Answer:
7.5 gallons
Step-by-step explanation:
Given:
The Thomas family went for a Sunday drive.
Before they left, Mr. Thomas noticed the gas tank was ¾ full.
When they returned home the gas tank was ⅓ full.
Total capacity of the gas tank = 18 gallons
<u>Question asked:</u>
How many gallons of gas did the car use on the drive?
<u>Solu</u>tion:
Before they left, quantity of gas in the tank = ![\frac{3}{4} \times18=\frac{54}{4} =13.5\ gallons](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%20%5Ctimes18%3D%5Cfrac%7B54%7D%7B4%7D%20%3D13.5%5C%20gallons)
When they returned, quantity of gas in the tank = ![\frac{1}{3} \times18=\frac{18}{3} =6\ gallons](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes18%3D%5Cfrac%7B18%7D%7B3%7D%20%3D6%5C%20gallons)
Quantity of gas used on the drive = 13.5 - 6 = 7.5 gallons
Therefore, 7.5 gallons of gas used on the drive by Thomas family.
It would last 13.5 weeks because you would make a proportion:
12/16 = x/18 and then cross multiply. You would get 216=16x, then you have to divide both sides by 16 to get x = 13.5
Answer:
The answer is A
Hoped it helped <3 tell me if I am wrong
Step-by-step explanation:
Answer:
![(a)\ P(x = 0) = 0.2725](https://tex.z-dn.net/?f=%28a%29%5C%20P%28x%20%3D%200%29%20%3D%200.2725)
![(b)\ P(x \ge 1) =0.7275](https://tex.z-dn.net/?f=%28b%29%5C%20P%28x%20%5Cge%201%29%20%3D0.7275)
![(c)\ P(x \le 2) = 0.8948](https://tex.z-dn.net/?f=%28c%29%5C%20P%28x%20%5Cle%202%29%20%3D%200.8948)
Step-by-step explanation:
Given
--- 8 friends
--- proportion that one-time fling
This question is an illustration of binomial probability, and it is represented as:
![P(X = x) = ^nC_x* p^x * (1 - p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20%5EnC_x%2A%20p%5Ex%20%2A%20%281%20-%20p%29%5E%7Bn-x%7D)
Solving (a): P(x = 0) --- None has done one time fling
![P(x = 0) = ^8C_0* (15\%)^0 * (1 - 15\%)^{8-0}](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%3D%20%5E8C_0%2A%20%2815%5C%25%29%5E0%20%2A%20%281%20-%2015%5C%25%29%5E%7B8-0%7D)
![P(x = 0) = 1* 1 * (1 - 0.15)^{8}](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%3D%201%2A%201%20%2A%20%281%20-%200.15%29%5E%7B8%7D)
![P(x = 0) = 0.85^8](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%3D%200.85%5E8)
![P(x = 0) = 0.2725](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%3D%200.2725)
Solving (b): ![P(x \ge 1)](https://tex.z-dn.net/?f=P%28x%20%5Cge%201%29)
To do this, we make use of compliment rule:
![P(x = 0) + P(x \ge 1) =1](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%2B%20P%28x%20%5Cge%201%29%20%3D1)
Rewrite as:
![P(x \ge 1) =1 - P(x = 0)](https://tex.z-dn.net/?f=P%28x%20%5Cge%201%29%20%3D1%20-%20P%28x%20%3D%200%29)
![P(x \ge 1) =1 - 0.2725](https://tex.z-dn.net/?f=P%28x%20%5Cge%201%29%20%3D1%20-%200.2725)
![P(x \ge 1) =0.7275](https://tex.z-dn.net/?f=P%28x%20%5Cge%201%29%20%3D0.7275)
Solving (c):
--- Not more than 2 has one time fling
This is calculated as:
![P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)](https://tex.z-dn.net/?f=P%28x%5Cle%202%29%20%3D%20P%28x%20%3D%200%29%20%2B%20P%28x%20%3D1%29%20%2B%20P%28x%20%3D%202%29)
We have:
![P(x = 0) = 0.2725](https://tex.z-dn.net/?f=P%28x%20%3D%200%29%20%3D%200.2725)
![P(x = 1) = ^8C_1* (15\%)^1 * (1 - 15\%)^{8-1}](https://tex.z-dn.net/?f=P%28x%20%3D%201%29%20%3D%20%5E8C_1%2A%20%2815%5C%25%29%5E1%20%2A%20%281%20-%2015%5C%25%29%5E%7B8-1%7D)
![P(x = 1) = 8* (0.15) * (1 - 0.15)^7](https://tex.z-dn.net/?f=P%28x%20%3D%201%29%20%3D%208%2A%20%280.15%29%20%2A%20%281%20-%200.15%29%5E7)
![P(x = 1) = 0.3847](https://tex.z-dn.net/?f=P%28x%20%3D%201%29%20%3D%200.3847)
![P(x = 2) = ^8C_2* (15\%)^2 * (1 - 15\%)^{8-2}](https://tex.z-dn.net/?f=P%28x%20%3D%202%29%20%3D%20%5E8C_2%2A%20%2815%5C%25%29%5E2%20%2A%20%281%20-%2015%5C%25%29%5E%7B8-2%7D)
![P(x = 2) = 28* (0.15)^2 * (1-0.15)^6](https://tex.z-dn.net/?f=P%28x%20%3D%202%29%20%3D%2028%2A%20%280.15%29%5E2%20%2A%20%281-0.15%29%5E6)
![P(x = 2) = 0.2376](https://tex.z-dn.net/?f=P%28x%20%3D%202%29%20%3D%200.2376)
So:
![P(x\le 2) = P(x = 0) + P(x =1) + P(x = 2)](https://tex.z-dn.net/?f=P%28x%5Cle%202%29%20%3D%20P%28x%20%3D%200%29%20%2B%20P%28x%20%3D1%29%20%2B%20P%28x%20%3D%202%29)
![P(x \le 2) = 0.2725 + 0.3847 + 0.2376](https://tex.z-dn.net/?f=P%28x%20%5Cle%202%29%20%3D%200.2725%20%2B%200.3847%20%2B%200.2376)
![P(x \le 2) = 0.8948](https://tex.z-dn.net/?f=P%28x%20%5Cle%202%29%20%3D%200.8948)