Answer:
20 percent
Step-by-step explanation:
(I had such a good explanation and accidentally refreshed the page)
So basics
48/60 is in
12/60 is out
Now we focus on out
we know this 12/60 becuase 48 is in and there are 60 tries so 60-48=12
So now 12/60 into a percent
A percent is basically x/100
So we gotta make 12/60 into a fraction with a denominator of 100
SO simplify fto make it easier (try to get it to 4,2,5,10,50,25 anything that goes into 100)
1/5
1/5 is 20 percent
thats a benchmark
But if you don’t know
You can always do a pro proton
1/5=x/100
Cross multiply
100=5x
x=20
Answer:
a>
−3x−4
x
Step-by-step explanation:
Answer:
radius r = 3.414 in
height h = 6.8275 in
Step-by-step explanation:
From the information given:
The volume V of a closed cylindrical container with its surface area can be expressed as follows:
![V = \pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2%20h)
![S = 2 \pi rh + 2 \pi r^2](https://tex.z-dn.net/?f=S%20%3D%202%20%5Cpi%20rh%20%2B%202%20%5Cpi%20r%5E2)
Given that Volume V = 250 in²
Then;
![\pi r^2h = 250 \\ \\ h = \dfrac{250}{\pi r^2}](https://tex.z-dn.net/?f=%5Cpi%20r%5E2h%20%3D%20250%20%20%5C%5C%20%5C%5C%20h%20%3D%20%5Cdfrac%7B250%7D%7B%5Cpi%20r%5E2%7D)
We also know that the cylinder contains top and bottom circle and the area is equal to πr²,
Hence, if we incorporate these areas in the total area of the cylinder.
Then;
![S = 2\pi r h + 2 \pi r ^2](https://tex.z-dn.net/?f=S%20%3D%202%5Cpi%20r%20h%20%2B%202%20%5Cpi%20r%20%5E2)
![S = 2\pi r (\dfrac{250}{\pi r^2}) + 2 \pi r ^2](https://tex.z-dn.net/?f=S%20%3D%202%5Cpi%20r%20%28%5Cdfrac%7B250%7D%7B%5Cpi%20r%5E2%7D%29%20%2B%202%20%5Cpi%20r%20%5E2)
![S = \dfrac{500}{r} + 2 \pi r ^2](https://tex.z-dn.net/?f=S%20%3D%20%5Cdfrac%7B500%7D%7Br%7D%20%2B%202%20%5Cpi%20r%20%5E2)
To find the minimum by determining the radius at which the surface by using the first-order derivative.
![S' = 0](https://tex.z-dn.net/?f=S%27%20%3D%200)
![- \dfrac{500}{r^2} + 4 \pi r = 0](https://tex.z-dn.net/?f=-%20%5Cdfrac%7B500%7D%7Br%5E2%7D%20%2B%204%20%5Cpi%20r%20%3D%200)
![r^3 = \dfrac{500 }{4 \pi}](https://tex.z-dn.net/?f=r%5E3%20%3D%20%5Cdfrac%7B500%20%7D%7B4%20%5Cpi%7D)
![r^3 = 39.789](https://tex.z-dn.net/?f=r%5E3%20%3D%2039.789)
![r =\sqrt[3]{39.789}](https://tex.z-dn.net/?f=r%20%3D%5Csqrt%5B3%5D%7B39.789%7D)
r = 3.414 in
Using the second-order derivative of S to determine the area is maximum or minimum at the radius, we have:
![S'' = - \dfrac{500(-2)}{r^3}+ 4 \pi](https://tex.z-dn.net/?f=S%27%27%20%3D%20-%20%5Cdfrac%7B500%28-2%29%7D%7Br%5E3%7D%2B%204%20%5Cpi)
![S'' = \dfrac{1000}{r^3}+ 4 \pi](https://tex.z-dn.net/?f=S%27%27%20%3D%20%20%5Cdfrac%7B1000%7D%7Br%5E3%7D%2B%204%20%5Cpi)
Thus, the minimum surface area will be used because the second-derivative shows that the area function is higher than zero.
Thus, from ![h = \dfrac{250}{\pi r^2}](https://tex.z-dn.net/?f=h%20%3D%20%5Cdfrac%7B250%7D%7B%5Cpi%20r%5E2%7D)
![h = \dfrac{250}{\pi (3.414) ^2}](https://tex.z-dn.net/?f=h%20%3D%20%5Cdfrac%7B250%7D%7B%5Cpi%20%283.414%29%20%5E2%7D)
h = 6.8275 in
Answer:
Step-by-step explanation:
rounded to the nearest cent his answer would be $212.24