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3 years ago

Define a minor arc. How do you name a minor arc?

Mathematics

2 answers:

Sonja [21]3 years ago

7 0

A minor arc is defined as an arc of a circle that consists of a measurement less than or equal to radians. The measure of a minor arc is always less than 180 degrees. When naming a minor arc, you should two letters on the circle. Major arcs and semicircles use three letters.

aleksklad [387]3 years ago

5 0

Answer:

If the arc length is less than 180 degrees, then it is called minor arc.

Minor arc length = m(AB), where "A" and "B" are the end points of the arc length.

Step-by-step explanation:

If you take two points on the circle and connect the points to the center of the the circle (radius). You will get the arc length subtend by the radi.

If the arc length is less than 180 degrees, then it is called minor arc.

If the arc length is greater than 180 degrees, then it is called major arc.

Minor arc is shortest arc length and major arc is the longest arc length.

The arc length marked with the endpoints of the arc length.

If you name the two points A and B of the minor arc.

The measure of the minor arc length represented by m(AB)

Herewith I have attached the figure.

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A government report gives a 99% confidence interval for the proportion of welfare recipients who have been receiving welfare ben

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The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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".

Solution to the problem

The population proportion have the following distribution

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

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

The estimation for the proportion for this case is $\hat p = 0.21$

And we know that the 99% confidence interval is given by:

$0.21 \pm 0.045$

So then the margin of error at 99% of confidence is 0.045, and the margin of error is given by this formula:

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

If we decrease the confidence level this margin of error can't be higher than 0.045 so then the correct answer for this case would be:

d. 21% ± 4.8%

Because if the z value decrease from 2.58 to 1.96 not makes sense that the margin of error increase from 0.045(4.5%) to 0.048(4.8%)

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3 years ago