So the train is pulling about 50 cars in total, and there's about 30 boxes of freight in each car.
30 x 50 = 1500
The best estimate would be near 1500 boxes of freight through the whole train.
E) 12 minutes
A normal curve has approximately 95% of graph between mean - 2sd and mean + 2sd
So 95% of the times will be between 0 and 12 minutes. 6 - 2x3 to 6 + 2x3
2.5% will take over 12 minutes
Strangely 2.5% will also take less than 0 minutes to process which shows the normal curve is not perfect in this example.
Answer:
72
Step-by-step explanation:
![f(x) = 4x+8\\g(x) = x + 4\\\\1. f(g(x)) = 4(x+4) + 8\\2. f(g(x)) = 4x + 16 + 8\\3. f(g(x))=4x + 24\\\\4. f(g(12)) = 4(12) + 24\\5. f(g(12)) = 48 + 24 = 72\\](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%2B8%5C%5Cg%28x%29%20%3D%20x%20%2B%204%5C%5C%5C%5C1.%20f%28g%28x%29%29%20%3D%204%28x%2B4%29%20%2B%208%5C%5C2.%20f%28g%28x%29%29%20%3D%204x%20%2B%2016%20%2B%208%5C%5C3.%20f%28g%28x%29%29%3D4x%20%2B%2024%5C%5C%5C%5C4.%20f%28g%2812%29%29%20%3D%204%2812%29%20%2B%2024%5C%5C5.%20f%28g%2812%29%29%20%3D%2048%20%2B%2024%20%3D%2072%5C%5C)
To do these, you have to place the entire function inside the parent function's variables.
You are inputting the value of the function g(x) into f(x)
It would have to be 3 because distance can't be a negative number.
Answer:
![x=5+\sqrt{12}](https://tex.z-dn.net/?f=x%3D5%2B%5Csqrt%7B12%7D)
or
![x=5-\sqrt{12}](https://tex.z-dn.net/?f=x%3D5-%5Csqrt%7B12%7D)
Step-by-step explanation:
![x^2-10x+13=0](https://tex.z-dn.net/?f=x%5E2-10x%2B13%3D0)
![x^2-10x=-13](https://tex.z-dn.net/?f=x%5E2-10x%3D-13)
![x^2-10x+(\frac{10}{2})^2 =-13+(\frac{10}{2})^2](https://tex.z-dn.net/?f=x%5E2-10x%2B%28%5Cfrac%7B10%7D%7B2%7D%29%5E2%20%3D-13%2B%28%5Cfrac%7B10%7D%7B2%7D%29%5E2)
![x^2-10x+(5)^2=-13+(5)^2](https://tex.z-dn.net/?f=x%5E2-10x%2B%285%29%5E2%3D-13%2B%285%29%5E2)
![x^2-10x+25=-13+25\\x^2-10x+25=12](https://tex.z-dn.net/?f=x%5E2-10x%2B25%3D-13%2B25%5C%5Cx%5E2-10x%2B25%3D12)
Factor.
![(x-5)^2=12](https://tex.z-dn.net/?f=%28x-5%29%5E2%3D12)
Extract the square root.
![x-5=\frac{+}{} \sqrt{12}](https://tex.z-dn.net/?f=x-5%3D%5Cfrac%7B%2B%7D%7B%7D%20%5Csqrt%7B12%7D)
Add 5
![x=5+\sqrt{12}](https://tex.z-dn.net/?f=x%3D5%2B%5Csqrt%7B12%7D)
or
![x=5-\sqrt{12}](https://tex.z-dn.net/?f=x%3D5-%5Csqrt%7B12%7D)