Answer:
![x^3 - 6x + 2](https://tex.z-dn.net/?f=%20x%5E3%20-%206x%20%2B%202%20)
Step-by-step explanation:
The given polynomials can be added together by adding like terms together as shown below:
=> Add together, the coefficient of all terms that have the power of 3.
![(2x^3) + (x^3) + (-3x^3)](https://tex.z-dn.net/?f=%20%282x%5E3%29%20%2B%20%28x%5E3%29%20%2B%20%28-3x%5E3%29%20)
![2x^3 + x^3 - 3x^3](https://tex.z-dn.net/?f=%202x%5E3%20%2B%20x%5E3%20-%203x%5E3%20)
![3x^3 - 3x^3](https://tex.z-dn.net/?f=%203x%5E3%20-%203x%5E3%20)
![x^3](https://tex.z-dn.net/?f=%20x%5E3%20)
=> ![(-4x^2) + (6x^2) + (2x^2)](https://tex.z-dn.net/?f=%20%28-4x%5E2%29%20%2B%20%286x%5E2%29%20%2B%20%282x%5E2%29%20)
![-4x^2 + 8x^2](https://tex.z-dn.net/?f=%20-4x%5E2%20%2B%208x%5E2%20)
![4x^2](https://tex.z-dn.net/?f=%204x%5E2%20)
=> ![(6x) + (-8x) + (-4x)](https://tex.z-dn.net/?f=%20%286x%29%20%2B%20%28-8x%29%20%2B%20%28-4x%29%20%20)
![6x - 8x - 4x](https://tex.z-dn.net/?f=%206x%20-%208x%20-%204x%20%20)
![-6x](https://tex.z-dn.net/?f=%20-6x%20)
=> ![(-3) + (12) +(-7)](https://tex.z-dn.net/?f=%20%28-3%29%20%2B%20%2812%29%20%2B%28-7%29%20)
![-3 + 12 - 7](https://tex.z-dn.net/?f=%20-3%20%2B%2012%20-%207%20)
![2](https://tex.z-dn.net/?f=%202%20)
The answer = ![x^3 - 6x + 2](https://tex.z-dn.net/?f=%20x%5E3%20-%206x%20%2B%202%20)
First, let's simplify the inequality
![\begin{gathered} \frac{4}{3}y](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cfrac%7B4%7D%7B3%7Dy%3C-8%20%5C%5C%20%5CRightarrow4y%3C-24%20%5C%5C%20%5CRightarrow%20y%3C-6%20%5Cend%7Bgathered%7D)
The graph looks like this:
Notice that the white dot is placed above the -6, it is important to include it like that.
Now, as an interval:
Answer:
1245
Step-by-step explanation:
-Given the standard deviation is $9000 and the margin of error is $500.
-the minimum sample size at a 95% confidence level can be calculated using the formula:
![n\geq( \frac{z\sigma}{MOE})^2\\\\\\\geq (\frac{1.96\times 9000}{500})^2\\\\\\\geq 1244.6784\approx 1245](https://tex.z-dn.net/?f=n%5Cgeq%28%20%5Cfrac%7Bz%5Csigma%7D%7BMOE%7D%29%5E2%5C%5C%5C%5C%5C%5C%5Cgeq%20%28%5Cfrac%7B1.96%5Ctimes%209000%7D%7B500%7D%29%5E2%5C%5C%5C%5C%5C%5C%5Cgeq%201244.6784%5Capprox%201245)
Hence, the minimum sample size is 1245
*Since there's no data fromw which we are drawing our variables, we can manually input our parameters in excel and calculate as attached.