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chubhunter [2.5K]
3 years ago
6

Find the area of the circle to find the nearest whole number. Use 3.14 or 22/7 for ip

Mathematics
1 answer:
sertanlavr [38]3 years ago
6 0

Answer:

You didn't provide the complete question as the radius or diameter of the circle isn't given. Please check the explanation below to see how to approach such questions.

Step-by-step explanation:

Area of a circle has a formula and it is given as:

Area = \pi r^{2}

where \pi is a constant and has a value of 3.14 or 22/7,

r is the radius of the circle (i.e the line drawn from the center of the circle to any point on the circle).

radius, r = diameter/2.

Example 1: Find the area of a circle with radius 7meters (7m) and correct to the nearest whole number. Use 3.14 or 22/7 for pi.

Solution:

Area = \pi r^{2} = \frac{22}{7} (7^{2})\\\\ Area = \frac{22}{7} (7)(7) = 22(7)\\\\ Area = 154squaremeters = 154m^{2}\\

NB: The unit of area is always in square units. In our case square meters

Example 2: Find the area of a circle with diameter 7feet(7ft). Use 3.14 or 22/7 for pi.

Solution:

Area = \pi r^{2}

But we were given the diameter not the radius.

Remember that I earlier said that radius, r = diameter/2 = \frac{7}{2}ft

Area = \frac{22}{7}(\frac{7}{2} )^{2} = \frac{22}{7} (\frac{7}{2} )(\frac{7}{2} )

Area = \frac{11(7)}{2} = \frac{77}{2} \\\\ Area = 36.5ft^{2}

So, if you have questions that ask for area, ensure you have the radius and if the diameter is given instead of the radius, carry out the neccessary calculation i.e. Diameter/2 to obtain the radius and use the area formula.

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Step-by-step explanation:

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The sides of a square are 3 2/7 inches long.<br> What is the area of the square?
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What is the slope of the linear function
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How do you simplify the value of (28x^4)÷(12x^3)?
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Our faucet is broken, and a plumber has been called. The arrival time of the plumber is uniformly distributed between 1pm and 7p
Ymorist [56]

Answer:

E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours

Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2

Step-by-step explanation:

Let A the random variable that represent "The arrival time of the plumber ". And we know that the distribution of A is given by:

A\sim Uniform(1 ,7)

And let B the random variable that represent "The time required to fix the broken faucet". And we know the distribution of B, given by:

B\sim Exp(\lambda=\frac{1}{30 min})

Supposing that the two times are independent, find the expected value and the variance of the time at which the plumber completes the project.

So we are interested on the expected value of A+B, like this

E(A +B)

Since the two random variables are assumed independent, then we have this

E(A+B) = E(A)+E(B)

So we can find the individual expected values for each distribution and then we can add it.

For ths uniform distribution the expected value is given by E(X) =\frac{a+b}{2} where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:

E(A)=\frac{1+7}{2}=4 hours

The expected value for the exponential distirbution is given by :

E(X)= \int_{0}^\infty x \lambda e^{-\lambda x} dx

If we use the substitution y=\lambda x we have this:

E(X)=\frac{1}{\lambda} \int_{0}^\infty y e^{-\lambda y} dy =\frac{1}{\lambda}

Where X represent the random variable and \lambda the parameter. If we apply this formula to our case we got:

E(B) =\frac{1}{\lambda}=\frac{1}{\frac{1}{30}}=30min

We can convert this into hours and we got E(B) =0.5 hours, and then we can find:

E(A+B) = E(A)+E(B)=4+0.5 =4.5 hours

And in order to find the variance for the random variable A+B we can find the individual variances:

Var(A)= \frac{(b-a)^2}{12}=\frac{(7-1)^2}{12}=3 hours^2

Var(B) =\frac{1}{\lambda^2}=\frac{1}{(\frac{1}{30})^2}=900 min^2 x\frac{1hr^2}{3600 min^2}=0.25 hours^2

We have the following property:

Var(X+Y)= Var(X)+Var(Y) +2 Cov(X,Y)

Since we have independnet variable the Cov(A,B)=0, so then:

Var(A+B)= Var(A)+Var(B)=3+0.25 hours^2=3.25 hours^2

3 0
3 years ago
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