Answer:
The probability of selecting two Democrats and two Republicans is 0.4242.
Step-by-step explanation:
The information provided is as follows:
- A city council consists of seven Democrats and five Republicans.
- A committee of four people is selected.
In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.
The formula to compute the combinations of k items from n is given by the formula:
![{n\choose k}=\frac{n!}{k!\times (n-k)!}](https://tex.z-dn.net/?f=%7Bn%5Cchoose%20k%7D%3D%5Cfrac%7Bn%21%7D%7Bk%21%5Ctimes%20%28n-k%29%21%7D)
Compute the number of ways to select four people as follows:
![{12\choose 4}=\frac{12!}{4!\times (12-4)!}=495](https://tex.z-dn.net/?f=%7B12%5Cchoose%204%7D%3D%5Cfrac%7B12%21%7D%7B4%21%5Ctimes%20%2812-4%29%21%7D%3D495)
Compute the number of ways to selected two Democrats as follows:
![{7\choose 2}=\frac{7!}{2!\times (7-2)!}=21](https://tex.z-dn.net/?f=%7B7%5Cchoose%202%7D%3D%5Cfrac%7B7%21%7D%7B2%21%5Ctimes%20%287-2%29%21%7D%3D21)
Compute the number of ways to selected two Republicans as follows:
![{5\choose 2}=\frac{5!}{2!\times (5-2)!}=10](https://tex.z-dn.net/?f=%7B5%5Cchoose%202%7D%3D%5Cfrac%7B5%21%7D%7B2%21%5Ctimes%20%285-2%29%21%7D%3D10)
Then the probability of selecting two Democrats and two Republicans as follows:
![P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242](https://tex.z-dn.net/?f=P%28%5Ctext%7B2%20Democrats%20and%202%20Republicans%7D%29%3D%5Cfrac%7B21%5Ctimes%2010%7D%7B495%7D%3D0.4242)
Thus, the probability of selecting two Democrats and two Republicans is 0.4242.
Answer:
answer is 89.23.I hope this answer will help you
Answer:
31,000 on apex
Step-by-step explanation:
Uee two points on the line to find the slope.
(-1,2) and (1,-4)
Slope = change in y over change in x;
Slope = (-4 - 2)/ (1 - -1) = (-6/2) = -3/1 = -3
The y intercept is y value where the blue line crosses the y axis, which is at -1
The equation would be y = -3x-1