<span>So we want to know how much ball bearings can be made with 5.24 cm^3 if one ball bearing has a diameter of 1 cm. We know that radius r=d/2=0.5cm So the volume V of one ball bearing is: V=(4/3)*pi*r^3 so V=(4/3)*3.14*(0.5)^3cm^3=0.524cm^3. Now we simply divide the volume of steel by the volume of the ball bearing: 5.24/0.524=10. So we can make 10 ball bearings from 5.24 cm^3 of steel</span>
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:
1. 180
2. x = 31
Step-by-step explanation:
1. the sum of the interior angles of every triangle is always 180
2. using what we know from problem 1, we can create an equation:
x + 10 + 2x - 5 + 2x + 20 = 180
add like terms: 5x + 25 = 180
subtract 25 from both sides: 5x = 155
divide both sides by 5: x = 31
Answer:
no. because they are bot equivalent ratios or proportions