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Maslowich
2 years ago
14

Shaded area is 54 pi cm squared. Find X

Mathematics
2 answers:
EleoNora [17]2 years ago
8 0

Answer:

  x = 3π/4 radians = 135°

Step-by-step explanation:

The area of a sector of central angle α is ...

  A = (1/2)r²α

Filling in the given values, we can find the central angle to be ...

  54π cm² = (1/2)(12 cm)²x

  x = (54π)/(72) = 3/4π . . . . radians

  x = 135°

Tanzania [10]2 years ago
7 0

Answer:

Step-by-step explanation:

The shaded area is a sector of the circle. The formula for determining the area of a sector is expressed as

expressed as

Area of sector = θ/360 × πr²

Where

θ represents the central angle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 12 cm

θ = x°

Area of sector = 54π

Therefore,

54π = x/360 × π × 12²

54π × 360 = x × π × 12

19440π = 144πx

Dividing through by π, it becomes

19440 = 144x

x = 19440/144

x = 135°

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The summer monsoon brings 80% of India's rainfall and is essential for the country's agriculture.
Natasha_Volkova [10]

Answer:

Step 1. Between 688 and 1016mm. Step 2. Less than 688mm.

Step-by-step explanation:

The <em>68-95-99.7 rule </em>roughly states that in a <em>normal distribution</em> 68%, 95% and 99.7% of the values lie within one, two and three standard deviation(s) around the mean. The z-scores <em>represent values from the mean</em> in a <em>standard normal distribution</em>, and they are transformed values from which we can obtain any probability for any normal distribution. This transformation is as follows:

\\ z = \frac{x - \mu}{\sigma} (1)

\\ \mu\;is\;the\;population\;mean

\\ \sigma\;is\;the\;population\;standard\;deviation

And <em>x</em> is any value which can be transformed to a z-value.

Then, z = 1 and z = -1 represent values for <em>one standard deviation</em> above and below the mean, respectively; values of z = 2 and z =-2, represent values for two standard deviations above and below the mean, respectively and so on.

Because of the 68-95-99.7 rule, we know that approximately 95% of the values for a normal distribution lie between z = -2 and z = 2, that is, two standard deviations below and above the mean as remarked before.

<h3>Step 1: Between what values do the monsoon rains fall in 95% of all years?</h3>

Having all this information above and using equation (1):

\\ z = \frac{x - \mu}{\sigma}  

For z = -2:

\\ -2 = \frac{x - 852}{82}

\\ -2*82 + 852 = x

\\ x_{below} = 688mm

For z = 2:

\\ 2 = \frac{x - 852}{82}

\\ 2*82 = x - 852

\\ 2*82 + 852 = x

\\ x_{above} = 1016mm

Thus, the values for the monsoon rains fall between 688mm and 1016mm for approximately 95% of all years.

<h3>Step 2: How small are the monsoon rains in the driest 2.5% of all years?</h3>

The <em>driest of all years</em> means those with small monsoon rains compare to those with high values for precipitations. The smallest values are below the mean and at the left part of the normal distribution.

As you can see, in the previous question we found that about 95% of the values are between 688mm and 1016mm. The rest of the values represent 5% of the total area of the normal distribution. But, since the normal distribution is <em>symmetrical</em>, one half of the 5% (2.5%) of the remaining values are below the mean, and the other half of the 5% (2.5%) of the remaining values are above the mean. Those represent the smallest 2.5% and the greatest 2.5% values for the normally distributed data corresponding to the monsoon rains.

As a consequence, the value <em>x </em>for the smallest 2.5% of the data is precisely the same at z = -2 (a distance of two standard deviations from the mean), since the symmetry of the normal distribution permits that from the remaining 5%, half of them lie below the mean and the other half above the mean (as we explained in the previous paragraph). We already know that this value is <em>x</em> = 688mm and the smallest monsoons rains of all year are <em>less than this value of x = </em><em>688mm</em>, representing the smallest 2.5% of values of the normally distributed data.

The graph below shows these values. The shaded area are 95% of the values, and below 688mm lie the 2.5% of the smallest values.

3 0
3 years ago
Can the polynomial below be factored into a perfect square? If not, select the answer that best describes why not.
pickupchik [31]

Answer:

C. It cannot be factored into a perfect square.

Step-by-step explanation:

Take the square roots of all the numbers present (64, 49, 8) and you will find that 8, the constant, is not a perfect square.

8 0
2 years ago
PLEASEEEEEEEEEEEEEEEEEEEEEE Edgar rolls two six-sided number cubes. What is the probability that he rolls a 2 on
frutty [35]

Answer:

The probability that he rolls a sum of 9 given the sample space is . 9/36, or 1/4.

What is the probability?

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The probability that he rolls a sum of 9 = cubes that have a sum of 9 / total number of cubes

9/36 = 1/4

5 0
2 years ago
3x + 2y = 2
iragen [17]
A) (-2,4) hope this helps 
6 0
3 years ago
Who needs help below 8th grade
luda_lava [24]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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