Answer:
(a)0.34
(b)0.5
(c)0.185
(d)0.544
(e)0.655
(f)Not disjoint events
(g)Independent events
Step-by-step explanation:
The summary of education levels among party lines is given in the table below
![\left|\begin{array}{c|ccc}&$Democrat &$Republican &$Total\\--&--&--&--\\$College Degree &37 &31 &68\\$No College Degree& 63 &69 &132\\--&--&--&--\\$Total &100 &100& 200\end{array}\right|](https://tex.z-dn.net/?f=%5Cleft%7C%5Cbegin%7Barray%7D%7Bc%7Cccc%7D%26%24Democrat%20%26%24Republican%20%26%24Total%5C%5C--%26--%26--%26--%5C%5C%24College%20Degree%20%2637%20%2631%20%2668%5C%5C%24No%20College%20Degree%26%2063%20%2669%20%26132%5C%5C--%26--%26--%26--%5C%5C%24Total%20%26100%20%26100%26%20200%5Cend%7Barray%7D%5Cright%7C)
(a)Probability a randomly selected participant has a college degree.
The probability a randomly selected participant has a college degree is:
![=\dfrac{68}{200} =0.34](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B68%7D%7B200%7D%20%3D0.34)
(b)The probability that a randomly selected participant is a democrat.
![=\dfrac{100}{200} =0.5](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B100%7D%7B200%7D%20%3D0.5)
(c)The probability that a randomly selected participant is a democrat and has a college degree.
![=\dfrac{37}{200} =0.185](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B37%7D%7B200%7D%20%3D0.185)
(d)Probability of being a democrat given that the participant has a college degree.
![=\dfrac{37}{68} \approx 0.544](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B37%7D%7B68%7D%20%5Capprox%200.544)
(e)The probability of begin a democrat or having a college degree
Number of Democrats =100
Number of Those with College degrees = 68
Number of democrats with College degrees =37
Therefore:
Probability of begin a democrat or having a college degree
![=\dfrac{100+68-37}{200} \\=\dfrac{131}{200}\\\\=0.655](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B100%2B68-37%7D%7B200%7D%20%5C%5C%3D%5Cdfrac%7B131%7D%7B200%7D%5C%5C%5C%5C%3D0.655)
(f)The event of having a college degree and being a democrat are not disjoint events as there are some democrats who have a college degree.
(g)The event of having a college degree and being a democrat are independent events as the outcome of one does not affect the other.
12 is correct because 12*1=12 and 6*2=12
Answer:
1. ![\( f\circ g(x)=0.05x-150](https://tex.z-dn.net/?f=%5C%28%20f%5Ccirc%20g%28x%29%3D0.05x-150)
2. ![\( g\circ f(x)=0.05x-3000](https://tex.z-dn.net/?f=%5C%28%20g%5Ccirc%20f%28x%29%3D0.05x-3000)
3. The first one represents Dale's commission
Explanation:
1. The composition of the function
means that you first apply the function g(x) and then f(x) on the output of g(x).
That is:
- f(x) = 0.05x
- g(x) = x - 3000
![f(g(x)=0.05(x - 3000)](https://tex.z-dn.net/?f=f%28g%28x%29%3D0.05%28x%20-%203000%29)
![f(g(x))=0.05x-150](https://tex.z-dn.net/?f=f%28g%28x%29%29%3D0.05x-150)
2. The composition of the function
means that you first apply the function f(x) and then g(x) on the output of f(x).
That is:
![g(f(x))=((0.05x)-3000)=0.05x-3000](https://tex.z-dn.net/?f=g%28f%28x%29%29%3D%28%280.05x%29-3000%29%3D0.05x-3000)
3. Which one represents Dale's commission
To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).
Therefore, you first use g(x).
Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.
Therefore, the composition that represents Dale's commission is the first one:
![f(g(x)=0.05(x - 3000)](https://tex.z-dn.net/?f=f%28g%28x%29%3D0.05%28x%20-%203000%29)
![f(g(x))=0.05x-150](https://tex.z-dn.net/?f=f%28g%28x%29%29%3D0.05x-150)
Answer:
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