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4 years ago

A central angle measuring 120° intercepts an arc in a circle whose radius is 3.

Mathematics

1 answer:

Kisachek [45]4 years ago

5 0

Answer:

6.28

Step-by-step explanation:

The length of arc which subtends an angle $\alpha$ at the center of a circle is given by $\alpha r$ where r is the radius of circle.

______________________________

given

the central angle of arc is 120°

$\pi = 180\\120 = (\pi /180)* 120\\120 = 2/3\pi$

we will use value of $\pi$ as 3.14

r = 3

Length of this arc is

$2/3( \pi *3) = 2\pi \\=2*3.14 = 6.28$

The length of the arc to the nearest hundredth of unit is 6.28

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Answer:

a. Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

b. The probability is 0.2029 or 20.29%

c. The probability is 0.2029 or 20.29%

d. The probability is 0.1671 or 16.71%

e. The probability is 0.9975 or 99.75%

Step-by-step explanation:

a. Yes, there are 10 independent trials, each with exactly two possible outcomes, and a constant probability associated with each possible outcome.

b. Let's use the binomial distribution table, this way:

Binomial distribution (n=10, p=0.697)

f(x) F(x) 1 - F(x)

x Pr[X = x] Pr[X ≤ x]

0 0.0000 0.0000

1 0.0002 0.0002

2 0.0016 0.0017

3 0.0095 0.0112

4 0.0384 0.0496

5 0.1059 0.1555

6 0.2029 0.3584

7 0.2668 0.6252

8 0.2301 0.8553

9 0.1176 0.9729

10 0.0271 1.0000

The probability is 0.2029 or 20.29%

c. If 69.7% of 18-20 years old consumed alcoholic beverages in 2008, therefore, 30.3% did not and the binomial distribution table is:

Binomial distribution (n=10, p=0.303)

f(x) F(x) 1 - F(x)

x Pr[X = x] Pr[X ≤ x]

0 0.0271 0.0271

1 0.1176 0.1447

2 0.2301 0.3748

3 0.2668 0.6416

4 0.2029 0.8445

5 0.1059 0.9504

6 0.0384 0.9888

7 0.0095 0.9983

8 0.0016 0.9998

9 0.0002 1.0000

10 0.0000 1.0000

The probability is 0.2029 or 20.29%

d. Let's use the binomial distribution table, this way:

Binomial distribution (n=5, p=0.697)

f(x) F(x) 1 - F(x)

x Pr[X = x] Pr[X ≤ x]

0 0.0026 0.0026

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2 0.1351 0.1671

3 0.3109 0.4779

4 0.3576 0.8355

5 0.1645 1.0000

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The probability is 0.1671 or 16.71%

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