Answer:
This means that, when the price of book from publisher is $60, the bookstore will sell it $88 to the students.
Step-by-step explanation:
Solution:
The cost of book from publisher = 40%
Sales tax = 7.5%
Price of books to the student = p(x) = 1.075x + 0.40x
Where, x is cost of book.
P (60) =?
We know that,
P(x) = 1.075 + 0.40
= 1.475%
=148
Given, Cost of book, x = 60
P (60) = 148 – 60
= 88
This means that, when the price of book from publisher is $60, the bookstore will sell it $88 to the students.
The pattern is: Ducks always swim on that pond <em><u>in powers of 2</u></em> .
Monday ........ 2⁰ = 1
Tuesday ........ 2¹ = 2
Wednesday ... 2² = 4
Thursday ....... 2³ = 8
So
Friday ........... 2⁴ = 16
<em>Saturday ...... 2⁵ = 32</em> <=== the answer
AND ...
If they kept doing this for a month, then
on the 31st day there would be
2³⁰ = <em>1,073,741,824</em> (more than 1 billion) ducks out there !
Answer:
It will take 3 days for their bird feeders to contain the same amount of bird seed
Step-by-step explanation:
Let the number of days it will take their bird feeder to contain the amount of bird seed be x
For Edith, the amount of birdseeds that will be left after x days will be;
4 1/2 - 3/4(x)
= 9/2 - 3x/4
For June, the amount of birdseeds that will remain after x days will be;
3 - 1/4(x)
= 3 - x/4
Since after x days, the amount of birdseeds will be equal;
Mathematically;
9/2 - 3x/4 = 3 - x/4
Let’s work with decimals to make things easier;
4.5 - 0.75x = 3 - 0.25x
4.5 -3 = -0.25x + 0.75x
1.5 = 0.5x
x = 1.5/0.5
x = 3
Given:
Fixed cost = b = $ 42,500
Production cost (Variable cost) /unit = m = $ 6/ unit
Let 'x' represent the number of unit, therefore the variable cost will be
![6x](https://tex.z-dn.net/?f=6x)
a) The cost function will be the sum of the fixed cost and the variable cost.
![C(x)=6x+42500](https://tex.z-dn.net/?f=C%28x%29%3D6x%2B42500)
b) The revenue function is the amount the product is sold per unit.
Recall: 'x' represents the number of units.
Therefore,
![11\times x=11x](https://tex.z-dn.net/?f=11%5Ctimes%20x%3D11x)
Hence, the revenue function R(x) is
![R(x)=11x](https://tex.z-dn.net/?f=R%28x%29%3D11x)
c) The profit function is the difference between the revenue function and the cost function.
![P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500](https://tex.z-dn.net/?f=P%5Cmleft%28x%5Cmright%29%3D11x-%5Cmleft%28425000%2B6x%5Cmright%29%3D5x-42500)
Hence, the profit function is
![P\mleft(x\mright)=5x-42500](https://tex.z-dn.net/?f=P%5Cmleft%28x%5Cmright%29%3D5x-42500)
d) Let us compute the profit (loss) values when the units are 6000 and 11000
Using the profit function
![P(x)=5x-42500](https://tex.z-dn.net/?f=P%28x%29%3D5x-42500)
Therefore,
![\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20P%286000%29%3D5%286000%29-42500%3D30000-42500%3D-%5Ctext%7B%20%5C%2412500%7D%20%5C%5C%20P%2811000%29%3D5%2811000%29-42500%3D55000-42500%3D%5Ctext%7B%20%5C%2412500%7D%20%5Cend%7Bgathered%7D)
Hence,