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Mumz [18]
3 years ago
5

find the area of the shaded sector, in square meters. leave your answer in terms of pi. need answer please help.

Mathematics
1 answer:
jasenka [17]3 years ago
6 0
Area of circle:
A = <span>πr^2
A = </span><span>π(8^2)
A = 64</span><span>π

Area of shaded:
135/360 = x / 64</span><span>π
360x = 8640</span><span>π
      x = 24</span><span>π

Answer
B. 24</span><span>π</span>
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blondinia [14]

Answer:

Length: 10

Surface Area: 20

Step-by-step explanation:

Length:

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240/24=10

Surface Area:

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6 0
3 years ago
An article suggested that yield strength (ksi) for A36 grade steel is normally distributed with μ = 42 and σ = 5.5.
alexandr1967 [171]

Answer:

a)P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

b) For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

X \sim N(42,25.5)  

Where \mu=42 and \sigma=5.5

And we want this probability:

P( X

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X

We want this probability:

P( X >64)

And using the z score formula given by:

z = \frac{x -\mu}{\sigma}

We got:

P( X >64) =P(Z> \frac{64-42}{5.5}) =P(Z>4)=0.0000316

Part b

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.25   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=0.674

And if we solve for a we got

a=42 +0.674*5.5=45.707

So the value of height that separates the bottom 75% of data from the top 25% is 45.707.  

8 0
3 years ago
Chin-li is building a brick wall along the front of his property. The wall will have 15 rows of bricks, with 32 bricks in each r
Finger [1]

Answer:

<h3>The solution is 480 bricks.</h3>

Step-by-step explanation:

We are given that number of rows of bricks in a wall = 15 rows.

Number of bricks in a row = 32 bricks.

In order to find the total number of bricks, we need to multiply number of rows with number of bricks in a row.

Total number of bricks in 15 rows = 15 × 32 = 480 bricks.

Therefore, will Chin-li will need 480 bricks.

<h3>The solution is 480 bricks.</h3>
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3 years ago
A dog's adult weight is 60 pounds. As a puppy, it is 10% of its adult weight. How much does it weigh as a puppy?
Oksi-84 [34.3K]

Answer:

Puppy weight= 6 pounds

Step-by-step explanation:

Giving the following information:

Adult weight= 60 pounds

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<u>To calculate the weight in pounds of a puppy, we need to use the following formula:</u>

Puppy weight= adult weight*puppy weight rate

Puppy weight= 60*0.1

Puppy weight= 6 pounds

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2 years ago
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faltersainse [42]
The answer is 3√5. You use the distance formula: √((x2-x1)^2+(y2-y1)^2)
3 0
3 years ago
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