1.99 or 199/100 or 1 99/100
2.25 or 9/4 or 2 1/4
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
![f(x)=2(3)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D2%283%29%5E%7Bx%7D)
This is a exponential function of the form
![y=a(b)^{x}](https://tex.z-dn.net/?f=y%3Da%28b%29%5E%7Bx%7D)
where
a is the initial value (y-intercept)
b is the base
r is the rate of change
b=(1+r)
In this problem
a=2
b=3
1+r=3
r=3-1=2
r=200%
using a graphing tool
The graph in the attached figure
Using the hypergeometric distribution, it is found that there is a 0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.
The people are chosen without replacement from the sample, hence the <em>hypergeometric distribution </em>is used to solve this question.
<h3>What is the
hypergeometric distribution formula?</h3>
The formula is:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![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)
The parameters are:
- x is the number of successes.
- N is the size of the population.
- n is the size of the sample.
- k is the total number of desired outcomes.
In this problem:
- There is a total of 18 people, hence
.
- 2 people will be chosen, hence
.
- David and Valerie corresponds to 2 people, hence
.
The probability that both get picked is P(X = 2), hence:
![P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20h%28x%2CN%2Cn%2Ck%29%20%3D%20%5Cfrac%7BC_%7Bk%2Cx%7DC_%7BN-k%2Cn-x%7D%7D%7BC_%7BN%2Cn%7D%7D)
![P(X = 2) = h(2,18,2,2) = \frac{C_{2,2}C_{16,0}}{C_{18,2}} = 0.0065](https://tex.z-dn.net/?f=P%28X%20%3D%202%29%20%3D%20h%282%2C18%2C2%2C2%29%20%3D%20%5Cfrac%7BC_%7B2%2C2%7DC_%7B16%2C0%7D%7D%7BC_%7B18%2C2%7D%7D%20%3D%200.0065)
0.0065 = 0.65% probability that both David and Valerie get picked for the Tahitian dance lesson.
You can learn more about the hypergeometric distribution at brainly.com/question/25783392
Answer:
$59.13
Step-by-step explanation:
6% of 55.78= 3.35
3.35+55.78=59.13