Answer: 142506
Step-by-step explanation:
Given : The total number of choices for people in committee = 30
The number of people need to be chosen =5
Since , here order doesn't matter, so we use combination.
The combination of r things taking from n at a time is given by :-
![C(n,r)=\dfrac{n!}{(n-r)!r!}](https://tex.z-dn.net/?f=C%28n%2Cr%29%3D%5Cdfrac%7Bn%21%7D%7B%28n-r%29%21r%21%7D)
Now, the number of possible combinations of 5 people be chosen from a total of 30 possible people :-
![C(30,5)=\dfrac{30!}{(30-5)!5!}\\\\=\dfrac{30\times29\times28\times27\times26}{120}\\\\=142506](https://tex.z-dn.net/?f=C%2830%2C5%29%3D%5Cdfrac%7B30%21%7D%7B%2830-5%29%215%21%7D%5C%5C%5C%5C%3D%5Cdfrac%7B30%5Ctimes29%5Ctimes28%5Ctimes27%5Ctimes26%7D%7B120%7D%5C%5C%5C%5C%3D142506)
Hence, the committee can be made in 142506 ways.
If you're going to around the 487 to the nearest hundredso are you around the next number be if after itso that would be 500
Sure let’s see.... I believe it is D, but I’m not 100%. Don’t give low ratings. I tried.
Using an exponential function, it is found that the Tequesta settlement is 1845 years old.
<h3>What is an exponential function?</h3>
The exponential equation for a decaying amount of a substance is given by:
![A(t) = A(0)e^{-rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-rt%7D)
In which:
- A(0) is the initial value.
- r is the decay rate, as a decimal.
Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.
![A(t) = A(0)e^{-rt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-rt%7D)
![0.5A(0) = A(0)e^{-5730r}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29e%5E%7B-5730r%7D)
![e^{-5730r} = 0.5](https://tex.z-dn.net/?f=e%5E%7B-5730r%7D%20%3D%200.5)
![\ln{e^{-5730r}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-5730r%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![5730r = -\ln{0.5}](https://tex.z-dn.net/?f=5730r%20%3D%20-%5Cln%7B0.5%7D)
![r = -\frac{\ln{0.5}}{5730}](https://tex.z-dn.net/?f=r%20%3D%20-%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B5730%7D)
![r = 0.00012096809](https://tex.z-dn.net/?f=r%20%3D%200.00012096809)
Hence, the equation is:
![A(t) = A(0)e^{-0.00012096809t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.00012096809t%7D)
The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).
![A(t) = A(0)e^{-0.00012096809t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.00012096809t%7D)
![0.8A(0) = A(0)e^{-0.00012096809t}](https://tex.z-dn.net/?f=0.8A%280%29%20%3D%20A%280%29e%5E%7B-0.00012096809t%7D)
![e^{-0.00012096809t} = 0.8](https://tex.z-dn.net/?f=e%5E%7B-0.00012096809t%7D%20%3D%200.8)
![\ln{e^{-0.00012096809t}} = \ln{0.8}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.00012096809t%7D%7D%20%3D%20%5Cln%7B0.8%7D)
![-0.00012096809t = \ln{0.8}](https://tex.z-dn.net/?f=-0.00012096809t%20%3D%20%5Cln%7B0.8%7D)
![t = -\frac{\ln{0.8}}{0.00012096809}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.8%7D%7D%7B0.00012096809%7D)
![t = 1845](https://tex.z-dn.net/?f=t%20%3D%201845)
The Tequesta settlement is 1845 years old.
You can learn more about exponential functions at brainly.com/question/25537936