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Setler79 [48]
3 years ago
12

What fraction of a given sample of radioactive nuclide remains after four half lives?

Mathematics
2 answers:
horsena [70]3 years ago
7 0
<span>1 half-life: 1/2 left 

2: half of that, or 1/4 

3: half of that, or 1/8 

4: half of that, or 1/16 

. (1/2)^4 = 1/16
so</span><span>after four half lives it would be 1/16
so correct option is D
</span>
Black_prince [1.1K]3 years ago
5 0
I believe the answer is D. 1/16.
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Step-by-step explanation:

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The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitor
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Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

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Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

We can use as an estimator for p \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16  

And rounded up we have that n=385

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3 years ago
The diagram shows the ratio of trees Maeve plants to the trees she harvests.
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Answer:

WEDNESDAY: 45 planted.

THURSDAY: 22 Harvested.

Step-by-step explanation:

Based on the information given in the problem, Maeve plants 5 trees for every 2 tree she harvests. Then the ratio can be expressed as following:

5:2 or \frac{5}{2}

Then, you can complete the values in the table as you can see below:

<u>WEDNESDAY</u>

\frac{5}{2}=\frac{planted}{18}\\\\planted=\frac{18*5}{2}\\\\planted=45

<u>THURDAY</u>

\frac{5}{2}=\frac{55}{harvested}\\\\(harvested)(\frac{5}{2})=55\\\\harvested=\frac{55*2}{5}\\\\harvested=22

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