Answer:
0.1505 = 15.05% probability that the hockey team wins 6 games in November
Step-by-step explanation:
For each game, there are only two possible outcomes. Either the team wins, or it does not. The probability of winning a game is independent of winning other games. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
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)
And p is the probability of X happening.
The probability that a certain hockey team will win any given game is 0.3723
So ![p = 0.3723](https://tex.z-dn.net/?f=p%20%3D%200.3723)
12 games in November
So ![n = 12](https://tex.z-dn.net/?f=n%20%3D%2012)
What is the probability that the hockey team wins 6 games in November?
This is ![P(X = 6)](https://tex.z-dn.net/?f=P%28X%20%3D%206%29)
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 6) = C_{12,6}.(0.3723)^{6}.(1-0.3723)^{6} = 0.1505](https://tex.z-dn.net/?f=P%28X%20%3D%206%29%20%3D%20C_%7B12%2C6%7D.%280.3723%29%5E%7B6%7D.%281-0.3723%29%5E%7B6%7D%20%3D%200.1505)
0.1505 = 15.05% probability that the hockey team wins 6 games in November
9514 1404 393
Answer:
√629 ≈ 25.08
Step-by-step explanation:
The distance formula is useful for this.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((-12 -13)² +(6 -8)²) = √(625 +4) = √629 ≈ 25.08
The distance between the points is about 25.08 units.
Answer:
Abebe will be exact twice as old as Aster in 8 years.
Step-by-step explanation:
Since Abebe is 12 years old, and his sister Aster is 2 years old, there is a difference of 10 years between them (12 - 2). Therefore, the difference between the two implies that Abebe is exactly twice as old as her sister when she is 10 years old, and she is 20 years old (10 x 2 = 20).
Therefore, since 20-12 equals 8, Abebe will be twice as old as her sister Aster hers in 8 years.
Answer:
A
Step-by-step explanation:
5:9 is the original ratio.
we know that anything times 5 would have the ones place of either 5 or 0 so we can eliminate c and d. Then we test out the other two choices.
25/5=5
45/9=5
A is correct.
15/5=3
45/9=5
Option B is incorrect.
so, the ratio is 25:45
The answer is A!