Answer:
i don't know how to do it
You can revise: the sum of the two adjacent angles is 180°
and the sum of the measurements of the three corners in a triangle is also 180°
<1= 180°-57°=123°
As <2=52°, so we have <3= 180°-(28°+71°+52°)= 180°-151°=29°
have fun
Answer:
yes
Step-by-step explanation:
-1 1/2 = -3/2
A rational number is a number that can be written as a fraction of integers.
-1 1/2 is the same as -3/2.
-3 and 2 are integers, so -3/2 is a fraction of integers.
Answer: yes
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:
20.02%
Step-by-step explanation:
Formula : ![NVP = 0 =-P_0 + \frac{P_1}{(1+IRR)} + \frac{P_2}{(1+IRR)^2} + . . . +\frac{P_n}{(1+IRR)^n}](https://tex.z-dn.net/?f=NVP%20%3D%200%20%3D-P_0%20%2B%20%5Cfrac%7BP_1%7D%7B%281%2BIRR%29%7D%20%2B%20%5Cfrac%7BP_2%7D%7B%281%2BIRR%29%5E2%7D%20%2B%20.%20.%20.%20%2B%5Cfrac%7BP_n%7D%7B%281%2BIRR%29%5En%7D)
n = 1,2,3,4,5
Substitute the values in the formula :
![0 =-275000 + \frac{92000}{(1+IRR)} + \frac{92000}{(1+IRR)^2} + \frac{92000}{(1+IRR)^3}+\frac{92000}{(1+IRR)^4}+\frac{92000}{(1+IRR)^5}](https://tex.z-dn.net/?f=%200%20%3D-275000%20%2B%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%7D%20%2B%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E2%7D%20%2B%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E3%7D%2B%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E4%7D%2B%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E5%7D)
![275000 = \frac{92000}{(1+IRR)} + \frac{92000}{(1+IRR)^2} + \frac{92000}{(1+IRR)^3}+\frac{92000}{(1+IRR)^4}+\frac{92000}{(1+IRR)^5}](https://tex.z-dn.net/?f=%20275000%20%3D%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%7D%20%2B%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E2%7D%20%2B%20%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E3%7D%2B%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E4%7D%2B%5Cfrac%7B92000%7D%7B%281%2BIRR%29%5E5%7D)
Solving for IRR using calculator
IRR = 20.02
Hence the internal rate of return if the initial cost of the project is $275,000 is 20.02%