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4 years ago

A coin has a diameter of 24.26 mm. What is the area of one face of the coin? Give your answer correct to 2 decimal places.

Mathematics

1 answer:

ivanzaharov [21]4 years ago

4 0

Answer:

462.2 mm

Step-by-step explanation:

R is radius and diameter is like 2r so divide the diameter by 2 which is 12.13

then 12.13 times 12.13 is 147.14 (rounded up)

the 147.14 times pie is 462.2 mm

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Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. Whe

kherson [118]

Answer:

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

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

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".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

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 $ME =\pm 0.03$ 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 don't have a prior estimation for the proportion $\hat p$ so we can use 0.5 as an approximation for this case

And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

5 0

3 years ago

Is 21 a multiple of 6

JulijaS [17]

No, 21 is a multiple of 7

8 0

3 years ago

Answer the following questions in complete sentences.

Anna71 [15]

The answer for both of these would be a rectangle.

A rectangular prism has 6 faces, all of which are rectangles. Slicing the prism parallel to any of the faces, whether they are end faces or bases, will result in a rectangular cross-section.

6 0

4 years ago

What is the next term in the pattern? 0.2, 0.22, 0.222, . . .

quester [9]

It would be 0.2222 so it's your answer

5 0

3 years ago

Read 2 more answers

An 8 oz glass of grape juice contains 0.6 mg of iron. About what percent of RDA of iron for an 15 year old male is provided by 8

babymother [125]

Answer:

5.45%

Step-by-step explanation:

To find info of a 15 year old male, you look at the Age Group of 14 - 18, beside Male.

The RDA of Iron is given as 11 mg

From a 8 oz glass of grape juice, he gets 0.6 mg.

<em>What percent is 0.6 mg of total 11 mg??</em>

Divide 0.6 by 11 and then multiply by 100 to get the answer. So we have:

$\frac{0.6}{11}=0.0545*100=5.45$

Thus, 5.45% of RDA of iron is provided by an 8 oz glass of grape juice.

6 0

4 years ago