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Express your answer to two significant figures and include the appropriate units.?
l = length of the metal block = 17.1 cm
w = width of the metal block = 3.2 cm
h = height of the metal block = 4.8 cm
V = volume of the metal block = to be determined
ρ = density of the metal block = to be determined
m = mass of the metal block = 1.5 kg
V = lwh
V = (17.1 cm)(3.2 cm)(4.8 cm)
V = 262.656 cm³
ρ = m/V
ρ = (1.5 kg)/(262.656 cm³)
ρ = 0.0057 kg/cm³ = 5.7 g/cm³ ANSWER
(a) Evaluate (684 µm)/(43 ms) to three significant figures… – Brainly.in – Add your answer and earn points. Now we need to find the answer in appropriate S.I units to three significant figures. So we have 684 μm = 684 x 10^-6 m….appropriate prefix express your answer to three significant figures and include the appropriate units. p: a value ro ? units 0.783 kg. Here, the only solution where the number of significant figures is three is gram. So, 0.783 kg If any other prefix is chosen then the significant figures will increase.ANSWER: Correct Part B At 4 ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Problem 6.21 A 3600 truck is parked on a 13 slope. Part A How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90.
Represent 0.783 kg with sl units having an appropriate prefix express… – Express your answer to two significant figures and include the appropriate units. Solution: The current i is flowing from the negative to the positive terminal; thus To two significant figures, power = -‐1300W or -‐1.3kW. Part B State whether the power is flowing from A to B or vice versa.High-level data models assist in conceptual design and helps express data requirements of the users and includes detailed descriptions of the 3.2 List the various cases where use of a null value would be appropriate. Null value would be appropriate when a Give examples to illustrate your answer.Get your answers by asking now.
Express your answer to two significant figures and include the… – SubmitPrev Previous Answers Request Answer X Incorrect; Try Again; 5 Attempts Remaining Part B 77 Ft/s Express Your Answer To Two Significant Figures And Include The Appropriate UnitsDo not include units in your numerical answers. The appropriate units should be shown just after the entry box. Eduspace uses the "E" notation for "times 10 to the" in scientific notation. For example, 56000, with 3 significant figures would be expressed 5.60 × 104, and should be entered in…In this case, all numbers including 2450 and between 2450 and 2550 (but not including 2550) are rounded to 2500 when rounding to the nearest 100. If you want to round off 2456 to 2 significant digits, you will need to write your answer with an accuracy of 100 units, but using only two figures.
Physics CH 0: General Introduction (9 of 20) Multiplying with Uncertainties in Measurements – .
Chemistry Lesson: Significant Digits & Measurements – .
Unit 2 Module 4 part 1 – In this next module, we're going to look
at another measure of association called the relative risks.
Instead of subtracting the risks in the different groups, what if we instead
divided them to make a ratio, that's called a relative risk.
There are several measures of relative risk and relative risks appear very
frequently in the medical literature. If you take two incidents rates and
divide them, that's called a rate ratio. You'll also see something in the
literature called a hazard ratio. A hazard ratio is also a ratio of
incidence rates. It's just a ratio of what we call
instantaneous incidence rates or hazard rates.
Hazard ratios actually come from a regression technique that we're going to
talk about much later in the course. But for now, you can just interpret them
exactly the same way you would interpret a rate ratio.
If you divide two cumulative risks, or two prevalences, we call that a risk
ratio. Now some people might call the ratio of
two prevalences a prevalence ratio, to distinguish it, but I tend to lump them
together and call them all a risk ratio because cumulative risks and prevalences
are both just proportions. Another measure of relative risk I'm
going to talk about a great deal this week is something called an odds ratio.
An odds ratio is a ratio of two odds and I'm going to have to tell you what an
odds is in a minute because you may not really understand what an odds is
already. But the odds ratio comes up a lot in the
medical literature for two reasons. The odds ratio is the only value measure
of relative risk for case control studies.
