Answer:
Following are the responses to the given question:
Step-by-step explanation:
Test statistic:
![t=\frac{(825-905)}{\frac{205}{\sqrt{(500)}}}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%28825-905%29%7D%7B%5Cfrac%7B205%7D%7B%5Csqrt%7B%28500%29%7D%7D%7D)
Let the p-value=0
We reject H0 because of the p-value <0.01. We have evidence that college kids who pay their credit card bills in full per month have a mean balance of less than $905.
Divide $14,000 by $9.99 = 1401 board games
Since we know $14,00 is how much has been spent on the board game in total, the price to make each board ($1.90) game isn't necessarily relevant.
So you take the profit made from each game and divide that from how much was spent for the board game.
Answer:
![5x+2 , 2x^2+5x-2,\frac{x^2+5x}{2-x^2}](https://tex.z-dn.net/?f=5x%2B2%20%2C%202x%5E2%2B5x-2%2C%5Cfrac%7Bx%5E2%2B5x%7D%7B2-x%5E2%7D)
Step-by-step explanation:
We are given f(x) and g(x)
1. (f+g)(x)
(f+g)(x) = f(x) + g(x)
= ![x^2+5x+2-x^2](https://tex.z-dn.net/?f=x%5E2%2B5x%2B2-x%5E2)
= ![5x+2](https://tex.z-dn.net/?f=5x%2B2)
Domain : All real numbers as it there exists a value of (f+g)(x) f every x .
2. (f-g)(x)
(f-g)(x) = f(x)-g(x)
= ![x^2+5x-2+x^2](https://tex.z-dn.net/?f=x%5E2%2B5x-2%2Bx%5E2)
=![2x^2+5x-2](https://tex.z-dn.net/?f=2x%5E2%2B5x-2)
Domain : All real numbers as it there exists a value of (f-g)(x) f every x .
Part 3 .
![(\frac{f}{g})(x)\\(\frac{f}{g})(x) = \frac{f(x)}{g(x)}\\=\frac{x^2+5x}{2-x^2}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%5C%5C%28%5Cfrac%7Bf%7D%7Bg%7D%29%28x%29%20%3D%20%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%5C%5C%3D%5Cfrac%7Bx%5E2%2B5x%7D%7B2-x%5E2%7D)
Domain : In this case we see that the function is not defined for values of x for which the denominator becomes 0 or less than zero . Hence only those values of x are defined for which
![2-x^2>0](https://tex.z-dn.net/?f=2-x%5E2%3E0)
or ![2>x^2](https://tex.z-dn.net/?f=2%3Ex%5E2)
Hence taking square roots on both sides and solving inequality we get.
![-\sqrt{2}](https://tex.z-dn.net/?f=-%5Csqrt%7B2%7D%20%3Cx%3C%5Csqrt%7B2%7D)
Answer:
x = 0
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(x+7)=−4x+14
(2)(x)+(2)(7)=−4x+14(Distribute)
2x+14=−4x+14
Step 2: Add 4x to both sides.
2x+14+4x=−4x+14+4x
6x+14=14
Step 3: Subtract 14 from both sides.
6x+14−14=14−14
6x=0
Step 4: Divide both sides by 6.
6x 0
6 =
6
x=0