A) See picture for the table.
To make the table, multiply 47774 by 1.5% to get total that have diabetes and multiply 5855 by 2.5% to get total unemployed that have it, then using subtraction fill in the other squares of the table.
B)
Hypothesis:
H0: No association between employment and diabetes.
H1: Association between the two
Using a graphing calculator or Excel, run a chi-test.
Chi squared equals 31.844 with 1 degrees of freedom.
The two-tailed P value is less than 0.0001
With this information we can reject the null hypothesis and conclude there is an association between diabetes and employment.
C)
Although there is a statistical significance, there really is no practical significance between an incidence rate of 1.5 or 2.5%
<span><span><span>22x</span>−11 over x to the second power - x - 30.</span></span>
Answer:
B. ![\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B11%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B24%7D%2C%20%5Cfrac%7B3%7D%7B25%7D%2C%20%20%5Cfrac%7B9%7D%7B100%7D)
Step-by-step explanation:
The question is not properly presented. See attachment for proper presentation of question
From the attachment, we have that:
![W = \frac{3}{25}](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B3%7D%7B25%7D)
![X = \frac{\sqrt{3}}{11}](https://tex.z-dn.net/?f=X%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B11%7D)
![Y = \frac{9}{100}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7B9%7D%7B100%7D)
![Z = \frac{\pi}{24}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B%5Cpi%7D%7B24%7D)
Required
Order from greatest to least
First, we need to simplify each of the given expression (in decimals)
![W = \frac{3}{25}](https://tex.z-dn.net/?f=W%20%3D%20%5Cfrac%7B3%7D%7B25%7D)
![W = 0.12](https://tex.z-dn.net/?f=W%20%3D%200.12)
![X = \frac{\sqrt{3}}{11}](https://tex.z-dn.net/?f=X%20%3D%20%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B11%7D)
Take square root of 3
![X = \frac{1.73205080757}{11}](https://tex.z-dn.net/?f=X%20%3D%20%5Cfrac%7B1.73205080757%7D%7B11%7D)
![X = 0.15745916432](https://tex.z-dn.net/?f=X%20%3D%200.15745916432)
--- approximated
![Y = \frac{9}{100}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7B9%7D%7B100%7D)
![Y = 0.09](https://tex.z-dn.net/?f=Y%20%3D%200.09)
![Z = \frac{\pi}{24}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B%5Cpi%7D%7B24%7D)
Take π as 3.14
![Z = \frac{3.14}{24}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B3.14%7D%7B24%7D)
![Z = 0.13083333333](https://tex.z-dn.net/?f=Z%20%3D%200.13083333333)
--- approximated
List out the results, we have:
![Z = 0.13](https://tex.z-dn.net/?f=Z%20%3D%200.13)
Order from greatest to least, we have:
![Y = 0.09](https://tex.z-dn.net/?f=Y%20%3D%200.09)
Hence, the order of arrangement is:
![Y = \frac{9}{100}](https://tex.z-dn.net/?f=Y%20%3D%20%5Cfrac%7B9%7D%7B100%7D)
i.e.
![\frac{\sqrt{3}}{11}, \frac{\pi}{24}, \frac{3}{25}, \frac{9}{100}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B11%7D%2C%20%5Cfrac%7B%5Cpi%7D%7B24%7D%2C%20%5Cfrac%7B3%7D%7B25%7D%2C%20%20%5Cfrac%7B9%7D%7B100%7D)
<span>
Let's analyze Hannah's work, step-by-step, to see if she made any mistakes. </span>In Step 1, Hannah wrote
![\dfrac{d}{dx} (-3+8x)](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%28-3%2B8x%29)
<span> as the sum of two separate derivatives </span>
![\dfrac{d}{dx}(-3)+ \dfrac{d}{dx} (8x)](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%28-3%29%2B%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%288x%29%20)
<span>using the </span><span>sum rule.
</span>
This step is perfectly fine. In Step 2,
![\dfrac{d}{dx}(8x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%288x%29)
was kept as it is, and
![\dfrac{d}{dx}(-3)](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%28-3%29%20)
was rewritten as
![0](https://tex.z-dn.net/?f=0)
using the constant rule.Indeed, according to the constant rule, the derivative of a constant number is equal to zero.
This step is perfectly fine. In Step 3,
![\dfrac{d}{dx} (8x)](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%20%288x%29%20)
was rewritten as
![\dfrac{d}{dx}(8) \dfrac{d}{dx}(x)](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%288%29%20%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%20%20)
supposedly using the constant multiple rule.
The problem is that according to the constant multiple rule,
![\dfrac{d}{dx}(8x) ](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bd%7D%7Bdx%7D%288x%29%0A)
should be rewritten as
![8 \dfrac{d}{dx}(x)](https://tex.z-dn.net/?f=8%20%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29%20)
and not as
![\dfrac{d}{dx}(8)\dfrac{d}{dx}(x)](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%7D%7Bdx%7D%288%29%5Cdfrac%7Bd%7D%7Bdx%7D%28x%29)
.
<span>
Therefore, Hannah made a mistake in this step.</span>