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LenaWriter [7]
3 years ago
15

What is the exact area and arc length of these sectors? Please helppp

Mathematics
1 answer:
Karolina [17]3 years ago
4 0

<u>Answers with step-by-step explanation:</u>

1. Area of sector 1 = \frac{90}{360} \times \pi \times 12^2 = 36\pi

2. Area of sector 2 = \frac{45}{360} \times \pi \times 19^2 = \frac{2527}{8} \pi

3. Area of sector 3 = \frac{270}{360} \times \pi \times 15^2 = \frac{675}{4} \pi

4. Area of sector 4 = \frac{270}{360} \times \pi \times 6^2 = 27 \pi

5. Arc length of sector 1 = \frac{90}{360} \times 2 \times \pi \times 12 = 6\pi

6. Arc length of sector 2 = \frac{315}{360} \times 2 \times \pi \times 19 = \frac{133}{4} \pi

7. Arc length of sector 3 = \frac{270}{360} \times 2 \times \pi \times 15 = \frac{45}{2}\pi

8. Arc length of sector 4 = \frac{270}{360} \times 2 \times \pi \times 6 = 9\pi

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1.Famous basketball player Michael Jordan had a free throw percentage of 0.83. (He made 83% of his free throw shots.) Assume tha
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Michael Jordan's Freethrow, the population of the 6 countries and the distribution of the uninsured drivers are illustrations of probabilities

<h3>1. Michael Jordan Freethrow</h3>

The given parameter is:

p = 83% -- the percentage of free throws he made

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The probability that he misses his 6th throw is:

P = P(He made the first 5 throws) * P(He lost the 6th)

This gives

P = (83%)^5 * (1 - 83%)^1

P = 0.0670

<u>Expected number of miss</u>

The expected number till he misses the first free throw is:

E(x) = np

This gives

E(x) = 6 * 83%

E(x) = 4.98

Approximate

E(x) = 5

Hence, the probability that he misses his 6th throw is 0.0670 and the expected number till he misses the first free throw is 5

<h3>2. Country Populations</h3>

The given parameters are:

Average population = 268.35 million

Standard deviation = 370.43 million

<u>The z-scores for the United States, Egypt, and Mexico</u>

This is calculated as:

z = (x - \mu)/\sigma

So, we have:

US = (332 million - 268.35 million)/ 370.43 million

US = 0.17

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By comparing the z-score of the countries, the order of the countries are:

Egypt, Japan, Mexico, Brazil, United States and India

The countries are ranked that way because the higher the z-score, the higher the population

<h3>3. Uninsured drivers</h3>

The given parameter is:

p = 12.6% -- the percentage of uninsured drivers

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This is calculated as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, we have:

P(5) = 30C5 * (12.6%)^5 * (1 - 12.6%)^(30-5)

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P(5) = 0.1561

<u>Probability that the next uninsured driver is the 7th</u>

This is calculated as:

P = P(First 6 are insured) * P(7th is unisured)

This gives

P = (1 - 12.6%)^6 * (12.6%)^1

P = 0.0562

The probability that exactly 5 drivers of 30 are uninsured is 0.1561, and the probability that the next uninsured driver is the 7th is 0.0562

Read more about probability at:

brainly.com/question/25870256

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A particle moves in the xy plane starting from time = 0 second and position (1m, 2m) with a velocity of v&gt;=2i-4tj^
guapka [62]

Given :

A particle moves in the xy plane starting from time = 0 second and position (1m, 2m) with a velocity of v=2i-4tj  .

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B. The acceleration of the particle at any time t .

Solution :

A )

Position of vector v is given by :

d=\int\limits {v} \, dt\\\\d=\int\limits {(2i-4tj)} \, dt \\\\d=(2t)i+\dfrac{4t^2}{2}j\\\\d=(2t)i+(2t^2)j

B )

Acceleration a is given by :

a=\dfrac{dv}{dt}\\\\a=\dfrac{2i-4tj}{dt}\\\\a=\dfrac{2i}{dt}-\dfrac{4tj}{dt}\\\\a=0-4j\\\\a=-4j

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2. <br> Find the area of the region bounded by the graphs of y = -x2 + 3x + 4 and y = 4. (5 points)
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Answer:

4.5 sq. units

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Answer:

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First, move the x over to the other side by subtracting x from both sides. This will get you -y > -x + 4.

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3 years ago
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