Answer:Answer: 175 %
Step-by-step explanation:
Given : A school year is 4 quarters.
To find : what percent of a school year is 7 quarters.
The percentage of a school year is 7 quarters will be given by :-
Since a school is 4 quarters , then
The percentage of a school year is 7 quarters will be :
Hence, the percent of a school year is 7 quarters = 175 %
I think its 144 because its the fifth square
Answer:
or ![3.6\ sec](https://tex.z-dn.net/?f=3.6%5C%20sec)
Step-by-step explanation:
we know that
To find out how much faster is Paloma than Savannah in the 100- meter dash, subtract the Paloma's time from the Savannah's time
so
![19.8-16\frac{1}{5}](https://tex.z-dn.net/?f=19.8-16%5Cfrac%7B1%7D%7B5%7D)
step 1
Convert mixed number to an improper fraction
![16\frac{1}{5}\ sec=\frac{16*5+1}{5}=\frac{81}{5}\ sec](https://tex.z-dn.net/?f=16%5Cfrac%7B1%7D%7B5%7D%5C%20sec%3D%5Cfrac%7B16%2A5%2B1%7D%7B5%7D%3D%5Cfrac%7B81%7D%7B5%7D%5C%20sec)
step 2
Convert decimal number in fraction number
![19.8\ sec=\frac{198}{10}\ sec](https://tex.z-dn.net/?f=19.8%5C%20sec%3D%5Cfrac%7B198%7D%7B10%7D%5C%20sec)
Simplify
![\frac{99}{5}\ sec](https://tex.z-dn.net/?f=%5Cfrac%7B99%7D%7B5%7D%5C%20sec)
step 3
Substitute the values
![19.8-16\frac{1}{5}=\frac{99}{5}-\frac{81}{5}=\frac{18}{5}\ sec](https://tex.z-dn.net/?f=19.8-16%5Cfrac%7B1%7D%7B5%7D%3D%5Cfrac%7B99%7D%7B5%7D-%5Cfrac%7B81%7D%7B5%7D%3D%5Cfrac%7B18%7D%7B5%7D%5C%20sec)
Convert to mixed number
![\frac{18}{5}\ sec=\frac{15}{5}+\frac{3}{5}=3\frac{3}{5}\ sec](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B5%7D%5C%20sec%3D%5Cfrac%7B15%7D%7B5%7D%2B%5Cfrac%7B3%7D%7B5%7D%3D3%5Cfrac%7B3%7D%7B5%7D%5C%20sec)
Convert to decimal number
![\frac{18}{5}\ sec=3.6\ sec](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B5%7D%5C%20sec%3D3.6%5C%20sec)
Answer:
The farmer should plant 14 additional trees, for maximum yield.
Step-by-step explanation:
Given
![Trees = 24](https://tex.z-dn.net/?f=Trees%20%3D%2024)
![Yield = 104](https://tex.z-dn.net/?f=Yield%20%3D%20104)
![x \to additional\ trees](https://tex.z-dn.net/?f=x%20%5Cto%20additional%5C%20trees)
So, we have:
![Trees = 24 + x](https://tex.z-dn.net/?f=Trees%20%3D%2024%20%2B%20x)
![Yield = 104 - 2x](https://tex.z-dn.net/?f=Yield%20%3D%20104%20-%202x)
Required
The additional trees to be planted for maximum yield
The function is:
![f(x) = Trees * Yield](https://tex.z-dn.net/?f=f%28x%29%20%3D%20Trees%20%2A%20Yield)
![f(x) = (24 + x) * (104 - 2x)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%2824%20%2B%20x%29%20%2A%20%28104%20-%202x%29)
Open bracket
![f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x](https://tex.z-dn.net/?f=f%28x%29%20%3D%2024%20%2A%20104%20%2B%20104x%20-%2024%20%2A%202x%20-%20x%20%2A%202x)
![f(x) = 2796 + 104x - 48x - 2x^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202796%20%2B%20104x%20-%2048x%20-%202x%5E2)
![f(x) = 2796 + 56x - 2x^2](https://tex.z-dn.net/?f=f%28x%29%20%3D%202796%20%2B%2056x%20-%202x%5E2)
Rewrite as:
![f(x) = - 2x^2 + 56x + 2796](https://tex.z-dn.net/?f=f%28x%29%20%3D%20-%202x%5E2%20%2B%2056x%20%2B%202796)
Differentiate
![f'(x) = -4x + 56](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20-4x%20%2B%2056)
Equate
to 0 and solve for x to get the maximum of x
![-4x + 56 = 0](https://tex.z-dn.net/?f=-4x%20%2B%2056%20%3D%200)
![-4x =- 56](https://tex.z-dn.net/?f=-4x%20%3D-%2056)
Divide by -4
![x =14](https://tex.z-dn.net/?f=x%20%3D14)
The farmer should plant 14 additional trees, for maximum yield.
A: 73%
b: 2% / 2.3%
c: 17.6%
d: 241.5%