Since you want to cancel something out, the book makes the 24 3 times eight so that both of the threes can be canceled out
Answer:
25
Step-by-step explanation:
From the given information;
Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.
= 1000x
Thus, the required number of hours it will take can be computed as:
![\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B100000%7D%7B1000x%7D%20%5C%5C%20%5C%5C%20%3D%5Cdfrac%7B100%7D%7Bx%7D)
cost per hour = 125
If each plate costs $20 to make, then the total number of plate will equal to 40x
∴
The total cost can be computed as:
![C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)](https://tex.z-dn.net/?f=C%28x%29%20%3D%20%28%5Cdfrac%7B100%7D%7Bx%7D%29%20%5Ctimes%20125%20%2B%2020%20x%20---%20%281%29)
![C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)](https://tex.z-dn.net/?f=C%27%28x%29%20%3D%20%28-%5Cdfrac%7B12500%7D%7Bx%5E2%7D%29%20%20%2B%2020%20%20---%20%282%29)
At C'(x) = 0
![\dfrac{12500}{x^2} = 20](https://tex.z-dn.net/?f=%5Cdfrac%7B12500%7D%7Bx%5E2%7D%20%3D%2020)
![\dfrac{12500}{20} = x^2](https://tex.z-dn.net/?f=%5Cdfrac%7B12500%7D%7B20%7D%20%3D%20x%5E2)
![x^2= 625](https://tex.z-dn.net/?f=x%5E2%3D%20625)
![x = \sqrt{625}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%7B625%7D)
x = 25
![C'' (x) = -12500 \times \dfrac{-2}{x^3} +0](https://tex.z-dn.net/?f=C%27%27%20%28x%29%20%3D%20-12500%20%5Ctimes%20%5Cdfrac%7B-2%7D%7Bx%5E3%7D%20%2B0)
![C'' (x) = \dfrac{25000}{x^3}](https://tex.z-dn.net/?f=C%27%27%20%28x%29%20%3D%20%5Cdfrac%7B25000%7D%7Bx%5E3%7D)
where; x = 25
![C'' (x) = \dfrac{25000}{25^3}](https://tex.z-dn.net/?f=C%27%27%20%28x%29%20%3D%20%5Cdfrac%7B25000%7D%7B25%5E3%7D)
C''(x) = 1.6
Thus, at x = 25, C'' > 0
As such, to minimize the cost, the printer needs to make 25 metal plates.
Answer:
475
Step-by-step explanation:
If each represents 100
For carousel, there are 4 whole and a 3/4
Hence,
4(100)+3/4(100)
=475
Answer:
I think the answer is 664....but I'm nt sure. Plz don't blame me if I'm wrong lol
Step-by-step explanation:
12x8x7= 672
672- 8= 664
1 1/4?? because 7/4 cant be a whole number its a mixed number when simplified