To achieve a positive profit p(x)>0, we start with:
Next, we solve for x:
The parameters are:
a = -2
b = 7
c = -3
We will apply the quadratic formula:
This yields two results—one a fraction, the other a whole number. We focus on the whole number since the muffins sold must be a complete unit. Thus we conclude:
x>3
The answer is 4 packs of medium cups and 6 packs of large cups.
Response:
- Marti is declared the winner
Step-by-step explanation:
Continuation of question:
- After 10 seconds, the race concluded. The winner is the racer farthest from the starting point. Which car deserves the title of winner? Use mathematical reasoning to support your conclusion.
- Table is attached
Solution
Greg
- Travel speed = 13 ft/s
- Initial position = 30.7 ft from the starting point after 2 seconds
Distance from the starting point after 10 seconds:
30.7 + 13*(10 - 2) = 30.7 + 13*8 = 30.7 + 104 = 134.7 ft
Marti
Travel speed = 16.5 ft/s
- Starting position = 2 ft from the beginning line
Distance from starting point after 10 seconds:
2 + 10*16.5 = 2 + 165 = 167 ft
- In comparing the distances from the start line, 134.7 ft against 167 ft, Marti is further from the start line and is thus declared the winner.
According to the rule of 72,
72/rate=time
72÷9.6=7.5 years
An alternative method for resolution using the main formula
2300=1150(1+0.096/4)^4t
Isolate t
t=((log(2,300÷1,150)÷log(1+(0.096÷4))÷4))=7.31 years
I hope this is helpful:-)
Answer:
This brings her total gross income to $140,000 ($3,000 + $500 + $41,500 + $90,000 + $5,000), with her farm gross income being $95,000 ($90,000 + $5,000). Since 67.9% (which is at least two-thirds) of her gross income derives from farming ($95,000 ÷ $140,000 = .679), she qualifies for the special estimated tax rules designed for qualified farmers.
Step-by-step explanation:
