<u>Part a)</u>
Given the expression
![54m^3n\:+\:81m^4n^2](https://tex.z-dn.net/?f=54m%5E3n%5C%3A%2B%5C%3A81m%5E4n%5E2)
Apply exponent rule: ![a^{b+c}=a^ba^c](https://tex.z-dn.net/?f=a%5E%7Bb%2Bc%7D%3Da%5Eba%5Ec)
∵ ![m^4n^2=m^3mnn](https://tex.z-dn.net/?f=m%5E4n%5E2%3Dm%5E3mnn)
Rewrite 81 as 3 · 27
Rewrite 54 as 2 · 27
![=2\cdot \:27m^3n+3\cdot \:27m^3mnn](https://tex.z-dn.net/?f=%3D2%5Ccdot%20%5C%3A27m%5E3n%2B3%5Ccdot%20%5C%3A27m%5E3mnn)
Factor out the common term: 27m³n
Therefore,
![54m^3n\:+\:81m^4n^2=54m^3n+81m^3mnn=27m^3n\left(2+3mn\right)](https://tex.z-dn.net/?f=54m%5E3n%5C%3A%2B%5C%3A81m%5E4n%5E2%3D54m%5E3n%2B81m%5E3mnn%3D27m%5E3n%5Cleft%282%2B3mn%5Cright%29)
<u>Part B)</u>
Given the expression
![15x^2y^3z+25x^3y^2z+35x^2y^2z](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z)
Apply exponent rule: ![a^{b+c}=a^ba^c](https://tex.z-dn.net/?f=a%5E%7Bb%2Bc%7D%3Da%5Eba%5Ec)
![15x^2y^3z+25x^3y^2z+35x^2y^2z=15x^2y^2yz+25x^2xy^2z+35x^2y^2z](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z%3D15x%5E2y%5E2yz%2B25x%5E2xy%5E2z%2B35x%5E2y%5E2z)
Rewrite as
![=3\cdot \:5y^2x^2zy+5\cdot \:5y^2x^2zx+7\cdot \:5y^2x^2z](https://tex.z-dn.net/?f=%3D3%5Ccdot%20%5C%3A5y%5E2x%5E2zy%2B5%5Ccdot%20%5C%3A5y%5E2x%5E2zx%2B7%5Ccdot%20%5C%3A5y%5E2x%5E2z)
Factor out common term 5y²x²z
![=5y^2x^2z\left(3y+5x+7\right)](https://tex.z-dn.net/?f=%3D5y%5E2x%5E2z%5Cleft%283y%2B5x%2B7%5Cright%29)
Therefore,
![15x^2y^3z+25x^3y^2z+35x^2y^2z=5y^2x^2z\left(3y+5x+7\right)](https://tex.z-dn.net/?f=15x%5E2y%5E3z%2B25x%5E3y%5E2z%2B35x%5E2y%5E2z%3D5y%5E2x%5E2z%5Cleft%283y%2B5x%2B7%5Cright%29)
Answer:
9200 dollars
Step-by-step explanation:
just minus it 77%
Well, one number is larger than the other, it has a bigger quantity, which makes the other smaller.
Answer:
Its standard deviation is 3.79.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
![\sigma = 125, n = 1089](https://tex.z-dn.net/?f=%5Csigma%20%3D%20125%2C%20n%20%3D%201089)
So
![s = \frac{125}{\sqrt{1089}} = 3.79](https://tex.z-dn.net/?f=s%20%3D%20%5Cfrac%7B125%7D%7B%5Csqrt%7B1089%7D%7D%20%3D%203.79)
Its standard deviation is 3.79.