1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Effectus [21]
3 years ago
8

Find the area of a 120° sector of a circle whose radius is 6.

Mathematics
1 answer:
katrin [286]3 years ago
3 0
First, determine the area of the whole circle by the equation, A = πr². Substituting,
                             A = π(6²) = 36π
Then, multiply this value with the ratio of the given angle to the whole revolution,
                            A(sector) = 36π x (120° / 360°)
The area of the sector is therefore 12π units².
You might be interested in
A couple book a cruise to Alaska that promises to refund 100 per day of rain on the seven day cruise up to a maximum of 300. The
zubka84 [21]

Answer:

the variance of the refund payment to the couple = 9463.394

Step-by-step explanation:

Given that :

A couple book a cruise to Alaska that promises to refund 100 per day of rain on the seven day cruise up to a maximum of 300.

It is possible that the couple won't be able to refund up 100 per day or more than 100 per day.

SO; let assume that the refund payment happens to be 0, 100,200,  300

Let X be the total refund payment on the seven day cruise.

We can say  X = 0, if there is no rain on all 7 days.

P(X = 0) = _nC_x * P^x * (1 - P)n-x

P(X = 0) =  _7C_o * 0.2^0 * (1-0.2)^{7-0

P(X = 0) =1 * 1* (1-0.2)^{7

P(X = 0) =(0.8)^{7

P(X = 0) =0.2097152

If it rains on any one day; then X = 100

P(X = 100) = _nC_x * P^x * (1 - P)n-x

P(X = 100) =  _7C_1 * 0.2^1 * (1-0.2)^{7-1

P(X = 0) =7 * 0.2* (1-0.2)^{6

P(X = 100) =7* 0.2* (0.8)^{6

P(X = 100) =0.3670016

if it rains on any two day  ; then X = 200

P(X = 200) = _nC_x * P^x * (1 - P)n-x

P(X = 200) =  _7C_2 * 0.2^2 * (1-0.2)^{7-2

P(X = 200) =  21 * 0.2^2 * (0.8)^{5

P(X = 200) = 0.2752512

if it rains on any three day or more than that ; then X = 300

P(X \ge 300) = 1 - P(X < 300)  \\ \\ P(X \ge 300) = 1 - [P(X = 0) + P(X = 100) + P(X = 200)] \\ \\ P(X \ge 300) = 1 - [0.2097152 + 0.3670016 + 0.2752512] \\ \\ P(X \ge 300) = 0.148032

Now; we have our probability distribution function as:

P(X = 0) = 0.2097152

P(X = 100) = 0.3670016

P(X = 200) = 0.2752512

P(X = 300) = 0.148032

In order to determine the variance of the refund payment to the couple; we use the formula:

variance of the refund payment to the couple[Var X] =E [X^2] - (E [X])^2

where;

E[X^2]  = \sum x^2 \times p \\ \\ E[X^2]  = 0^2 * 0.2097152 + 100^2 * 0.3670016 + 200^2 * 0.2752512 + 300^2 * 0.148032 \\ \\  E[X^2]  = 0  + 3670.016 + 11010.048+ 13322.88  \\ \\  E[X^2]  =28002.944

(E [X]) = \sum x * p\\ \\  (E [X]) =  0 * 0.2097152 + 100 * 0.3670016 + 200 * 0.2752512 + 300 * 0.148032 \\ \\ (E [X]) = 0 + 36.70016 + 55.05024 + 44.4096\\ \\ (E [X]) = 136.16 \\ \\ (E [X])^2 = 136.16^2 \\ \\ (E [X])^2 = 18539.55

NOW;

the variance of the refund payment to the couple = 28002.944 - 18539.55

the variance of the refund payment to the couple = 9463.394

7 0
3 years ago
Jasmine is getting a new playground in her backyard she graphed them playground area on the coordinate grid shown blow Each squa
Serhud [2]
The answer would be 20 /)
7 0
2 years ago
Read 2 more answers
Mark has a shipping business. If your package weighs 2 pounds or less, the shipping costs $4. If your package weighs more than 2
maks197457 [2]
<span>So far I have:

(1.25 + 1) </span><span>if </span>x<span> is in the interval</span><span> (-inf,7]
(2.25 +1) </span><span>if </span>x<span> is in the interval (7,13)</span><span>
(3.50+1+3) </span><span>if </span>x<span> is in the interval [13,inf)</span>
7 0
3 years ago
Can some one help me with some math problems
Tatiana [17]
It's C, Y = 2x + 3. This is cause, if we use the table and say that y = 5 and x = 1, then 5 = 1 x 2 + 3 which is correct
4 0
3 years ago
3/8 or 11/12 which one is greater
Mazyrski [523]

Answer:11/12

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • How is 6.3 written in scientific notation?<br> 6.3 x 10°<br> 63 x 10-1<br> 6.3 x 102<br> 63 x 10°
    6·1 answer
  • What is the solution set?<br><br> −4.9x+1.3&gt;11.1<br><br> Enter your answer in the box.
    11·1 answer
  • What is 4-5 as a percentage
    11·2 answers
  • Pick all that apply (multiple answers)
    13·1 answer
  • 3.<br> QR<br> find the arc length<br> 02.83<br> 021.99<br> O 12.57<br> 0 34.56
    13·1 answer
  • How do I solve this problem?
    13·1 answer
  • Help PLEASE I FORGOT HOW TO DO THIS LMDAOAOAOAOAOOA
    10·2 answers
  • NEED ANWSERS 16-21 FAST
    9·1 answer
  • Jessica bought 9 bags of candy. Each bag had the same number of candies. She had a total of 54 candies. How many candies were in
    11·2 answers
  • Find the value of x. If necessary, round your answer to the nearest tenth. The figures are not drawn to scale.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!