Answer:
2.5 teaspoons
Step-by-step explanation:
75/15 = 5
1/2 · 5 = 2.5
Answer:
![P(ABC) = 0.110592](https://tex.z-dn.net/?f=P%28ABC%29%20%3D%200.110592)
![P(ABC^c) = 0.119808](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%200.119808)
![P(AB^cC) = 0.119808](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%200.119808)
![P(A^cBC) = 0.119808](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%200.119808)
![P(AB^cC^c) = 0.129792](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%200.129792)
![P(A^cBC^c) = 0.129792](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%3D%200.129792)
![P(A^cB^cC) = 0.129792](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%200.129792)
![P(A^cB^cC^c) = 0.140608](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%200.140608)
Step-by-step explanation:
Given
![P(A) = P(B) = P(C) = 48\%](https://tex.z-dn.net/?f=P%28A%29%20%3D%20P%28B%29%20%3D%20P%28C%29%20%3D%2048%5C%25)
Convert the probability to decimal
![P(A) = P(B) = P(C) = 0.48](https://tex.z-dn.net/?f=P%28A%29%20%3D%20P%28B%29%20%3D%20P%28C%29%20%3D%200.48)
Solving (a): P(ABC)
This is calculated as:
![P(ABC) = P(A) * P(B) * P(C)](https://tex.z-dn.net/?f=P%28ABC%29%20%3D%20P%28A%29%20%2A%20P%28B%29%20%2A%20P%28C%29)
This gives:
![P(ABC) = 0.48*0.48*0.48](https://tex.z-dn.net/?f=P%28ABC%29%20%3D%200.48%2A0.48%2A0.48)
![P(ABC) = 0.110592](https://tex.z-dn.net/?f=P%28ABC%29%20%3D%200.110592)
Solving (b): ![P(ABC^c)](https://tex.z-dn.net/?f=P%28ABC%5Ec%29)
This is calculated as:
![P(ABC^c) = P(A) * P(B) * P(C^c)](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%20P%28A%29%20%2A%20P%28B%29%20%2A%20P%28C%5Ec%29)
In probability:
![P(C^c) = 1 - P(C)](https://tex.z-dn.net/?f=P%28C%5Ec%29%20%3D%201%20-%20P%28C%29)
So, we have:
![P(ABC^c) = P(A) * P(B) * (1 - P(C))](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%20P%28A%29%20%2A%20P%28B%29%20%2A%20%281%20-%20P%28C%29%29)
![P(ABC^c) = 0.48 * 0.48 * (1 - 0.48)](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%200.48%20%2A%200.48%20%2A%20%281%20-%200.48%29)
![P(ABC^c) = 0.48 * 0.48 * 0.52](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%200.48%20%2A%200.48%20%2A%200.52)
![P(ABC^c) = 0.119808](https://tex.z-dn.net/?f=P%28ABC%5Ec%29%20%3D%200.119808)
Solving (c): ![P(AB^cC)](https://tex.z-dn.net/?f=P%28AB%5EcC%29)
This is calculated as:
![P(AB^cC) = P(A) * P(B^c) * P(C)](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%20P%28A%29%20%2A%20P%28B%5Ec%29%20%2A%20P%28C%29)
![P(AB^cC) = P(A) * [1 - P(B)] * P(C)](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%20P%28A%29%20%2A%20%5B1%20-%20P%28B%29%5D%20%2A%20P%28C%29)
![P(AB^cC) = 0.48 * (1 - 0.48)* 0.48](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%200.48%20%2A%20%281%20-%200.48%29%2A%200.48)
![P(AB^cC) = 0.48 * 0.52* 0.48](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%200.48%20%2A%200.52%2A%200.48)
![P(AB^cC) = 0.119808](https://tex.z-dn.net/?f=P%28AB%5EcC%29%20%3D%200.119808)
Solving (d): ![P(A^cBC)](https://tex.z-dn.net/?f=P%28A%5EcBC%29)
This is calculated as:
![P(A^cBC) = P(A^c) * P(B) * P(C)](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%20P%28A%5Ec%29%20%2A%20P%28B%29%20%2A%20P%28C%29)
![P(A^cBC) = [1-P(A)] *P(B) * P(C)](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%20%5B1-P%28A%29%5D%20%2AP%28B%29%20%2A%20P%28C%29)
![P(A^cBC) = (1 - 0.48)* 0.48 * 0.48](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%20%281%20-%200.48%29%2A%200.48%20%2A%200.48)
