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2 years ago

What is Half of 2pi/3

Mathematics

2 answers:

lukranit [14]2 years ago

8 0

Answer: The half of $\dfrac{2\pi}{3}$ is $\dfrac{\pi}{3}.$

Step-by-step explanation: We are given to find the half of $\dfrac{2\pi}{3}.$

Let us consider that

$x=\dfrac{2\pi}{3}.$

Then, the half of x is given by

$\dfrac{1}{2}x=\dfrac{1}{2}\times\dfrac{2\pi}{3}=\dfrac{\pi}{3}.$

Thus, the half of $\dfrac{2\pi}{3}$ is $\dfrac{\pi}{3}.$

kaheart [24]2 years ago

6 0

Is that cos (2pi/3) or cos^2 (pi/3) ????
1/2 of 2 =1
cos (2pi/3) = - 1/2 
cos (pi/3) = 1/2
cos^2 (pi/3) = 1/4

take your pick!

pi/3 radians = 60 degrees, and cos is looking for the side adjacent to the 60 degree angle
in a 30-60-90 triangle, the sides are in the ratio 1-sqrt(3)-2
so cos 60 = 1/2

2(pi/3) = 120 degrees-- the same triangle, except now, x is negative ==> cos 2pi/3 = -1/2

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What is the area of the shaded region?

azamat

Answer:

$(25\pi\ -24)\ cm^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the circle minus the area of the two isosceles triangles

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

where r is the radius of the circle

In this problem we have

$r=5\ cm$

substitute

$A=\pi (5)^{2}$

$A1=25\pi\ cm^{2}$

Find the area of the two triangles

The area of the two isosceles triangles is equal to

$A=2[\frac{1}{2}bh]=bh$

we have

$b=6\ cm$

$h=5-1=4\ cm$

substitute

$A2=6*4=24\ cm^{2}$

Find the area of the shaded region

$A1-A2=(25\pi\ -24)\ cm^{2}$

5 0

2 years ago

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Mason owns a trucking company. For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an

emmasim [6.3K]

Answer: The required system of equations are

y = 30x

13x + y = 258

Step-by-step explanation:

Let x represent the number of hours

that the driver worked.

Let y represent the number of miles that the truck drove.

For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. If on a particular day, his total expenses for the driver, gas and truck maintenance were $258, it means that

13x + y = 258

On that particular day, the driver drove an average of 30 miles per hour.

Speed = distance/time

It means that

y/x = 30

y = 30x

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2 years ago

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An online article about an opinion poll says that "41% of Americans own a gun." The poll is based on online survey interviews wi

sergejj [24]

Answer:

See below

Step-by-step explanation:

A) The population of the poll is the United States Population EXCLUDING New England States. In other words, the population is all USA population except the New England population. Remember that population is all the set of individuals from where you extract your sample. The sample are those 2,700 adults interviewed.

B) The sampling used is, as said in the statement, a randome sampling.

C) Yes! There could be a bias because of the exclusion of New England States if the people who lives there tends to have more guns than the average american population. This could be, for example, due to that those states have the least gun owning in America or, contrary, if they have the highest. If Rode Island is the most violent state and has the highest gun owning rate, the results could be biased. However, we can't confirm it without seeing the data, but there is possible.

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2 years ago

Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in

Hitman42 [59]

Answer:

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

(3) A survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

Step-by-step explanation:

We are given that a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of Americans who decide to not go to college = 48%

n = sample of American adults = 331

p = population proportion of Americans who decide to not go to

college because they cannot afford it

Here for constructing a 90% confidence interval we have used a One-sample z-test for proportions.

So, 90% confidence interval for the population proportion, p is ;

P(-1.645 < N(0,1) < 1.645) = 0.90 {As the critical value of z at 5% level

of significance are -1.645 & 1.645}

P(-1.645 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.645) = 0.90

P( $-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\hat p-p$ < $1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

P( $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.90

90% confidence interval for p = [ $\hat p-1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.645 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.48 -1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ , $0.48 +1.96 \times {\sqrt{\frac{0.48(1-0.48)}{331} } }$ ]

= [0.4348, 0.5252]

(1) Therefore, a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it is [0.4348, 0.5252].

(2) The interpretation of the above confidence interval is that we can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval.

3) Now, it is given that we wanted the margin of error for the 90% confidence level to be about 1.5%.

So, the margin of error = $Z_(_\frac{\alpha}{2}_) \times \sqrt{\frac{\hat p(1-\hat p)}{n} }$

$0.015 = 1.645 \times \sqrt{\frac{0.48(1-0.48)}{n} }$

$\sqrt{n} = \frac{1.645 \times \sqrt{0.48 \times 0.52} }{0.015}$

$\sqrt{n}$ = 54.79

n = $54.79^{2}$

n = 3001.88 ≈ 3002

Hence, a survey should include at least 3002 people if we wanted the margin of error for the 90% confidence level to be about 1.5%.

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2 years ago

A student solved the problem below by first dividing 20 by 10. What mistake did the student make? A baseball team has won 20 gam

andreev551 [17]

Answer:

Step-by-step explanation: The student divided the number of wins by the number of losses.

The student should have divided the number of wins by the total number of games.

The student should have first added 20 and 10 to find that there were a total of 30 games.

8 0

2 years ago

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