Using the percentage concept, it is found that 75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
<h3>What is a percentage?</h3>
The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
![P = \frac{a}{b} \times 100\%](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Ba%7D%7Bb%7D%20%5Ctimes%20100%5C%25)
In this problem, we have that:
- We consider that the population of both Beautiful Sunrise and Gorgeous Sunset islands is of x.
- There is a fiesta at Beautiful Sunrise, and a number a of people from Gorgeous Sunset are coming, hence, there will be x + a people at Beautiful Sunrise and x - a people t Gorgeous Sunset.
The percentage of people from Gorgeous Sunset is on Beautiful Sunrise now is:
![P = \frac{a}{x} \times 100\%](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Ba%7D%7Bx%7D%20%5Ctimes%20100%5C%25)
Now the number of people on Beautiful Sunrise is seven times the number of people on Gorgeous Sunset, hence:
![\frac{x + a}{x - a} = 7](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2B%20a%7D%7Bx%20-%20a%7D%20%3D%207)
We can find a <u>as a function of x</u> to find the percentage:
![\frac{x + a}{x - a} = 7](https://tex.z-dn.net/?f=%5Cfrac%7Bx%20%2B%20a%7D%7Bx%20-%20a%7D%20%3D%207)
![7(x - a) = x + a](https://tex.z-dn.net/?f=7%28x%20-%20a%29%20%3D%20x%20%2B%20a)
![7x - 7a = x + a](https://tex.z-dn.net/?f=7x%20-%207a%20%3D%20x%20%2B%20a)
![8a = 6x](https://tex.z-dn.net/?f=8a%20%3D%206x)
![a = \frac{3x}{4}](https://tex.z-dn.net/?f=a%20%3D%20%5Cfrac%7B3x%7D%7B4%7D)
Then, the percentage is:
![P = \frac{a}{x} \times 100\%](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7Ba%7D%7Bx%7D%20%5Ctimes%20100%5C%25)
![P = \frac{\frac{3x}{4}}{x} \times 100\%](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B%5Cfrac%7B3x%7D%7B4%7D%7D%7Bx%7D%20%5Ctimes%20100%5C%25)
![P = \frac{3}{4} \times 100\%](https://tex.z-dn.net/?f=P%20%3D%20%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes%20100%5C%25)
![P = 75\%](https://tex.z-dn.net/?f=P%20%3D%2075%5C%25)
75% of the population of Gorgeous Sunset is on Beautiful Sunrise now.
You can learn more about the percentage concept at brainly.com/question/10491646
Answer: D
Step-by-step explanation:
2 x 2 x 3 x 3
This is really easy to search up btw
Answer: d. 6
Explanation: you multiply each number by 6 every time
Answer:
![a_n=100 \left(\dfrac15\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D100%20%5Cleft%28%5Cdfrac15%5Cright%29%5E%7Bn-1%7D)
Step-by-step explanation:
General equation of geometric sequence: ![a_n=ar^{n-1}](https://tex.z-dn.net/?f=a_n%3Dar%5E%7Bn-1%7D)
Given:
![\implies a_1=a=100](https://tex.z-dn.net/?f=%5Cimplies%20a_1%3Da%3D100)
![\implies a_2=100 \cdot r=20](https://tex.z-dn.net/?f=%5Cimplies%20a_2%3D100%20%5Ccdot%20r%3D20)
![\implies a_3=100 \cdot r^2=4](https://tex.z-dn.net/?f=%5Cimplies%20a_3%3D100%20%5Ccdot%20r%5E2%3D4)
Common ratio:
![r=\dfrac{a_3}{a_2}=\dfrac{4}{20}=\dfrac15](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Ba_3%7D%7Ba_2%7D%3D%5Cdfrac%7B4%7D%7B20%7D%3D%5Cdfrac15)
Therefore:
![a_n=100 \left(\dfrac15\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D100%20%5Cleft%28%5Cdfrac15%5Cright%29%5E%7Bn-1%7D)