4.288 rounded to the nearest hundreth is 4.29
4.288 = 4.29
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
__
<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
_____
<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:
-14
Step-by-step explanation:
(1/4)2⁵-3×2³+2²-2
=(1/4)32-3×8+4-2
=(32/4)-24+4-2
8-24+4-2
=-14
Answer:
It would be the first table because if you graph the points on a graph, it would get you a zero slope which is a horizontal line across the graph.
The interval given was 33% to 37%
This means that subtracting the margin of error from the percentage of the population that visit the library once a year gives the lower end and adding the margin of error to the percentage of the population that visit the library once a year gives the upper end
Let x denote margin of error and y denotes the percentages of the population that visit the library once a year
we can get the following equations and solve for the values of x and y
![y - x = 33\%.......eqn1 \\ y + x = 37\%........eqn2](https://tex.z-dn.net/?f=y%20-%20x%20%3D%2033%5C%25.......eqn1%20%5C%5C%20y%20%2B%20x%20%3D%2037%5C%25........eqn2)
Adding eqn1 and eqn2 to gives
![2y = 70\% \\ y = 35\%](https://tex.z-dn.net/?f=2y%20%3D%2070%5C%25%20%5C%5C%20y%20%3D%2035%5C%25)
Putting the value of y into any of the equations
![35\% + x = 37\% \\ x = 37\% - 35\% \\ x = 2\%](https://tex.z-dn.net/?f=35%5C%25%20%2B%20x%20%3D%2037%5C%25%20%5C%5C%20x%20%3D%2037%5C%25%20-%2035%5C%25%20%5C%5C%20x%20%3D%202%5C%25)
Thus, the margin of error is
![\pm2\%](https://tex.z-dn.net/?f=%20%20%5Cpm2%5C%25)
Therefore we enter 2 in the box