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Rzqust [24]
3 years ago
14

The circumference of a great circle of a sphere is 44π. Find the Surface Area of the sphere.

Mathematics
1 answer:
alexdok [17]3 years ago
3 0

Answer:

1936 π square units

Step-by-step explanation:

Given the information:

<em>The circumference of a great circle of a sphere is 44π.</em>

As we know the formula used to find a circle's circumference is:

C = 2πr , where r is the radius of the circle

In this situation, we know C = 44π

<=> 2πr  = 44π

<=> r = 22 units

Hence, the Surface Area of the sphere

S.A = 4πr^{2}

= 4π22^{2}

= 1936 π square units

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Jack is renting a boat to go fishing with his friends. One rental company charges a fee of $20 plus $13.50 an hour. A second ren
zvonat [6]

Answer:

4 hours of rental

Step-by-step explanation:

y1 = 20 + 13.5x

y2 = 6 + 17x

20 + 13.5x = 6 + 17x

20 - 6 = 17x - 13.5x

14 = 3.5x

x = 4

Costs y1 and y2 are equal on renting for 4 hours

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3 years ago
Read 2 more answers
I toss an unfair coin 12 times. This coin is 65% likely to show up heads. Calculate the probability of the following.
mars1129 [50]

Answer:

a. 0.0368

b. 0.99992131

c. 0.2039

d. 0.0048

e. 0.6533

Step-by-step explanation:

Let the probability of obtaining a head be p = 65% = 13/20 = 0.65. The probability of not obtaining a head is q = 1 - p = 1 -13/20 = 7/20 = 0.35

Since this is a binomial probability, we use a binomial probability.

a. The probability of obtaining 11 heads is ¹²C₁₁p¹¹q¹ = 12 × (0.65)¹¹(0.35) = 0.0368

b. Probability of 2 or more heads P(x ≥ 2) is

P(x ≥ 2) = 1 - P(x ≤ 1)

Now P(x ≤ 1) = P(0) + P(1)

= ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹

= (0.65)⁰(0.35)¹² + 12(0.65)¹(0.35)¹¹

= 0.000003379 + 0.00007531

= 0.0007869

P(x ≥ 2) = 1 - P(x ≤ 1)

= 1 - 0.00007869

= 0.99992131

c. The probability of obtaining 7 heads is ¹²C₇p⁷q⁵ = 792(0.65)⁷(0.35)⁵ = 0.2039

d. The probability of obtaining 7 heads is ¹²C₉q⁹p³ = 220(0.65)³(0.35)⁹ = 0.0048

e. Probability of 8 heads or less P(x ≤ 8) = ¹²C₀p⁰q¹² + ¹²C₁p¹q¹¹ + ¹²C₂p²q¹⁰ + ¹²C₃p³q⁹ + ¹²C₄p⁴q⁸ + ¹²C₅p⁵q⁷ + ¹²C₆p⁶q⁶ + ¹²C₇p⁷q⁵ + ¹²C₈p⁸q⁴

= = ¹²C₀(0.65)⁰(0.35)¹² + ¹²C₁(0.65)¹(0.35)¹¹ + ¹²C₂(0.65)²(0.35)¹⁰ + ¹²C₃(0.65)³(0.35)⁹ + ¹²C₄(0.65)⁴(0.35)⁸ + ¹²C₅(0.65)⁵(0.35)⁷ + ¹²C₆(0.65)⁶(0.35)⁶ + ¹²C₇(0.65)⁷(0.35)⁵ + ¹²C₈(0.65)⁸(0.35)⁴

= 0.000003379 + 0.00007531 + 0.0007692 + 0.004762 + 0.01990 + 0.05912 + 0.1281 + 0.2039 + 0.2367

= 0.6533

3 0
3 years ago
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Fiesta28 [93]

Answer:

option (c) $18,032

Step-by-step explanation:

Data provided in the question;

Amount deposited at the end of each day = $1

Interest paid = 8% compounded daily = 0.08

Daily interest rate = \frac{\textup{0.08}}{\textup{365}}  =  0.000219

Duration = 20 years = 20 × 365 days = 7300 days

Now,

the Future value is given as:

Future value = Part payment × \frac{(1+r)^n-1}{r}

here, r is the interest rate

n is the duration

thus,

Future value = $1 × \frac{(1+0.0002192)^{7300}-1}{0.0002192}

or

Future value = $18033.56 ≈ $18,032

Hence, the correct answer is option (c) $18,032

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Three hundread and forty-seven million three hundread and sixteen thousand and twenty-nine....347,316,029
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