That's one reason. The other reason that odds ratios come up
a lot, is that a lot of researchers want to do a regression technique called
logistic regression. It's a multivariate regression technique
that's used when you have a binary outcome, and you want to adjust for
confounders. It turns out that logistic regression
gives you out odds ratios. So even if you're doing a covert study,
or a cross sectional study, if you use logistic regression, you're going to get
out odds ratios. So, odds ratios are all over the
literature. But as we're going to see in this module
and the next module, they're a little bit of a funny measure and sometimes they're
tricky to interpret. [BLANK<u>AUDIO] So how do we interpret
relative risk?</u> So the rate ratio and the hazard ratio,
you can interpret as the percent increase or decrease in the rate of the outcome.
The risk ratio is the percent increase or decrease in the risk or prevalence of the
outcome. The odds ratio is the percent increase or
decrease in the odds of the outcome, and again I'll fill you in on what an odds is
in a minute. If you have a relative risk that's equal
to 1.0, that means that the risks in the two groups are equal, because, say if the
risk is 20% in one group and 20% in the other group, if you divide 20% by 20%
you're going to get 1.0. So that represents where there's no
difference between the groups, we call that the null value.
If you have a relative risk that's less than one, that indicates a protective
effect. Whatever was in the numerator is
protecting you from the outcome. If you have a relative risk that's
greater than one, that indicates a harmful effect, an increased risk.
Let's calculate the rate ratio first starting with the GI event data from the
Vioxx study we've been talking about. Incident rates were 2.1 and 4.5 again.
All we have to do here to make a rate ratio is to divide the two incidents
rates. And notice because we're dividing two
rates, the units here, the 100 person-years actually cancels out.
And the rate ratio doesn't have any units, it's unitless.
We come out with a rate ratio of 0.46. The interpretation is that Vioxx reduces
the rate of GI events by 54%. I got that 54% simply by subtracting 1
minus 0.46. So that's a 40, 54% reduction in the rate
of GI events. If I want to calculate the risk ratio for
this same data, I'm just going to divide the risk in the Vioxx group by the risk
in the Naproxen group. Interestingly I get exactly the same a
number here, 0.46. So in this case the rate ratio and the
risk ratio are identical because, remember, the person-years of follow up
was exactly the same in both groups. So, if you're following people for the
same amount of time and the risk ratio and the weight ration would come out to
be the same. However, if there was a differential
follow up between the groups then this wouldn't be the case.
Because if one group was followed for longer than the other group, that would
increase the risk in the group that was followed longer, and it would change the
risk ratio compared with the, the rate ratio.
Now I want to read to you what they put in the pay, in the paper's abstract.
During a median follow-up of 9 months, 2.1 confirmed GI events per 100
patient-years occurred with the rofecoxib, that is the Vioxx group, as
compared with 4.5 per 100 patient years with naproxen.
Now they're going to give the relative risk.
The relative risk is 0.5 so they rounded up from 0.46 to, to 0.5.
95% confidence interval, 0.3 to 0.6 and it's highly statistically significant.
I want to spend just a minute here to walk you through what that confidence
interval means. We're going to spend a lot of time on
confidence intervals in an upcoming week of the course.
But I want to just give you sort of a conceptual understanding of what that
confidence interval means here. So the relative risk that we calculated
in the study, what we call the point estimate.
What we calculated in the study was exactly 0.46 rounded up to .5.
So that indicates a halving of risk. But that's just what we saw in the study.
And of course, whenever we do a study, we know that there's going to be some
uncertainty. In other words the true effect of Vioxx
on GI events might not be exactly 0.5. We understand that when we do a study,
there's uncertainty. We have to put a margin of error around
our estimate. That margin of error is what we call the
95% confidence interval. So the 95% confidence interval here is
0.3 to 0.6. That gives us a plausible range of values
for the true effect. The real effect of Vioxx on on GI events
we believe is somewhere between 0.3 and 0.6.
Another way to interpret it is we say we can be 95% confident that the true effect
of Vioxx verus naproxen is between a 40% and 70% reduction in the rate of GI
events. Where did that 40% and 70% come from?
The upper limit of the confidence interval is a relative risk of 0.6.
