Write the inequalities that are given by the :
<span>x: the number of batches of muffins
y: the number of batches of cakes
</span>Each batch of muffin requires 7 liters of milk and each batch of cakes
require 4 liters of milk.
=> liters of milk use = 7x + 4y
<span>Tania
has 56 liters of milk.=> 7x + 4y ≤ 56
Which means that the amount of muffins and cakes made are limited by the availability of 56 liter of milk.
The inequality 7x + 4y ≤ 56 is graphed by drawing the line 7x + 4y = 56 and shading the region below that line.
The line 7x + 4y = 56 has these x and y intercepts:
y-intercept: x =0 => 4y = 56 => y = 56/4 => 14 => point (0,14)
x-intercept => y = 0 => 7x = 56 => x = 56/7= 8 => point (8,0)
So, the line passes through the poins (0,8) and (14,0) and the solution region is below that line.
Also, you know that x and y are restricted to be positive or zero =>
x ≥ 0
y ≥ 0.
So, the solution region is restricted to the first quadrant.
That implies that the answer is:
</span><span>
Line joining ordered pairs 0, 14 and 8, 0. Shade the portion of the graph below this line which lies within the first quadrant
</span>
If there is such a scalar function <em>f</em>, then
Integrate both sides of the first equation with respect to <em>x</em> :
Differentiate both sides with respect to <em>y</em> :
Integrate both sides with respect to <em>y</em> :
Plug this into the equation above with <em>f</em> , then differentiate both sides with respect to <em>z</em> :
Integrate both sides with respect to <em>z</em> :
So we end up with
If the budget is $200 and he have 15 members then we have divide the two. 200 / 15 = $13.33 per shorts. 15x =< $200. x represents 13.33. So the solution represents the coach may spend up to $13.33 per pair of shorts. If it was even 1 cent more than $13.33 than he wouldn't have enough.So he can spend up to $13.33 or less per pair of shorts.
Step-by-step explanation:
Exponential Functions:
y=ab^x
y=ab
x
a=\text{starting value = }1600
a=starting value = 1600
r=\text{rate = }5.25\% = 0.0525
r=rate = 5.25%=0.0525
\text{Exponential Growth:}
Exponential Growth:
b=1+r=1+0.0525=1.0525
b=1+r=1+0.0525=1.0525
\text{Write Exponential Function:}
Write Exponential Function:
y=1600(1.0525)^x
y=1600(1.0525)
x
Put it all together
\text{Plug in time for x:}
Plug in time for x:
y=1600(1.0525)^{25}
y=1600(1.0525)
25
y= 5750.0628984
y=5750.0628984
Evaluate
y\approx 5750.06
y≈5750.06
Answer:
10.22 she save
Step-by-step explanation:
18 3/4 x 2.80=51.1
51.1 x 20%=10.22