![P(A^cBC) = 0.52* 0.48 * 0.48](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%200.52%2A%200.48%20%2A%200.48)
![P(A^cBC) = 0.119808](https://tex.z-dn.net/?f=P%28A%5EcBC%29%20%3D%200.119808)
Solving (e): ![P(AB^cC^c)](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29)
This is calculated as:
![P(AB^cC^c) = P(A) * P(B^c) * P(C^c)](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%20P%28A%29%20%2A%20P%28B%5Ec%29%20%2A%20P%28C%5Ec%29)
![P(AB^cC^c) = P(A) * [1-P(B)] * [1-P(C)]](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%20P%28A%29%20%2A%20%5B1-P%28B%29%5D%20%2A%20%5B1-P%28C%29%5D)
![P(AB^cC^c) = 0.48 * [1-0.48] * [1-0.48]](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%200.48%20%2A%20%5B1-0.48%5D%20%2A%20%5B1-0.48%5D)
![P(AB^cC^c) = 0.48 * 0.52*0.52](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%200.48%20%2A%200.52%2A0.52)
![P(AB^cC^c) = 0.129792](https://tex.z-dn.net/?f=P%28AB%5EcC%5Ec%29%20%20%3D%200.129792)
Solving (f): ![P(A^cBC^c)](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29)
This is calculated as:
![P(A^cBC^c) = P(A^c) * P(B) * P(C^c)](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%20%3D%20P%28A%5Ec%29%20%2A%20P%28B%29%20%2A%20P%28C%5Ec%29)
![P(A^cBC^c) = [1-P(A)] * P(B) * [1-P(C)]](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%20%3D%20%5B1-P%28A%29%5D%20%2A%20P%28B%29%20%2A%20%5B1-P%28C%29%5D)
![P(A^cBC^c) = [1-0.48] * 0.48 * [1-0.48]](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%20%3D%20%5B1-0.48%5D%20%2A%200.48%20%2A%20%5B1-0.48%5D)
![P(A^cBC^c) = 0.52 * 0.48 * 0.52](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%20%3D%200.52%20%2A%200.48%20%2A%200.52)
![P(A^cBC^c) = 0.129792](https://tex.z-dn.net/?f=P%28A%5EcBC%5Ec%29%20%20%3D%200.129792)
Solving (g): ![P(A^cB^cC)](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29)
This is calculated as:
![P(A^cB^cC) = P(A^c) * P(B^c) * P(C)](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%20P%28A%5Ec%29%20%2A%20P%28B%5Ec%29%20%2A%20P%28C%29)
![P(A^cB^cC) = [1-P(A)] * [1-P(B)] * P(C)](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%20%5B1-P%28A%29%5D%20%2A%20%5B1-P%28B%29%5D%20%2A%20P%28C%29)
![P(A^cB^cC) = [1-0.48] * [1-0.48] * 0.48](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%20%5B1-0.48%5D%20%2A%20%5B1-0.48%5D%20%2A%200.48)
![P(A^cB^cC) = 0.52 * 0.52 * 0.48](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%200.52%20%2A%200.52%20%2A%200.48)
![P(A^cB^cC) = 0.129792](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%29%20%20%3D%200.129792)
Solving (h): ![P(A^cB^cC^c)](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29)
This is calculated as:
![P(A^cB^cC^c) = P(A^c) * P(B^c) * P(C^c)](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%20P%28A%5Ec%29%20%2A%20P%28B%5Ec%29%20%2A%20P%28C%5Ec%29)
![P(A^cB^cC^c) = [1-P(A)] * [1-P(B)] * [1-P(C)]](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%20%5B1-P%28A%29%5D%20%2A%20%5B1-P%28B%29%5D%20%2A%20%5B1-P%28C%29%5D)
![P(A^cB^cC^c) = [1-0.48] * [1-0.48] * [1-0.48]](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%20%5B1-0.48%5D%20%2A%20%5B1-0.48%5D%20%2A%20%5B1-0.48%5D)
![P(A^cB^cC^c) = 0.52*0.52*0.52](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%200.52%2A0.52%2A0.52)
![P(A^cB^cC^c) = 0.140608](https://tex.z-dn.net/?f=P%28A%5EcB%5EcC%5Ec%29%20%20%3D%200.140608)
If we put the value of X as 0 we will get the answer zero, So I guess the value of X as 0 will make sense.
Answer:
45.8366236105
Step-by-step explanation:
1200=pi*5^2*(h/3)
15.2788745368
=h/3
45.8366236105
120,000 years would be the answer.