Gallons per day.......gallons / day.....so u put the gallons over the number of days, then divide
(1/2) / 6 = 1/2 * 1/6 = 1/12 of a gallon per day <==
Answer:
Hello!
The correct answer is <u><em>B,</em></u> or <u><em>1.2</em></u>
<u><em /></u>
<u><em /></u>
Step-by-step explanation:
So first off we, have the number 1, two lines away from the dot, and there are 10 lines to the next number, which is 2, so it goes something like this:
1.
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.
so on and so forth, into infinity. But as for your problem, we can simply count the lines up to the dot, which puts us at <u><em>1.2</em></u>
<u><em></em></u>
<em>:^)</em>
Answer:
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
Step-by-step explanation:
Given
![Rooms = 240](https://tex.z-dn.net/?f=Rooms%20%3D%20240)
![Price= \$40](https://tex.z-dn.net/?f=Price%3D%20%5C%2440)
![Increment = \$2](https://tex.z-dn.net/?f=Increment%20%3D%20%5C%242)
First, we calculate the revenue.
![Revenue (r) = Price (p) * Number\ of\ Rooms(n)](https://tex.z-dn.net/?f=Revenue%20%28r%29%20%3D%20Price%20%28p%29%20%2A%20Number%5C%20of%5C%20Rooms%28n%29)
![r = p*n](https://tex.z-dn.net/?f=r%20%3D%20p%2An)
Let x be the change in rate.
i.e.
For every 2x increment in price (p) i.e. p + 2x
There will be 4 fewer rooms (n) i.e. n - 4x
So, the revenue is updated as:
![r = (p + 2x) * (n - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%28p%20%2B%202x%29%20%2A%20%28n%20-%204x%29)
![Price = 40](https://tex.z-dn.net/?f=Price%20%3D%2040)
So:
![r = (40 + 2x) * (n - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%2840%20%2B%202x%29%20%2A%20%28n%20-%204x%29)
![Rooms = 240](https://tex.z-dn.net/?f=Rooms%20%3D%20240)
So:
![r = (40 + 2x) * (240 - 4x)](https://tex.z-dn.net/?f=r%20%3D%20%2840%20%2B%202x%29%20%2A%20%28240%20-%204x%29)
Expand
![r = 40 * 240 - 40 * 4x + 2x * 240 - 2x*4x](https://tex.z-dn.net/?f=r%20%3D%2040%20%2A%20240%20-%2040%20%2A%204x%20%2B%202x%20%2A%20240%20-%202x%2A4x)
![r = 9600 - 160x + 480x - 8x^2](https://tex.z-dn.net/?f=r%20%3D%209600%20-%20160x%20%2B%20480x%20-%208x%5E2)
Reorder
![r = -8x^2 - 160x + 480x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20-%20160x%20%2B%20480x%20%2B%209600)
![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
The maximum of a function is calculated as:
![Max = -\frac{b}{2a}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
In: ![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
![c = 9600](https://tex.z-dn.net/?f=c%20%3D%209600)
So:
![Max = -\frac{b}{2a}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7Bb%7D%7B2a%7D)
![Max = -\frac{320}{-8}](https://tex.z-dn.net/?f=Max%20%3D%20-%5Cfrac%7B320%7D%7B-8%7D)
![Max = \frac{320}{8}](https://tex.z-dn.net/?f=Max%20%3D%20%5Cfrac%7B320%7D%7B8%7D)
![Max = 40](https://tex.z-dn.net/?f=Max%20%3D%2040)
To get the maximum revenue;
Substitute 40 for x in ![r = -8x^2 +320x + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8x%5E2%20%2B320x%20%2B%209600)
![r = -8(40)^2 + 320 * 40 + 9600](https://tex.z-dn.net/?f=r%20%3D%20-8%2840%29%5E2%20%2B%20320%20%2A%2040%20%2B%209600)
![r = 9600](https://tex.z-dn.net/?f=r%20%3D%209600)
The daily rate that maximizes the revenue is $40 and the maximum revenue is $9600
Answer:
The area in factored form is
.
The area in standard form is
.
Step-by-step explanation:
The area of a rectangle is length times width.
So the area here is (x+2)(x-5).
They are probably not looking for A=(x+2)(x-5) because it requires too little work.
They probably want A in standard form instead of factored form.
Let's use foil:
First x(x)=x^2
Outer: x(-5)=-5x
Inner: 2(x)=2x
Last: 2(-5)=-10
---------------------Adding together:
.
The area in factored form is
.
The area in standard form is
.