Answer:
The expression represents Ann's membership cost as a function of how many times she brings John along. For t = 5 the cost is 275, for t = 10, the cost is 250 and for t = 20 the cost is 200.
Step-by-step explanation:
The expression "300 - 5*t" represents the cost of Ann's membership plan on the local gym, where "t" is the number of visits John pays Ann. This means that the more times John goes to the gym with Ann, the less is her cost to pay the membership.
For t = 5:
![cost = 300 - 5*t\\cost = 300 - 5*5 = 275](https://tex.z-dn.net/?f=cost%20%3D%20300%20-%205%2At%5C%5Ccost%20%3D%20300%20-%205%2A5%20%3D%20275)
For t = 10:
![cost = 300 - 5*t\\cost = 300 - 5*10 = 250](https://tex.z-dn.net/?f=cost%20%3D%20300%20-%205%2At%5C%5Ccost%20%3D%20300%20-%205%2A10%20%3D%20250)
For t = 20:
![cost = 300 - 5*t\\cost = 300 - 5*20 = 200](https://tex.z-dn.net/?f=cost%20%3D%20300%20-%205%2At%5C%5Ccost%20%3D%20300%20-%205%2A20%20%3D%20200)
You can extract two balls of the same colour in two different way: either you pick two black balls or two red balls. Let's write the probabilities of each pick in each case.
Case 1: two black balls
The probability of picking the first black ball is 2/5, because there are two black balls, and 5 balls in total in the urn.
The probability of picking the second black ball is 1/4, because there is one black ball remaining in the urn, and 4 balls in total (we just picked the other black one!)
So, the probability of picking two black balls is
![P(\text{two blacks}) = \dfrac{2}{5} \cdot \dfrac{1}{4} = \dfrac{2}{20} = \dfrac{1}{10}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Btwo%20blacks%7D%29%20%3D%20%5Cdfrac%7B2%7D%7B5%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B4%7D%20%3D%20%5Cdfrac%7B2%7D%7B20%7D%20%3D%20%5Cdfrac%7B1%7D%7B10%7D%20)
Case 2: two red balls
The probability of picking the first black ball is 3/5, because there are three red balls, and 5 balls in total in the urn.
The probability of picking the second red ball is 2/4=1/2, because there are two red balls remaining in the urn, and 4 balls in total (we just picked the other red one!)
So, the probability of picking two red balls is
![P(\text{two reds}) = \dfrac{3}{5} \cdot \dfrac{1}{2} = \dfrac{3}{10}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Btwo%20reds%7D%29%20%3D%20%5Cdfrac%7B3%7D%7B5%7D%20%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%20%3D%20%5Cdfrac%7B3%7D%7B10%7D%20)
Finally, the probability of picking two balls of the same colour is
![P(\text{same colour}) = P(\text{two blacks})+ P(\text{two reds}) = \dfrac{1}{10} + \dfrac{3}{10} = \dfrac{4}{10} = \dfrac{2}{5}](https://tex.z-dn.net/?f=%20P%28%5Ctext%7Bsame%20colour%7D%29%20%3D%20P%28%5Ctext%7Btwo%20blacks%7D%29%2B%20P%28%5Ctext%7Btwo%20reds%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B10%7D%20%2B%20%5Cdfrac%7B3%7D%7B10%7D%20%3D%20%5Cdfrac%7B4%7D%7B10%7D%20%3D%20%5Cdfrac%7B2%7D%7B5%7D%20)
It depends, for what equation you want to write. Like, do you want to do addition or subtraction? I usually use like my everyday life to represent a real-world situation problem. For example, Amber have 30 bags of chips, she ate 10 bags. How many bags does she have left? Answer: 20 bags (30 - 10 = 20)