Answer:
3 1/3 cups
Step-by-step explanation:
one and one half dozen = 1.5 * 12 = 18 cookies
18 cookies 90 cookies
---------------- = -------------
2/3 cup x cups
using cross products
18 * x = 2/3 * 90
18 x = 60
divide each side by 18
x = 60/18
divide top and bottom by 6
x = 10/3
change the improper fraction to a mixed number
3 goes into 10 3 times with 1 left over
x = 3 1/3 cups
-x>-7 is the answer the line
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Answer:
x = 50*e∧ -t/100
Step-by-step explanation:
We assume:
1.-That the volume of mixing is always constant 300 gallons
2.-The mixing is instantaneous
Δ(x)t = Amount in - Amount out
Amount = rate * concentration*Δt
Amount in = 3 gallons/ min * 0 = 0
Amount out = 3 gallons/min * x/ 300*Δt
Then
Δ(x)t/Δt = - 3*x/300 Δt⇒0 lim Δ(x)t/Δt = dx/dt
dx/dt = - x/100
dx/ x = - dt/100
A linear first degree differential equation
∫ dx/x = ∫ - dt/100
Ln x = - t/100 + C
initial conditions to determine C
t= 0 x = 50 pounds
Ln (50) = 0/100 * C
C = ln (50)
Then final solution is:
Ln x = - t/100 + Ln(50) or
e∧ Lnx = e ∧ ( -t/100 + Ln(50))
x = e∧ ( -t/100) * e∧Ln(50)
x = e∧ ( -t/100) * 50
x = 50*e∧ -t/100
Answer:
2/5
Step-by-step explanation:
First by looking, you have a slope going upward to the right so it is a positive slope.
Two points on the line that seem to go directly through the grid at the intersection points are ( -60, -90) and ( 40, -50).
Slope is Rise (y axis) over the Run (x axis). The numbers above have x first and y second.
So the rise is the total distance between -90 and -50 which is 40.
The run is the total distance between 40 and -60 which is a total of 100.
It takes 40 units to get back to the 0 mark on the x axis and the another 60 units to get to the -60 point.
So you slop is 40/100. You can simplify this down to 4/10 or even further to give you 2/5.
