Answer:
The answer is C
Step-by-step explanation:
Solution :
The data is normally distributed.
The standard deviation is 18 days
Here the data is normally distributed and 54 days is 3 days of standard deviation.
Therefore, the percentage of the births that would be
within the 54 days of the mean
length is given by :
= P( -3 < Z < 3)
= 0.9544
= 95 %
Therefore, about 95% of the births would be
within 54 days of the men
length.
Answer:
b^-6
Step-by-step explanation:
(b^-2) / (b^4) = b^(-2 - 4)
Answer:
![\displaystyle f'(x) = \frac{4}{x^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Limit Rule [Variable Direct Substitution]:
![\displaystyle \lim_{x \to c} x = c](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%20%5Cto%20c%7D%20x%20%3D%20c)
Differentiation
- Derivatives
- Derivative Notation
The definition of a derivative is the slope of the tangent line: ![\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%20%2B%20h%29%20-%20f%28x%29%7D%7Bh%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
<em />![\displaystyle f(x) = -\frac{4}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20-%5Cfrac%7B4%7D%7Bx%7D)
<u>Step 2: Differentiate</u>
- [Function] Substitute in <em>x</em>:
![\displaystyle f(x + h) = -\frac{4}{x + h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%20%2B%20h%29%20%3D%20-%5Cfrac%7B4%7D%7Bx%20%2B%20h%7D)
- Substitute in functions [Definition of a Derivative]:
![\displaystyle f'(x) = \lim_{h \to 0} \frac{-\frac{4}{x + h} - \big( -\frac{4}{x} \big)}{h}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B-%5Cfrac%7B4%7D%7Bx%20%2B%20h%7D%20-%20%5Cbig%28%20-%5Cfrac%7B4%7D%7Bx%7D%20%5Cbig%29%7D%7Bh%7D)
- Simplify:
![\displaystyle f'(x) = \lim_{h \to 0} \frac{4}{x(x+ h)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7B4%7D%7Bx%28x%2B%20h%29%7D)
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
![\displaystyle f'(x) = \frac{4}{x(x+ 0)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7B4%7D%7Bx%28x%2B%200%29%7D)
- Simplify:
![\displaystyle f'(x) = \frac{4}{x^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7B4%7D%7Bx%5E2%7D)
∴ the derivative of the given function will be equal to 4 divided by x².
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Learn more about derivatives: brainly.com/question/25804880
Learn more about calculus: brainly.com/question/23558817
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
<span>2 x^2 y^6 z^5
5 x^4 y^5 z^3
---------------
10 ^6 ^11 ^8</span>