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Answer:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
Step-by-step explanation:
Given
See attachment for complete question
Required
Match equivalent expressions
Solving (a):
![3 + 12 + 48 + 192 + 768](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n](https://tex.z-dn.net/?f=3%20%2B%2012%20%2B%2048%20%2B%20192%20%2B%20768%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%20%2A%204%5En)
Solving (b):
![4 + 32 + 256 + 2048 + 16384](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n](https://tex.z-dn.net/?f=4%20%2B%2032%20%2B%20256%20%2B%202048%20%2B%2016384%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%204%20%2A%208%5En)
Solving (c):
![2 + 6 + 18 + 54 + 162](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n](https://tex.z-dn.net/?f=2%20%2B%206%20%2B%2018%20%2B%2054%20%2B%20162%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%202%2A%203%5En)
Solving (d):
![3 + 15 + 75 + 375 + 1875](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875)
The expression can be written as:
--- 0
---- 1
--- 2
---- 3
---- 4
For the nth term, the expression is:
---- n
So, the summation is:
![3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n](https://tex.z-dn.net/?f=3%20%2B%2015%20%2B%2075%20%2B%20375%20%2B%201875%20%3D%20%5Csum%5Climits%5E4_%7Bn%3D0%7D%203%2A%205%5En)
Answer:
112
Step-by-step explanation:
180 - 40 - 28 = 112
Answer:
A: Independent
Step-by-step explanation:
About 3.40 rounded to the tenths place