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g100num [7]
3 years ago
14

A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.

Mathematics
1 answer:
Slav-nsk [51]3 years ago
7 0

Answer:

Part 1) The exact value of the arc length is \frac{25}{6}\pi \ in

Part 2) The approximate value of the arc length is 13.1\ in

Step-by-step explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

C=2\pi r

we have

r=5\ in

substitute

C=2\pi (5)

C=10\pi\ in

step 2

Find the exact value of the arc length by a central angle of 150 degrees

Remember that the circumference of a circle subtends a central angle of 360 degrees

by proportion

\frac{10\pi}{360} =\frac{x}{150}\\ \\x=10\pi *150/360\\ \\x=\frac{25}{6}\pi \ in

step 3

Find the approximate value of the arc length

To find the approximate value, assume

\pi =3.14

substitute

\frac{25}{6}(3.14)=13.1\ in

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So now

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Let X denote the time from the present until the stock market hits 25,000. If X ≤ 1, you win $10, 000X. If X > 1, you win not
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Answer: $6321

Step-by-step explanation:

Expected value is given as exactly what you might think it means intuitively, the return you can expect for some type of action.

The basic expected value formula is the probability of an event multiplied by the amount of times the event happens:(P(x) * n).

he formula for the Expected Value for a binomial random variable is:

P(x) * X.

X is the number of trials and P(x) is the probability of success.

The formula for calculating the Expected Value where there are multiple probabilities is:

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The equation is basically the same, but here you are adding the sum of all the gains multiplied by their individual probabilities instead of just one probability.

Calculating the expected value of winning as follows:

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Fx= e^-x, x is greater or equal to 0

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[-e^-x] ^1

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Based on the above given information,

y= $10000 0

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The expected value of winning:

E(y) = ΣyP(y)

E(y) = 10000 × 0.6321 + 0 × 0.3679

E(y) = $6321

Therefore, the expected value of winning is $6321

5 0
3 years ago
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