A, 6 tb, 6gb, 6/12 or 1/2 chance of picking either one
Answer:
18 minutes for each exhibit.
Step-by-step explanation:
Answer:
<em>( 8, - 2 )</em>
Step-by-step explanation:
Answer:
![f(8) = 81](https://tex.z-dn.net/?f=f%288%29%20%3D%2081)
![(g\ o\ f)(x) = x^2 + 2x -4](https://tex.z-dn.net/?f=%28g%5C%20o%5C%20f%29%28x%29%20%3D%20x%5E2%20%2B%202x%20-4)
Step-by-step explanation:
Solving (a):
![f(x) = x^2 + 2x +1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%202x%20%2B1)
![g(x) = x - 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%20-%205)
Solve for f(8)
We have:
![f(x) = x^2 + 2x +1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%202x%20%2B1)
Substitute 8 for x
![f(8) = 8^2 + 2*8 +1](https://tex.z-dn.net/?f=f%288%29%20%3D%208%5E2%20%2B%202%2A8%20%2B1)
Solve
![f(8) = 64 + 16 +1](https://tex.z-dn.net/?f=f%288%29%20%3D%2064%20%2B%2016%20%2B1)
![f(8) = 81](https://tex.z-dn.net/?f=f%288%29%20%3D%2081)
Solving (b):
![(g\ o\ f)(x)](https://tex.z-dn.net/?f=%28g%5C%20o%5C%20f%29%28x%29)
This is solved by:
![(g\ o\ f)(x) = g(f(x))](https://tex.z-dn.net/?f=%28g%5C%20o%5C%20f%29%28x%29%20%3D%20g%28f%28x%29%29)
So, we have:
![g(x) = x - 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%20x%20-%205)
![g(f(x)) = f(x) - 5](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20f%28x%29%20-%205)
Substitute: ![f(x) = x^2 + 2x +1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%202x%20%2B1)
![g(f(x)) = x^2 + 2x + 1 - 5](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20x%5E2%20%2B%202x%20%2B%201%20-%205)
![g(f(x)) = x^2 + 2x -4](https://tex.z-dn.net/?f=g%28f%28x%29%29%20%3D%20x%5E2%20%2B%202x%20-4)
Hence:
![(g\ o\ f)(x) = x^2 + 2x -4](https://tex.z-dn.net/?f=%28g%5C%20o%5C%20f%29%28x%29%20%3D%20x%5E2%20%2B%202x%20-4)
Answer:
130356 grams.
Step-by-step explanation:
The table shown in the picture is a proportion table. What I did here was divide 34932 by 4.1. That gave me 8520. So, 1 cm³ of metal is 8520 grams. Now multiply that by 15.3.
8520/1 * 153/10
<em>Cross-cancellation (8520 becomes 852, 10 becomes 1 (GCF: 10))</em>
852 * 153
<em>Multiply 852 by 153 to get 130356.</em>
130356
15.3 cm³ of metal weighs 130,356 grams.
<em>(Long multiplication work is below.</em>