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3 years ago

The area of a circle is 144π ft². What is the circumference, in feet? Express your answer in terms of \piπ.

Mathematics

1 answer:

max2010maxim [7]3 years ago

3 0

Answer:

24π inches

Step-by-step explanation:

Area = π × r²

144π = π × r²

r² = 144

r = 12

Circumference = 2 π × r

= 2 × π × 12

= 24π in

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The symphonic choir and the jazz choir are recording songs for an album. The album can be no more than 72 minutes long. The jazz

zimovet [89]

Answer:

The symphonic choir can record a maximum of 14 songs.

Step-by-step explanation:

We know that the album cannot be more than 72 minutes long, and the jazz choir records a total of $7 (3min) = 21$ song minutes.

If we call $c$ the number of songs the symphonic choir records , and each song is 3.5 minute long, then the song minutes for the symphonic choir are $3.5c$ ; therefore, we have the inequality

$3.5c+21\leq 72$ (this says the song minutes for jazz choir plus song minutes for symphonic choice cannot exceed 72 minutes )

We solve this inequality by subtracting 21 from both sides and then dividing by 3.5:

$3.5c\leq 51$

$c\leq \frac{51}{3.5}$

$c\leq 14.47$

The maximum integer value $c$ can take is 14; therefore, the maximum number of songs the symphonic choir can record is 14 songs.

3 0

3 years ago

Underage drinking, Part I: Data collected by the Substance Abuse and Mental Health Services Administration (SAMSHA) suggests tha

dezoksy [38]

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

1 0.0294 0.0319

2 0.1351 0.1671

3 0.3109 0.4779

4 0.3576 0.8355

5 0.1645 1.0000

P(0) + P(1) + P (2) = 0.0026 + 0.0294 + 0.1351

The probability is 0.1671 or 16.71%

e. Using the same binomial distribution table we used in d. we have:

P(1) + P (2) + P(3) + P(4) + P (5) = 0.0294 + 0.1351 + 0.3109 + 0.3576 + 0.1645

The probability is 0.9975 or 99.75%

7 0

3 years ago

Find the domain of the following relation. R={(19,96),(20,101),(21,106),(22,111)}

mafiozo [28]

(x, y)

The domain are all the x-values, the range are all the y-values.

R={(19,96),(20,101),(21,106),(22,111)}

The domain is: 19, 20, 21, and 22
The range is: 96, 101, 106, and 111

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3 years ago

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Given the following Venn diagram: Find M N.

aliina [53]

If you want the intersect of M and N, then:

M∩N = {4,7} (common part in M AND N)

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4 years ago

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gizmo_the_mogwai [7]

Answer: