Answer:
The <u>last graph</u> is a <u>function.</u>
Step-by-step explanation:
They are reflected off of each other, aka they are in an organized pattern. The other graphs are a series of random plots, meaning they have no function.
Using proportions, it is found that the federal tax rate is of 10%.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax rate is the <u>proportion that $17.50 is of $175</u>, hence:
r = 17.50/175 = 0.1 = 10%.
The federal tax rate is of 10%.
More can be learned about proportions at brainly.com/question/24372153
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Answer:
(-1,5) and
are points on the graph
Step-by-step explanation:
Given
![g(x) = \frac{1}{5}^x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ex)
Required
Determine which point in on the graph
To get which of point A to D is on the graph, we have to plug in their values in the given expression using the format; (x,g(x))
A. (-1,5)
x = -1
Substitute -1 for x in ![g(x) = \frac{1}{5}^x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ex)
![g(x) = \frac{1}{5}^{-1}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5E%7B-1%7D)
Convert to index form
![g(x) = 1/(\frac{1}{5})](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2F%28%5Cfrac%7B1%7D%7B5%7D%29)
Change / to *
![g(x) = 1*(\frac{5}{1})](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2A%28%5Cfrac%7B5%7D%7B1%7D%29)
![g(x) = 5](https://tex.z-dn.net/?f=g%28x%29%20%3D%205)
This satisfies (-1,5)
<em>Hence, (-1,5) is on the graph</em>
<em></em>
B. (1,0)
x = 1
Substitute 1 for x
![g(x) = \frac{1}{5}^x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ex)
![g(x) = \frac{1}{5}^1](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5E1)
![g(x) = \frac{1}{5}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D)
<em>(1,0) is not on the graph because g(x) is not equal to 0</em>
C. ![(3, \frac{1}{125})](https://tex.z-dn.net/?f=%283%2C%20%5Cfrac%7B1%7D%7B125%7D%29)
x = 3
Substitute 3 for x
![g(x) = \frac{1}{5}^x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ex)
![g(x) = \frac{1}{5}^3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5E3)
Apply law of indices
![g(x) = \frac{1}{5} * \frac{1}{5} * \frac{1}{5}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%20%2A%20%5Cfrac%7B1%7D%7B5%7D%20%2A%20%5Cfrac%7B1%7D%7B5%7D)
![g(x) = \frac{1}{125}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B125%7D)
This satisfies ![(3, \frac{1}{125})](https://tex.z-dn.net/?f=%283%2C%20%5Cfrac%7B1%7D%7B125%7D%29)
<em>Hence, </em>
<em> is on the graph</em>
<em></em>
D. ![(-2, \frac{1}{25})](https://tex.z-dn.net/?f=%28-2%2C%20%5Cfrac%7B1%7D%7B25%7D%29)
x = -2
Substitute -2 for x
![g(x) = \frac{1}{5}^x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5Ex)
![g(x) = \frac{1}{5}^{-2}](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B5%7D%5E%7B-2%7D)
Convert to index form
![g(x) = 1/(\frac{1}{5}^2)](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2F%28%5Cfrac%7B1%7D%7B5%7D%5E2%29)
![g(x) = 1/(\frac{1}{5}*\frac{1}{5})](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2F%28%5Cfrac%7B1%7D%7B5%7D%2A%5Cfrac%7B1%7D%7B5%7D%29)
![g(x) = 1/(\frac{1}{25})](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2F%28%5Cfrac%7B1%7D%7B25%7D%29)
Change / to *
![g(x) = 1*(\frac{25}{1})](https://tex.z-dn.net/?f=g%28x%29%20%3D%201%2A%28%5Cfrac%7B25%7D%7B1%7D%29)
![g(x) = 25](https://tex.z-dn.net/?f=g%28x%29%20%3D%2025)
This does not satisfy ![(-2, \frac{1}{25})](https://tex.z-dn.net/?f=%28-2%2C%20%5Cfrac%7B1%7D%7B25%7D%29)
<em>Hence, </em>
<em> is not on the graph</em>
Answer:
C. 873.67
Step-by-step explanation:
399.17 + 150 + 69 + 200 + 55.5 = 873.67
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