Answer:
A: cost = 10+x; customers = 16-2x
B: -2x² -4x +160 ≥ 130
Step-by-step explanation:
In these price and revenue optimization problems, the relation between price and sales is given in the problem statement. After that is translated to math terms, the revenue as the product of price and sales can be determined.
<h3>Part A</h3>
The variable x is defined as the number of $1 increases from a price of $10. That means ...
Cost = 10 +x
For each $1 increase, the number of customers decreases by 2 from a starting value of 16:
Customers = 16 -2x
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<h3>Part B</h3>
The problem statement tells you the revenue (per hour) is the product of cost and number of customers. The owner wants this to be at least 130:
(Cost)(Customers) ≥ 130
(10 +x)(16 -2x) ≥ 130
160 -20x +16x -2x² ≥ 130 . . . . eliminate parentheses
-2x² -4x +160 ≥ 130 . . . . . . . . . put in required standard form
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<em>Additional comment</em>
The attached graph shows the solution to this quadratic inequality is ...
-5 ≤ x ≤ 3
and that revenue can be increased by $2 per hour by decreasing cost $1 (x=-1).
Answer:
The length of the pool is 400 feet.
The width of the pool is 120 feet.
Step-by-step explanation:
We are given the width (W) is 30% of the length (L).
We are also given the perimeter of the pool is 1040.
So in equation form this is what we have:
W=.3L (of means multiply)
2L+2W=1040
We are going to plug the first equation into the second like so:
2L+2(.3L)=1040
2L+.6L=1040
2.6L=1040
Divide both sides by 2.6
L=1040/2.6
L=400
The length of the pool is 400 feet.
W=.3L
W=.3(400)
W=120
The width of the pool is 120 feet.
Im going to say that u meant to put 9 blue marbles:)
and ill say the probablitly of drawing a blue marble is very likely
9/13 times u have a chance of drawing out a blue marble
:P
I would say it's 45 because it can't be the same measurement as gh.
Answer: 20.4% decrease
Step-by-step explanation:
First, find how many fewer cats were adopted out this year: 1,526 - 1214 = 312.
Now, find what percent of 1,526 312 is: 1,526 * x = 312 → x = .204 * 100 = 20.4% :)