Answer:
98.01% probability of getting 5 clean sheets
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this problem, the order that the sheets are chosen is not important, so we use the combinations formula to solve this problem.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
0.4% of the sheets contain spots
Of 500, that is 0.004*500 = 2.
What is the probability of getting 5 clean sheets although 0.4% of the sheets contain spots?
Desired outcomes
2 are defective, so 5 sheets from a set of 500 - 2 = 498.
![D = C_{498,5} = \frac{498!}{5!493!} = 250160254344](https://tex.z-dn.net/?f=D%20%3D%20C_%7B498%2C5%7D%20%3D%20%5Cfrac%7B498%21%7D%7B5%21493%21%7D%20%3D%20250160254344)
Total outcomes
5 sheets from a set of 500.
![T = C_{500,5} = \frac{500!}{5!495!} = 255244687600](https://tex.z-dn.net/?f=T%20%3D%20C_%7B500%2C5%7D%20%3D%20%5Cfrac%7B500%21%7D%7B5%21495%21%7D%20%3D%20255244687600)
Probability:
![P = \frac{D}{T} = \frac{250160254344}{255244687600} = 0.9801](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7BD%7D%7BT%7D%20%3D%20%5Cfrac%7B250160254344%7D%7B255244687600%7D%20%3D%200.9801)
98.01% probability of getting 5 clean sheets
Answer:
70:28
Step-by-step explanation:
70:28 because you just multiply 14 by both numbers and get your answer.
The circumference of any circle is (pi) x (the diameter of the circle).
The problem gives you both numbers, so all you have to do is multiply them.
Circumference = (pi) x (diameter) = (3.14) x (21cm) = <span>65.94 cm .</span>
Answer:
Rockefeller HS = 31%
Clayton West = 51%
Clayton South = 18%
Step-by-step explanation:
Given the following:
Championship wins shared by 3 basketball teams :
Rockefeller HS = 12
Clayton West = 20
Clayton South = 7
Percentage of total wins each team has :
Total number of wins = (12 + 20 + 7) = 39 wins
Percentage wins :
[(Number of wins per team) / total number of wins)] × 100
Rockefeller HS:
(12 / 39) * 100 = 30.769% = 31%
Clayton West :
(20/39) * 100 = 51.28% = 51%
Clayton South:
(7/39) * 100 = 17.948% = 18%
Let the number of girls be g.
Let the number of boys be b.
Now we can write these equations;
3g + 4b = 92 ..........(1)
g + b = 26 ...............(2)
b = 26 - g ................(3)
Plugging the expression for b in (3) into (1), we get:
3g + 104 - 4g = 92 ......(4)
Solving (4) we get
g = 12
So the number of girls in the class is 12.