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olasank [31]
3 years ago
15

State the two quantities that are being compared in each rate. Then calculate the equivalent unit rate.

Mathematics
1 answer:
stealth61 [152]3 years ago
6 0
101.25 dollars are being compared to 9 hours. The unit rate is 11.25 dollars
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Find area of the shaded region.
Monica [59]

Answer:

The area of the shaded region is about 38.1 square centimeters.

Step-by-step explanation:

We want to find the area of the shaded region.

To do so, we can first find the area of the sector and then subtract the area of the triangle from the sector.

The given circle has a radius of 6 cm.

And the given sector has a central angle of 150°.

The area for a sector is given by the formula:

\displaystyle A=\pi r^2\cdot \frac{\theta}{360^\circ}

In this case, r = 6 and θ = 150°. Hence, the area of the sector is:

\displaystyle \begin{aligned}A&=\pi(6)^2\cdot \frac{150}{360}\\ &=36\pi\cdot \frac{5}{12}\\&=3\pi \cdot 5\\&=15\pi \text{ cm}^2\end{aligned}

Now, we can find the area of the triangle. We can use an alternative formula:

\displaystyle A=\frac{1}{2}ab\sin(C)

Where a and b are the side lengths, and C is the angle between them.

Both side lengths of the triangle are the radii of the circle. So, both side lengths are 6.

And the angle C is 150°. Hence, the area of the triangle is:

\displaystyle A=\frac{1}{2}(6)(6)\sin(150)=18\sin(150)

The area of the shaded region is equivalent to the sector minus the triangle:

A_{\text{shaded}}=A_{\text{sector}}-A_{\text{triangle}}

Therefore:

A_{\text{shaded}}=15\pi -18\sin(150)

Use a calculator:

A_{\text{shaded}}=38.1238...\approx 38.1\text{ cm}^2

The area of the shaded region is about 38.1 square centimeters.

6 0
2 years ago
FlybynightSavings.com is offering a savings account that pays 33% compounded continuously. How much interest would a deposit of
pychu [463]
The exact calculations:
Principal, P=3000
interest rate = 33% per year
Period, t=10 years

Future value
F=Pe^(it)
=3000e^(0.33*10)
=81337.92

Interest 
= future value - principal
= 81337.92-3000
= 78337.92  (to the nearest cent)


6 0
3 years ago
4<br> The points (2, r) and (4, -8) lie on a line with slope - 1. Find the missing coordinate r.
maksim [4K]
R=-6


Mark brainliest please


Hope this helps you
6 0
3 years ago
How tall is a building that casts a ​78-ft shadow when the angle of elevation of the sun is 30 degrees​?
Marta_Voda [28]

Answer: 45.03\ ft

Step-by-step explanation:

Given

The length of the shadow is 78 ft

the angle of elevation is \theta =30^{\circ}

Suppose the height of the building is h

From the figure, we can write

\tan 30^{\circ}=\dfrac{h}{78}\\\\h=78\tan 30^{\circ}\\\\h=45.03\ ft

The height of the building is 45.03 ft

8 0
2 years ago
Solve the following:<br><br> 1 - .008 =
kykrilka [37]

Answer:

0.992

Step-by-step explanation:

do you not have a calculator

3 0
2 years ago
Read 2 more answers
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