That's a 40% reduction in risk. The lower limit in the confidence
interval is a relative risk of 0.3. That's a 70% reduction in risk.
Now let's move to the heart attack data from the study.
What's the rate ratio going to be here. The rate ratio will be the rate in the
Vioxx group divided by the rate in the Naproxen group.
When you do that division it comes out to be 4.2, if the risk ratio is actually
identical, as I said before, because the groups should follow for equal amounts of
time. The risk ration and the rate ratio are
the same. How do we interpret these results?
We would interpret this that Vioxx increases the rate or risk of heart
attacks by fourfold, or you would say by 320%.
But let's see what the authors actually put in the abstract here.
So, here's the abstract from the paper. The incidence of myocardial infarction,
heart attack, was lower among patients in the naproxen group than among those in
the Vioxx group. 0.1% versus 0.4%.
We already saw that number in the last module.
Relative risk 0.2, 95% confidence interval, 0.1 to 0.7.
So notice that when the authors reported the data on GI events, they put the
naproxen in the denominator. They put the naproxen as the reference
group, but when they report the data on heart attacks, they're flipping things
around. They're making Vioxx the reference group.
They're putting Vioxx in the denominator. And you can probably think of the reason
that they might have wanted to do that. So there are actually two funny things
going on here, as I alluded to in the last module.
So firstly, they reported risks rather than rates.
For the primary outcome GI events, remember they actually reported the
incidence rates, they reported the risks here, likely because the risk difference
here looks smaller than the rate difference.
Secondly, they flipped the relative risk. They divided the risk in the Naproxen
group by the risk in the Vioxx group rather than the other way around.
So remember the risk in the Vioxx group was 0.42.
The risk in the Naproxen group is 0.1. If you divide 0.1 by 0.42 you get a
relative risk of 0.24 and they rounded down in the abstract to 0.2.
They rounded to one decimal place. So they twisted the message here, right.
They twisted the message to make it look like naproxen is protective rather than
that Vioxx is harmful. And technically, they haven't done
anything wrong mathematically. The numbers are correct.
But flipping the relative risk of course completely shifts the take home message,
and people missed it. Not one person wrote a letter to the
editor of the New England Journal, after this article was published, questioning
the author's logic here. People bought into the story that the
authors were trying to sell, that Naproxen is this miracle heart protective
drug. instead of that Vioxx is a dangerous
drug. Here's the, what they wrote in the
paper's conclusion. I showed you this in the teaser earlier.
Thus, our results are consistent with the theory that Naproxen has a coronary
protective effect. And highlight the fact that rofecoxib
Vioxx does not provide this type of protection.
The finding that naproxen therapy was associated with a lower rate of
myocardial infarction needs further confirmation in larger studies.
Of course, naproxen is the reference group, the control group in this study.
So every comparison really outta be Vioxx versus naproxen, not naproxen versus
Vioxx. But they totally put the focus on
naproxen to take the focus away from Vioxx and it worked.
in fact it turns out that naproxen has a very small, if any cardio protective
affect. So here was clear evidence sitting in the
literature in 2000 that Vioxx raises the risk of cardiovascular events.
Some people think that if if people had actually looked at this study more
carefully and kind of questioned the reasoning of the authors here, that Vioxx
might have actually been pulled off the shelves sooner than 2004.
The data were sitting here showing us that there's this cardio harmful effect
of nap, of Vioxx. And there's actually a lot of backstory
here that I'm not telling you. There was actually some data omitted from
the New England Journal of Med, of Medicine paper.
if you're interested in all of this, you can Google it, you can find out more
about this story. people made a big deal about the fact
that some of the heart, actually three heart attacks that probably should have
been included in that New England Journal paper that weren't.
But in fact, that data that was already available in the paper really told the
whole story. It's just that the authors had managed to
spin that story and people bought it. So the bigger lesson here, is that it's
very important when you're reading a medical paper to always look at the data
yourself. And then interpret the data yourself.
Because you allow the authors to lead you through their interpretation of the data,
you can easily get sucked into the story they want to tell you.
And that's what happened here. .