You will need 119 cups to sell all of the lemonade.
Step-by-step explanation:
Given,
Diameter of cups = 9 cm
Radius of cup = 
Height of cups = 12 cm
We will find volume of cup.

Putting all the values

Therefore;
Each cup can hold 254.34 cubed centimeter of lemonade.
Number of gallons = 8
1 gallon = 3785 cm³
8 gallons = 3785*8 = 30280 cm³
Let,
x = Number of cups
Volume of lemonade in one cup * Number of cups = Volume of 8 gallons
254.34x=30280
Dividing both sides by 254.34

Rounding off to nearest whole number
x = 119
You will need 119 cups to sell all of the lemonade.
Keywords: volume, division
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To solve this problem you must appy the proccedure shown below:
1. You have the following function given in the problem above:
f(x)=e^2x
2. You can rewrite is:
y=e^2x
3. Interchange the variables, as below:
x=e^2y
3. The inverse of an exponential function is the logarithm function. Thereforem you have:
ln(x)=ln(e^2y)
ln(x)=2y
4.Then, you have:
y=ln(x)/2
Therefore, the answer is:
f^-1(x)=ln(x)/2