Answer:
Step-by-step explanation:
time to cross will be the distance divided by the velocity in that direction.
a) t = d/v = 45/2.75 = 16.363636... 16.4 s
In the same time that the otter is swimming cross stream, the stream is also moving perpendicularly at its own pace.
b) d = vt = 2.5(16.36) = 40.9090... 40.9 m
As velocity is a vector, An observer on the bank would see the velocity as the vector addition of the cross stream and down stream velocities
c) v = √(2.75² + 2.5²) = 3.716517... 3.72 m/s magnitude
θ = arctan2.5/2.75 = 42.2736... 42.3° downstream of a line straight across
Answer:
9
Step-by-step explanation:
Composite Numbers before 10: 4, 6, 8, and 9
The only one of those 4 that is NOT a multiple of 2: 9
Answer:
Step-by-step explanation:
Given that a fair coin is flipped twelve times.
It means the number of possible sequences of heads and tails would be:
2¹² = 4096
We can determine the number of ways that such a sequence could contain exactly 9 tails is the number of ways of choosing 9 out of 12, using the formula
![nCr=\frac{n!}{r!\left(n-r\right)!}](https://tex.z-dn.net/?f=nCr%3D%5Cfrac%7Bn%21%7D%7Br%21%5Cleft%28n-r%5Cright%29%21%7D)
Plug in n = 12 and r = 9
![=\frac{12!}{9!\left(12-9\right)!}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B12%21%7D%7B9%21%5Cleft%2812-9%5Cright%29%21%7D)
![=\frac{12!}{9!\cdot \:3!}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B12%21%7D%7B9%21%5Ccdot%20%5C%3A3%21%7D)
∵ ![\frac{12!}{9!}=12\cdot \:11\cdot \:10](https://tex.z-dn.net/?f=%5Cfrac%7B12%21%7D%7B9%21%7D%3D12%5Ccdot%20%5C%3A11%5Ccdot%20%5C%3A10)
∵ ![3!\:=\:3\times 2\times 1=6](https://tex.z-dn.net/?f=3%21%5C%3A%3D%5C%3A3%5Ctimes%202%5Ctimes%201%3D6)
![=220](https://tex.z-dn.net/?f=%3D220)
Thus, the probability will be:
![P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}](https://tex.z-dn.net/?f=P%5Cleft%28E%5Cright%29%3D%5Cfrac%7Bn%5Cleft%28E%5Cright%29%7D%7Bn%5Cleft%28S%5Cright%29%7D)
![=\frac{220}{4096}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B220%7D%7B4096%7D)
![=\frac{55}{1024}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B55%7D%7B1024%7D)
Thus, the probability of the coin landing tails up exactly nine times will be:
<span>the distribution is 43
</span>