I have 81¥ and I'm going to the US, so I need to convert my Yen into US Dollars, if i get 1 USD (US Dollar) for every 9¥, how many USD will i have if i convert all of my Yen?
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.
Answer:
P= Rs 60000
A= Rs 79860
T=1 & 1/2 year = 3/2 years
= 3/2 x 2 = 3 half years
R= ?
Applying the formula A= P (1+r/100)^T
79860 = 60000 (1+ r/100)^3
79860/60000 = (1+r/100)^3
1331/1000 = (1+r/100)^3
root(3)(1331/1000) = (1+r/100)
11/10 = 1+r/100
11/10 -1 = r/100
1/10 = r/100
r= 10 %
Step-by-step explanation:
Answer:
Daniiel is 33 years old.
The son is 7 years old.
Step-by-step explanation:
x+26=3x
The x represents the son.
To solve for x:
-26=x-3x
-26=-2x
x=13
Since the father will be 3 times his son's age in six years we subtract 6.
x=7
This means the son is 7 years old as of right now. To find the father's age you do 7+26=33
What is the mean, median and mode for...45,50,55,55,55,60,60,60,65,65,70?
Alexxx [7]
Answer:
Mean = 58.18
Median = 60
Modes = 55 and 60
Step-by-step explanation:
To find the mean/average, add up all the numbers and divide the sum by the # of numbers there are (ex. there are 11 numbers so divide the sum by 11).
The median is the middle number of a set. In this case, the middle number is easy to see because the # of numbers is odd, but if it was even, just find the average of the two middle numbers.
The mode is/are the most frequent number(s) in the set. In this set, the numbers that appear the most are 55 and 60.