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spin [16.1K]
2 years ago
11

. Find the area of the regular dodecagon inscribed in a circle if one vertex is at (3, 0).

Mathematics
1 answer:
devlian [24]2 years ago
4 0

Answer:

Area of the regular dodecagon inscribed in a circle will be 27 square units.

Step-by-step explanation:

A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.

Since angle formed at the center by a polygon = \frac{360}{n}

Therefore, angle at the center of a dodecagon = \frac{360}{12} = 30°

Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units

Now area of a small triangle = \frac{1}{2}.(a).(b).sin\theta

where a and b are the sides of the triangle and θ is the angle between them.

Now area of the small triangle = \frac{1}{2}.(3).(3).sin30

= \frac{9}{4}

Area of dodecagon = 12×area of the small triangle

= 12×\frac{9}{4}

= 27 unit²

Therefore, area of the regular octagon is 27 square unit.

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What is 82×68 this is very hard
zubka84 [21]

Answer:

5576

Step-by-step explanation:

4 0
2 years ago
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In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home. Give the value of th
astra-53 [7]

Answer:

The value of the standard error for the point estimate is of 0.0392.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In a randomly selected sample of 100 students at a University, 81 of them had access to a computer at home.

This means that n = 100, p = \frac{81}{100} = 0.81

Give the value of the standard error for the point estimate.

This is s. So

s = \sqrt{\frac{0.81*0.19}{100}} = 0.0392

The value of the standard error for the point estimate is of 0.0392.

7 0
2 years ago
You build a seahorse hotel that’s 6 inches wide and 12 inches tall. It has a volume of 864 cubic inches. What is the hotel’s len
blondinia [14]

Answer:

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4 0
2 years ago
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Which statement explains how the lines 2x + y = 4 and y = one halfx + 4 are related?
KatRina [158]

Answer:

They are perpendicular

Step-by-step explanation:

To solve this problem .

we will convert the equations in slope intercept form.

Slope intercept  form of equation is y = mx+c

where m is slope of line and c is y intercept.

________________________________

equation 1 is

2x+y = 4

=> y =4 - 2x or y = -2x + 4

comparing it with y = mx + c

m = -2  , c = 4

_________________________________________

equation 2 is y = one halfx + 4 ( one half is same as 1/2)

so equation is

y = x/2 +4

comparing it with y = mx + c

m = 1/2  , c = 4

_________________________________________

Now lets evaluate options

They are parallel.  wrong option

For lines to be parallel slope should be same.

But here slope are different -2 and 1/2 .

Thus lines are not parallel.

__________________________________________

They are perpendicular.  correct option

For lines to be perpendicular, product of slope should be equal to -1.

-2*1/2 = -1

we can see that product of slope should be equal to -1 .

Thus lines are  perpendicular

______________________________________

They are the same line.  wrong option

For lines to be same both slope and y intercept should  be same.

Y intercept is same but the slopes are different -2 and 1/2  .

Thus lines are not  the same line.

__________________________________________

They are not related.       wrong option

As we have found that the lines are perpendicular .

So this option is intuitively wrong

4 0
3 years ago
PLEASE HELP ASAP 25 POINTS
Lisa [10]

We're going to go ahead and eliminate one answer out of the four. It <u>cannot be B</u> (the second answer) <em>because the graph is made of dotted lines. </em>

Dotted Lines = > or <

Solid Lines = ≤ or ≥

Next, let's focus on the straight line on the graph.

The equation for the line is  

y = x - 4

Since the shaded region is <em>below </em>the line,

the equation will be <u>y <  x - 4 </u>

We can now <u>eliminate </u>answer <u>A </u>

Since the second equation is y < - l x - 2 l

It will be shaded below the graph since it uses the ( < ) (less than symbol)


This means <em><u>the answer is  C</u></em>

Hope I helped, message me if you have any questions : )

8 0
3 years ago
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