Answer:
use math papa
Step-by-step explanation:
It would be x^5-1 fjjbdbxjwjxjs
Answer: 1.67 kilometers.
Step-by-step explanation:
To solve this problem you must apply the proccedure shown below:
1. You have a right triangle, as you can see in the figure attached, where the angle is 37° (
), the hypotenuse is 2.1 and you can call
the distance between Stella and the skydiving center, which is the adjacent side of the triangle.
2. Therefore, you have:
![cos(\alpha)=\frac{adjacent}{hypotenuse}](https://tex.z-dn.net/?f=cos%28%5Calpha%29%3D%5Cfrac%7Badjacent%7D%7Bhypotenuse%7D)
3. Substitute values and solve for
:
![cos(37)\frac{x}{2.1}\\x=(2.1)[cos(37)]\\x=1.67](https://tex.z-dn.net/?f=cos%2837%29%5Cfrac%7Bx%7D%7B2.1%7D%5C%5Cx%3D%282.1%29%5Bcos%2837%29%5D%5C%5Cx%3D1.67)
Answer:
![P(X=10) = 0.1222](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.1222)
Step-by-step explanation:
Represent Green with G
So,
![G = 50\%](https://tex.z-dn.net/?f=G%20%3D%2050%5C%25)
Required
Determine the probability that 10 out of 16 prefer green
This question is an illustration of binomial distribution and will be solved using the following binomial distribution formula.
![P(X=x) = ^nC_xG^x(1-G)^{n-x}](https://tex.z-dn.net/?f=P%28X%3Dx%29%20%20%3D%20%5EnC_xG%5Ex%281-G%29%5E%7Bn-x%7D)
In this case:
-- number of people
-- those that prefer green
So, the expression becomes:
![P(X=10) = ^{16}C_{10}G^{10}(1-G)^{16-10}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7DG%5E%7B10%7D%281-G%29%5E%7B16-10%7D)
![P(X=10) = ^{16}C_{10}G^{10}(1-G)^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7DG%5E%7B10%7D%281-G%29%5E%7B6%7D)
Substitute 50% for G (Express as decimal)
![P(X=10) = ^{16}C_{10}*0.50^{10}*(1-0.50)^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%7D%2A%281-0.50%29%5E%7B6%7D)
![P(X=10) = ^{16}C_{10}*0.50^{10}*0.50^{6}](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%7D%2A0.50%5E%7B6%7D)
Apply law of indices
![P(X=10) = ^{16}C_{10}*0.50^{10+6](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B10%2B6)
![P(X=10) = ^{16}C_{10}*0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5E%7B16%7DC_%7B10%7D%2A0.50%5E%7B16)
Solve 16C10
![P(X=10) = \frac{16!}{(16-10)!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%21%7D%7B%2816-10%29%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16!}{6!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%21%7D%7B6%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11*10!}{6!10!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%2A10%21%7D%7B6%2110%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11}{6!} *0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%7D%7B6%21%7D%20%2A0.50%5E%7B16)
![P(X=10) = \frac{16*15*14*13*12*11}{6*5*4*3*2*1} * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B16%2A15%2A14%2A13%2A12%2A11%7D%7B6%2A5%2A4%2A3%2A2%2A1%7D%20%2A%200.50%5E%7B16)
![P(X=10) = \frac{5765760}{720} * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%20%5Cfrac%7B5765760%7D%7B720%7D%20%2A%200.50%5E%7B16)
![P(X=10) = 8008 * 0.50^{16](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%208008%20%2A%200.50%5E%7B16)
![P(X=10) = 8008 * 0.00001525878](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%208008%20%2A%200.00001525878)
![P(X=10) = 0.12219231024](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.12219231024)
![P(X=10) = 0.1222](https://tex.z-dn.net/?f=P%28X%3D10%29%20%20%3D%200.1222)
<em>Hence, the required probability is 0.1222</em>