Answer:
the answer is 29
Step-by-step explanation:
i don't really know how to explain it but hopefully it right
Answer:
I believe it would be B.
Step-by-step explanation:
Range: area of variation with real numbers
Also, seeing the quadrant it is in means there are negative numbers. This takes out the possibility of option A.
It is unchanged because the same number would still be in the middle and there would still be the same amount of numbers
if
11,15,21,22,23,27,30 before 22 is the median
if
11,15,21,22,23,27,30 after 22 is still the median
The median is unchanged
Answer:
See Explanation.
General Formulas and Concepts:
<u>Pre-Algebra</u>
<u>Algebra II</u>
- Log/Ln Property:
![ln(\frac{a}{b} ) = ln(a) - ln(b)](https://tex.z-dn.net/?f=ln%28%5Cfrac%7Ba%7D%7Bb%7D%20%29%20%3D%20ln%28a%29%20-%20ln%28b%29)
<u>Calculus</u>
Derivatives
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative of Ln: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
![ln(\frac{2x-1}{x-1} )=t](https://tex.z-dn.net/?f=ln%28%5Cfrac%7B2x-1%7D%7Bx-1%7D%20%29%3Dt)
<u>Step 2: Differentiate</u>
- Rewrite:
![t = ln(\frac{2x-1}{x-1})](https://tex.z-dn.net/?f=t%20%3D%20ln%28%5Cfrac%7B2x-1%7D%7Bx-1%7D%29)
- Rewrite [Ln Properties]:
![t = ln(2x-1) - ln(x - 1)](https://tex.z-dn.net/?f=t%20%3D%20ln%282x-1%29%20-%20ln%28x%20-%201%29)
- Differentiate [Ln/Chain Rule/Basic Power Rule]:
![\frac{dt}{dx} = \frac{1}{2x-1} \cdot 2 - \frac{1}{x-1} \cdot 1](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B1%7D%7B2x-1%7D%20%5Ccdot%202%20-%20%5Cfrac%7B1%7D%7Bx-1%7D%20%5Ccdot%201)
- Simplify:
![\frac{dt}{dx} = \frac{2}{2x-1} - \frac{1}{x-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2%7D%7B2x-1%7D%20-%20%5Cfrac%7B1%7D%7Bx-1%7D)
- Rewrite:
![\frac{dt}{dx} = \frac{2(x-1)}{(2x-1)(x-1)} - \frac{2x-1}{(2x-1)(x-1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B2%28x-1%29%7D%7B%282x-1%29%28x-1%29%7D%20-%20%5Cfrac%7B2x-1%7D%7B%282x-1%29%28x-1%29%7D)
- Combine:
![\frac{dt}{dx} = \frac{-1}{(2x-1)(x-1)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdt%7D%7Bdx%7D%20%3D%20%5Cfrac%7B-1%7D%7B%282x-1%29%28x-1%29%7D)
- Reciprocate:
![\frac{dx}{dt} = -(2x-1)(x-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20-%282x-1%29%28x-1%29)
- Distribute:
![\frac{dx}{dt} = (1-2x)(x-1)](https://tex.z-dn.net/?f=%5Cfrac%7Bdx%7D%7Bdt%7D%20%3D%20%281-2x%29%28x-1%29)