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laiz [17]
3 years ago
10

If r = 3.2, what is the area of the shaded region? Round your answer to the nearest hundredth. Use your calculator's value of π.

Mathematics
1 answer:
MrRa [10]3 years ago
8 0

Answer: The shaded area is 99.55 units squared.

Step-by-step explanation:

r = 3.2

Now, we can see that the sides of the square are equal to two times the diameter of the circles (or four times the radius of the circles), so the length of the sides of the square is:

L = 2*(2*3.2) = 12.8

The area of the square is A1 = L^2 = 12.8*12.8 = 163.84 units squared.

the shaded semicircle has a diameter of 4 times r (so the radius is 2 times r), and the area is equal to half the area of a circle:

A2 = (1/2)*pi*(2r)^2 = (1/2)*3.14*(6.4)^2 = 64.31 units squared.

And now we must subtract the area of the four smaller circles inside the square, the area of each one is:

A3 = pi*r^2 = 3.14*(3.2)^2 = 32.15 units squared.

Then the shaded area is:

A = A1 + A2 - 4*A3 = 163.84 + 64.31 - 4* 32.15 = 99.55 units squared.

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If f(x) and its inverse function, f^-1(x), are both plotted on the same coordinate plane, where is their point of intersection?
zloy xaker [14]

Answer:

Step-by-step explanation:

Their point of intersection, assuming there is one, will be somewhere on the line y = x.  This line, y = x, is the line of symmetry between a function and its inverse.  So if the two do in fact intersect, it will be at some point on that line

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3 years ago
299,792,458 rounded to the greatest place value
andrew11 [14]

Answer:

300,000,000

Step-by-step explanation:

299,792,458

2 rounded to 9 is the answer

4 0
3 years ago
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What is the LCM of 120 and 150​
Mrac [35]
The LCM of 120 and 150 is 600
4 0
3 years ago
A professor gives her 100 students an exam; scores are normally distributed. The section has an average exam score of 80 with a
frozen [14]

Answer:

6.18% of the class has an exam score of A- or higher.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\mu = 80, \sigma = 6.5

What percentage of the class has an exam score of A- or higher (defined as at least 90)?

This is 1 subtracted by the pvalue of Z when X = 90. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{90 - 80}{6.5}

Z = 1.54

Z = 1.54 has a pvalue of 0.9382

1 - 0.9382 = 0.0618

6.18% of the class has an exam score of A- or higher.

4 0
3 years ago
The circumference of a circle is 36pi cm what is the radius
alexdok [17]

Answer:

The radius is 18 cm

Step-by-step explanation:

The formula for circumference with radius is

C = 2*pi*r

We know the circumference is 36 pi

36 pi = 2 * pi *r

Divide by pi

36 pi/pi = 2 * pi/pi *r

36 = 2r

Divide by 2

36/2 = 2r/2

18 = r

8 0
3 years ago
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