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3 years ago

A circle with area 9 pi, has sector with central angle of 17/9 pi radians

Mathematics

1 answer:

mr_godi [17]3 years ago

3 0

Answer:

The area of the sector is 17/2 π

Step-by-step explanation:

pi = π

To solve this problem we first have to find the fraction that corresponds to this angle of the total, for this we must divide the angle that they give us by 2π radians, since that is the angle of a circle

(17π/9 rad) / (2π rad) = 17/18

Now we multiply the area of the circle by this fraction and we will obtain the area of the sector that we want

9π * 17/18 = 17/2 π

The area of the sector is 17/2 π

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There are two diffrent maps of Ohio the scale on the first map is 1 cm to 5 km. The distance from Cleveland to Cincinnati is 25

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6.25 cm

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4 years ago

In a Harris poll, adults were asked if they are in favor of abolishing the penny. Among the responses,1229 answered "no," 484

Sholpan [36]

Answer:

C.^p=0.229The symbol p with caret<="">p is used to represent a sample proportion.

Step-by-step explanation:

Data given

1229 people answered "no"

484 people answered "yes"

400 people had no opinion

The grand total is 1229+484+400=2113 people

Let p= true proportion of yes responses for the population

$\hat p$ the proportion of yes estimated in th sample

Solution to the problem

The estimate population proportions is givn by the following formula:

$\hat p = \frac{X}{n}$

Where X represent the people with a characteristic specified and n the sample size. For our case we have this:

$\hat p =\frac{484}{2113}=0.229$

If we analyze one by one the possible options we have this:

A.p=0.229 The symbol p is used to represent a sample proportion

False the estimated proportion $\hat p$ is not equal to the population proportion p

B.^p=0.283 The symbol ^p is used to represent a sample proportion.

False, the estimated proportion of yes was 0.229 not 0.283

C.^p=0.229 The symbol p with caret<="">p is used to represent a sample proportion.

True, the estimated proportion of yes is 0.229 and the correct way to express the estimation is $\hat p$

D.p=0.283 The symbol p is used to represent a sample proportion.

False, the estimated proportion is 0.229 and not 0.283.

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4 years ago

Determine whether quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1) is a trapezoid.

lisabon 2012 [21]

Answer:

We are given a quadrilateral ABCD with vertices A(–4, –5), B(–3, 0), C(0, 2), and D(5, 1).

Step 1:

We find the slope of side AB.

with vertices A(-4,-5) and B(-3,0)

Hence, the slope of two points (a,b) and (c,d) is calculates as:

$\dfrac{d-b}{c-a}$

So, the slope of AB is:

$\dfrac{0-(-5)}{-3-(-4)}\\\\=\dfrac{5}{-3+4}\\\\=\dfrac{5}{1}=5$

Hence slope AB=5.

Step 2:

Now we have to find the slope of DC.

with vertices D(5,1) and C(0,2)

So, the slope of DC is:

$\dfrac{2-1}{0-5}\\\\=\dfrac{1}{-5}=-\dfrac{1}{5}$

Hence slope AB=-1/5.

Step 3:

slope of BC with vertices B(-3,0) and C(0,2) is:

$\dfrac{2-0}{0-(-3)}\\\\=\dfrac{2}{3}$

Step 4:

slope of AD with vertices A(-4,-5) and D(5,1) is:

$=\dfrac{1-(-5)}{5-(-4)}\\\\=\dfrac{1+5}{5+4}\\\\=\dfrac{6}{9}\\\\=\dfrac{2}{3}$

As we know that parallel sides have same slope.

As slope of BC=AD.

Hence AD is parallel to BC.

and the slope of two opposite sides are not equal hence the two sides are not parallel.

Hence, the given quadrilateral ABCD is a trapezoid. ( since it has a pair of opposite sides which are parallel and a pair of non-parallel opposite sides)

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3 years ago

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