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3 years ago

15

Fiona drew a regular polygon that first maps directly onto itself after rotating 15 degrees. How many sides does the polygon hav

e? 12 15 24 48

1 answer:

AlexFokin [52]3 years ago

5 0

Answer:

24

Step-by-step explanation:

Let n = number of sides

15n = 360

divide both sides of the equation by 15

n = 24

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How to calculate confidence interval with standard deviation?

barxatty [35]

Confidence interval of a standard deviation

A confidence interval can be computed for almost any value computed from a sample of data, including the standard deviation.

The SD of a sample is not the same as the SD of the population

It is straightforward to calculate the standard deviation from a sample of values. But how accurate is that standard deviation? Just by chance you may have happened to obtain data that are closely bunched together, making the SD low. Or you may have randomly obtained values that are far more scattered than the overall population, making the SD high. The SD of your sample does not equal, and may be quite far from, the SD of the population.

Confidence intervals are not just for means

Confidence intervals are most often computed for a mean. But the idea of a confidence interval is very general, and you can express the precision of any computed value as a 95% confidence interval (CI). Another example is a confidence interval of a best-fit value from regression, for example a confidence interval of a slope.

The 95% CI of the SD

<span>The sample SD is just a value you compute from a sample of data. It's not done often, but it is certainly possible to compute a CI for a SD. GraphPad Prism does not do this calculation, but a free GraphPad QuickCalc does.</span>

Interpreting the CI of the SD is straightforward. If you assume that your data were randomly and independently sampled from a Gaussian distribution, you can be 95% sure that the CI contains the true population SD.

How wide is the CI of the SD? Of course the answer depends on sample size (n). With small samples, the interval is quite wide as shown in the table below.

n 95% CI of SD

2 0.45*SD to 31.9*SD

3 0.52*SD to 6.29*SD

5 0.60*SD to 2.87*SD

10 0.69*SD to 1.83*SD

25 0.78*SD to 1.39*SD

50 0.84*SD to 1.25*SD

100 0.88*SD to 1.16*SD

500 0.94*SD to 1.07*SD

1000 0.96*SD to 1.05*SD

Example

Data: 23, 31, 25, 30, 27

Mean: 27.2

SD: 3.35

The sample standard deviation computed from the five values is 3.35. But the true standard deviation of the population from which the values were sampled might be quite different. From the n=5 row of the table, the 95% confidence interval extends from 0.60 times the SD to 2.87 times the SD. Thus the 95% confidence interval ranges from 0.60*3.35 to 2.87*3.35, from 2.01 to 9.62. When you compute a SD from only five values, the upper 95% confidence limit for the SD is almost five times the lower limit.

Most people are surprised that small samples define the SD so poorly. Random sampling can have a huge impact with small data sets, resulting in a calculated standard deviation quite far from the true population standard deviation.

Note that the confidence interval is not symmetrical around the computed SD. Why? Since the SD is always a positive number, the lower confidence limit can't be less than zero. This means that the upper confidence interval usually extends further above the sample SD than the lower limit extends below the sample SD. With small samples, this asymmetry is quite noticeable.

Computing the Ci of a SD with Excel

These Excel equations compute the confidence interval of a SD. n is sample size; alpha is 0.05 for 95% confidence, 0.01 for 99% confidence, etc.:

Lower limit: =SD*SQRT((n-1)/CHIINV((alpha/2), n-1))

<span>Upper limit: =SD*SQRT((n-1)/CHIINV(1-(alpha/2), n-1))
</span>

7 0

3 years ago

Is .75 degrees a positive or a negative <br> Is 0.75degrees a positive or a negative

Neko [114]

as long as it is at least a decimal <u>above 0.00</u> then any number is positive.

<h2><u>yes it is positive.</u></h2>

good luck

5 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for fraction bar(s)

Bingel [31]

Answer: f(x) = 4 if -1 ≤x ≤ 1

f(x) = x - 1 if 3≤ x ≤ 5

Step-by-step explanation:

if -1 ≤x ≤ 1

We can see that in this range the function is constant, f(x) = 4

if 3≤ x ≤ 5

In this region we can see a linear relationship, with the points (3, 2) and (5, 4)

as the extremes, we can find the slope of this linear equation as:

s = (4 - 2)/(5 - 3) = 2/2 = 1

So our equation is

f(x) = 1*x + b

to find the value of b we can evaluate our function in the first point, we know that when x = 3, y = 2, so we have:

2 = 1*3 + b

b = 2- 3 = -1

then f(x) = 1*x - 1

Then we have:

f(x) = 4 if -1 ≤x ≤ 1

f(x) = x - 1 if 3≤ x ≤ 5

6 0

3 years ago

Find area of the shaded region.

Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

$\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}$

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

$\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}$

Now, we can find the area of the triangle. We can use an alternative formula:

$\displaystyle A=\frac{1}{2}ab\sin(C)$

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

$\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)$

The area of the shaded region is equivalent to the sector minus the triangle:

$A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}$

Therefore:

$A_{\text{shaded}}=15\pi -18\sin(150)$

Use a calculator:

$A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2$

The area of the shaded region is about 38.1 square centimeters.

6 0

3 years ago

NEEXDD QUICK ANSWER TIMED TEST

IRINA_888 [86]

First option because the (or) means the arrows aren’t connected and the open circle means not equal to and closed circle vice versa

8 0

3 years ago