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lisabon 2012 [21]

3 years ago

15

You are out with friends. Half of you want to go bowling and the other half want to go to a movie. How will you make a fair deci

sion about
whether to go to a movie or go bowling using a fair coin and assuming that all of you want to go to either of the places together? (Let H =
heads and T = tails)

1 answer:

lyudmila [28]3 years ago

6 0

Answer: The answer is option B.

Step-by-step explanation:

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1.) A 20° sector in a circle has an area of 21.5π yd².

a_sh-v [17]

<u>Part 1)</u> A 20° sector in a circle has an area of 21.5π yd².

What is the area of the circle?

we know that

the area of a circle represent a sector of $360$ degrees

so by proportion

$\frac{21.5\pi }{20} =\frac{x}{360} \\ \\ x*20=360*21.5\pi \\ \\x=(360*21.5*3.14)/20\\ \\x= 1,215.18\ yd^{2}$

therefore

<u>the answer part 1) is</u>

The area of the circle is $1,215.18\ yd^{2}$

<u>Part 2)</u> What is the area of a sector with a central angle of 3π/5 radians and a diameter of 21.2 cm?

we know that

the area of the circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

in this problem we have

$Diameter=21.2\ cm\\ r=Diameter/2\\r=21.2/2\\r= 10.6\ cm$

<u>Find the area of the circle</u>

$A=\pi r^{2}$

$A=\pi*10.6^{2}$

$A=352.8104\ cm^{2}$

<u>Find the area of the sector</u>

we know that the area of the circle represent a sector of $2\pi$ radians

by proportion

$\frac{352.8104}{2\pi }=\frac{x}{(3\pi/5)} \\\\x*2\pi=(3\pi*352.8104)/5\\ \\x= 105.84\ cm^{2}$

therefore

<u>the answer part 2) is</u>

the area of the sector is

$105.84\ cm^{2}$

7 0

4 years ago

9) Find the average rate of change for the function modeled by the graph 5 points

aleksklad [387]

B. 2 I believe that’s right

4 0

3 years ago

Find the values of x and y. Pls helpI’m helpless at math

Svetradugi [14.3K]

Answer:

x = 1

$y=\frac{\sqrt{3}}{2}$

Step-by-step explanation:

From the given right-angle triangle

The angle = ∠60°

The adjacent to the angle ∠60° is 1/2.

The opposite to the angle ∠60° is y.

The hypotenuse = x

<u>Determining the value of x:</u>

Using the trigonometric ratio

cos 60° = adjacent / hypotenuse

substituting adjacent = 1/2 and hypotenuse = x

$cos\:60^{\circ }=\:\:\frac{\frac{1}{2}}{x}$

$\cos \left(60^{\circ \:}\right)=\frac{1}{2x}$

$\frac{1}{2}=\frac{1}{2x}$ ∵ cos (60°) = 1/2

$2x=2$

Dividing both sides by 2

$\frac{2x}{2}=\frac{2}{2}$

Simplify

$x=1$

Thus, the value of hypotenuse x is:

x = 1

<u>Determining the value of y:</u>

Using the trigonometric ratio

sin 60° = opposite / hypotenuse

As we have already determined the value of hypotenuse x = 1

substituting opposite = y and hypotenuse = 1

sin 60° = y/1

y = 1 × sin 60°

$y=\frac{\sqrt{3}}{2}$ ∵ $\sin \left(60^{\circ \:}\right)=\frac{\sqrt{3}}{2}$

Therefore, the value of y is:

$y=\frac{\sqrt{3}}{2}$

Summary:

x = 1

$y=\frac{\sqrt{3}}{2}$

5 0

3 years ago

Cuál es el resultado

IrinaVladis [17]

Answer:

Shoes for men

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Is 61/100 bigger than, less than, or equal to 2/5

sergey [27]

$\dfrac{2}{5}=\dfrac{40}{100}$

so $\dfrac{61}{100}$ is bigger

5 0

4 years ago