completely the curvature of the earth. Because otherwise we know that Ah, gravity is pointing towards the centre of the earth. So, actually, if this is the Earth, I'm sorry. This is the earth. Gravity is always pointing to the center, So gravity here, the gravity, the force of gravity changes. It's direction depending on where on the earth you are. But the thing is, uh, so not considering that the earth has a curvature is the same insane flat. So why is it a good scientific supposition to to say that when we're calculating project highest trajectories, it's reasonable to consider that locally, the earth is flat? And that's mainly because the radius of the earth is much bigger than the range of the project time. So, for example, I'm gonna draw here. I say this is part of yours. Okay, This is part of the earth here on the the right side. And then you throw a projectile, OK, notice that the earth is much, much bigger than the range of the project time. This is the range, and the radius of the earth is waving. Or so the rate is go way up there. Wait. Now there. Uh, So if you zoom in, if you take this part of the earth and zoom in locally, the curvature of the earth is gonna be so small that you're not gonna be able to see anything. OK, so it's gonna be almost flat so locally. It's a good supposition to suppose that ah, the earth is more or less flat because through all the trajectory of the project tile, the direction of the acceleration of gravity will not change much. That would change if the Project tile waas thrown between two continents, for example. Then we would have to take into account the change in the direction of the acceleration of gravity. But for most daily ah situations, it's perfectly useful to consider that the earth is locally flat. This is me that the earth is flat as a whole. It just means that locally, it's a good approximation to make this supposition

Everybody. So here is We need to fund Were given a 50 100 1500 for the Hubble. And we're just trying to figure out the, um yes, I can't hear. One year divided by 3.154 times 10 to 7 seconds. Okay. Divided by. And we actually, we're gonna, like, make sure this is a little bigger. Other by Tobi Um, em he see, um times 3.86 times 10 to the 19 kilometers. About a but PC. Okay, in this whole thing and we Pallister calculators will be 1.95 times 10 to the 10 years. Um, you could put in billions if you want, but we don't have Teoh. And now what's going dio the 100 kilometers and this whole thing is the exact same thing of above, But, uh, I'll just write it humor you, Um but for your own work, you don't need to unless you have a teacher that wants you to completely show you work everywhere you go, um, or unless you personally get lost. And, um, all these units were given to is actually in the previous problem. Um, so if You're curious how I got the number it was already given to us in the book. Good. And this one is going to eagle 9.78 times, 10 to the nine years. And actually, you can just write this technically as 10 billion years. Um, as well. If you round it up, it's not gonna hurt you. You do that. Okay. But we can keep it in years for my keep everything kind of the same. But technically, it is about close to, um, 10 billion years. Okay. Thank you, God.

What we have here is a graph showing two data points. Measurements of temperature taken at a specific altitude. Hey, our temperatures in degrees Celsius or else to his kilometers. So you can see, At 3.2 kilometers, the temperature recorded was eight degrees, and it's 6.1 kilometers. The temperature recorded was negative, 10.3 degrees Celsius. So according to the mean value, the're, um can we say for 100% um, assurance that somewhere between these two data points here and here that we're going to exceed the lapse rate off seven degrees Celsius per kilometre. Try it. So what we need to do is find out what the lobster it is here or what? The rate of change is here. Okay, so the way we do that is our slow formula. Okay, so I'm going to take eight, and I'm going to subtract. Negative 10.3. I'm gonna take 3.2. It's attract 6.1. This is gonna give me 18.3 down here. I'm gonna have a negative 2.9. Okay, we calculate that out. We get negative. Six weight, 31 degrees Celsius per kilometre. Okay, because this does not exceed seven degrees Celsius per kilometer, which is the lapse rate were asking about, we can say for certain. Or we can say that there is no certainty that somewhere between these two points that we will exceed the lapse rate of seven degrees Celsius her kilometer.

15 is the valiant fear. I accept that if it is a continuous function on the clothes they Turkle A and B and the friendship on the open in terrible ah A and be a vendor exist a point c b such that it's a special season. Quinto every B minus very over B minus. And so, uh, we are given that f off three a point is equal to eight. And if off 6.1 is equal to negative. Kim publicly. Therefore, if Dash C on a minus 8/6 0.1 minor, three point and Muslims equal toe negative, 6.3 sleet is dumped from this, we cannot conclude that and the lapse rate exceed the three short value off. Seven A sleazy is where kilometer on some intermediate innovations.


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