What is equivalent to 12\16?

d1i1m1o1n [39]

Ah! I love these questions!

To find the area of the shaded region, you must find the area of the circle. Then, you must find the area of the triangle inscribed in the circle. Lastly, you must subtract the area of the triangle from the area of the circle.

Area of Circle: $\pi$ x $r^{2}$
= $\pi$ x 10^2
= $\pi$ x 100
Usually these problems will not require you to convert pi into a decimal, but if it does, then the area of the circle would be 314.

Area of Equilateral Triangle: $\frac{ s^{2} \sqrt{3} }{4}$
To find the side, draw a perpendicular line from the center to a side of a triangle. This line will create two more triangles inside the big triangle. You will notice how in these smaller triangles, the angles are 30, 60, 90. From that we can deduce that half the length of a side is 5 $\sqrt{3}$ because of the 30, 60, 90 ratio. Multiply that by 2 to get 10 $\sqrt{3}$ as the length of the side of the large triangle. Now substitute this value into the formula above.
$\frac{ (10 \sqrt{3}) ^{2} x \sqrt{3} }{4} = \frac{300 \sqrt{3} }{4} = 75 \sqrt{3}$

Final Answer: 100 $\pi$ - 75 $\sqrt{3}$

6 0

3 years ago

Assume that the ages for first marriages are normally distributed with a mean of 26 years and a standard deviation of 4 years. W

Snowcat [4.5K]

Answer:

0.7743

Step-by-step explanation:

Mean of age = u = 26 years

Standard Deviation = $\sigma$ = 4 years

We need to find the probability that the person getting married is in his or her twenties. This means the age of the person should be between 20 and 30. So, we are to find P( 20 < x < 30), where represents the distribution of age.

Since the data is normally distributed we can use the z distribution to solve this problem. The formula to calculate the z score is:

$z=\frac{x-u}{\sigma}$

20 converted to z score will be:

$z=\frac{20-26}{4}=-1.5$

30 converted to z score will be:

$z=\frac{30-26}{4}=1$

So, now we have to find the probability that the z value lies between -1.5 and 1.

P( 20 < x < 30) = P( -1.5 < z < 1)

P( -1.5 < z < 1 ) = P(z < 1) - P(z<-1.5)

From the z-table:

P(z < 1) = 0.8413

P(z < -1.5) =0.067

So,

P( -1.5 < z < 1 ) = 0.8413 - 0.067 = 0.7743

Thus,

P( 20 < x < 30) = 0.7743

So, we can conclude that the probability that a person getting married for the first time is in his or her twenties is 0.7743

6 0

3 years ago

I got 10.6 am i wrong?

lubasha [3.4K]

Answer:

15.3

Step-by-step explanation:

because 15 is the number I think

7 0

3 years ago

What does break-even mean in Maths Lit

Readme [11.4K]

Answer:

Break-even point is where the business is at an activity level (doing business) at which total cost = total sales, i.e. you have made enough income to cover the costs.

4 0

3 years ago

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Determine the value for which the rational expression 5x/6x

KiRa [710]

Step-by-step explanation:

5x/6x
(5/6)×(x/x)

Here, x cancels each others

5/6
0.833

8 0

3 years ago

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