Answer:
40 members
Step-by-step explanation:
Let the total members = x
<u>Given the following data;</u>
Number of sixth graders = 12 members
The mathematical expression is;
x = 40
<em>Therefore, the total members in the middle school coding club is 40 members</em>.
The 5 rounds to 3 so it is 4.3
A parallelogram is a polygon with two sets of opposite, parallel sides.
A rhombus is a type of parallelogram with four congruent sides and angles but no right angles.
So, all rhombuses are parallelograms, but not all parallelograms are rhombuses.
Answer:
![\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%202e%5E%7B2x%7D)
![\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%203e%5E%7B3x%7D)
General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Exponential Rule [Multiplying]:

<u>Calculus</u>
Derivatives
Derivative Notation
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^x] = e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D%20%3D%20e%5Ex)
Derivative Rule [Product Rule]: ![\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Step-by-step explanation:
<u>Step 1: Define</u>
<u />
<u />
<u />
<u />
<u />
<u>Step 2: Differentiate</u>
<u />
<u />
- [Derivative] Product Rule:
![\displaystyle \frac{d}{dx}[e^{2x}] = \frac{d}{dx}[e^x]e^x + e^x\frac{d}{dx}[e^x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5De%5Ex%20%2B%20e%5Ex%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5D)
- [Derivative] eˣ Derivative:
![\displaystyle \frac{d}{dx}[e^{2x}] = e^x \cdot e^x + e^x \cdot e^x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20e%5Ex%20%5Ccdot%20e%5Ex%20%2B%20e%5Ex%20%5Ccdot%20e%5Ex)
- [Derivative] Multiply [Exponential Rule - Multiplying]:
![\displaystyle \frac{d}{dx}[e^{2x}] = e^{2x} + e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%20e%5E%7B2x%7D%20%2B%20e%5E%7B2x%7D)
- [Derivative] Combine like terms [Addition]:
![\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%20%3D%202e%5E%7B2x%7D)
![\displaystyle \frac{d}{dx}[e^{3x}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D)
- [Derivative] Product Rule:
![\displaystyle \frac{d}{dx}[e^{3x}] = \frac{d}{dx}[e^x]e^{2x} + e^x\frac{d}{dx}[e^{2x}]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Ex%5De%5E%7B2x%7D%20%2B%20e%5Ex%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D)
- [Derivative] eˣ Derivatives:
![\displaystyle \frac{d}{dx}[e^{3x}] = e^x(e^{2x}) + e^x(2e^{2x})](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20e%5Ex%28e%5E%7B2x%7D%29%20%2B%20e%5Ex%282e%5E%7B2x%7D%29)
- [Derivative] Multiply [Exponential Rule - Multiplying]:
![\displaystyle \frac{d}{dx}[e^{3x}] = e^{3x} + 2e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%20e%5E%7B3x%7D%20%2B%202e%5E%7B3x%7D)
- [Derivative] Combine like terms [Addition]:
![\displaystyle \frac{d}{dx}[e^{3x}] = 3e^{3x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B3x%7D%5D%20%3D%203e%5E%7B3x%7D)
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
The p-value is 0.1867.
Step-by-step explanation:
Employees at a construction and mining company claim that the mean salary of the company's mechanical engineers is less than that of the one of its competitors, which is $68,000.
At the null hypothesis we test that the salary is the same of the competitor, that is:

At the alternate hypothesis, we test that it is more than 68000. So

The test statistic is:

In which X is the sample mean,
is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
68000 is tested at the null hypothesis:
This means that 
A random sample of 20 of the company's mechanical engineers has a mean salary of $66,900. Assume the population standard deviation is $5500.
This means that 
Value of the test statistic:



P-value:
The pvalue is the probability of finding a sample mean below 66900, which is the pvalue of z = -0.89.
Looking at the z-table, z = -0.89 has a pvalue of 0.1867.
The p-value is 0.1867.