Answer:
Step-by-step explanation:
Given
Balloon in the east makes an angle of elevation of
and is at height of 461 m
Balloon in the west makes an angle of elevation of
and is at height of 296 m
Erica height is 1.6 m tall so net altitude of Red balloon is 459.4 m
and net height of Blue balloon is 294.4 m
using trigonometry
![\tan 36=\frac{459.4}{d_1}](https://tex.z-dn.net/?f=%5Ctan%2036%3D%5Cfrac%7B459.4%7D%7Bd_1%7D)
![\tan 51=\frac{294.4}{d_2}](https://tex.z-dn.net/?f=%5Ctan%2051%3D%5Cfrac%7B294.4%7D%7Bd_2%7D)
![d_1=632.30 m](https://tex.z-dn.net/?f=d_1%3D632.30%20m)
![d_2=238.4 m](https://tex.z-dn.net/?f=d_2%3D238.4%20m)
Distance between two Balloons
![d=d_1+d_2](https://tex.z-dn.net/?f=d%3Dd_1%2Bd_2)
![d=870.70 m](https://tex.z-dn.net/?f=d%3D870.70%20m)
Answer:
Step-by-step explanation:
12 maybe
Answer:
![P(x \le 3) = 0.2352](https://tex.z-dn.net/?f=P%28x%20%5Cle%203%29%20%3D%200.2352)
Step-by-step explanation:
Given
--- male committing a crime in an episode
-- Number of episodes
Required
Determine the probability of male committing a crime at least 3 times
This question illustrates binomial distribution and will be solved using;
![P(x) = ^nC_x * p^x * (1 - p)^{n-x](https://tex.z-dn.net/?f=P%28x%29%20%3D%20%5EnC_x%20%2A%20p%5Ex%20%2A%20%281%20-%20p%29%5E%7Bn-x)
So, the required probability is represented as:
![P(x \ge 3)](https://tex.z-dn.net/?f=P%28x%20%5Cge%203%29)
And will be calculated using:
![P(x \ge 3) = P(x = 3) + P(x = 4) + P(x = 5)](https://tex.z-dn.net/?f=P%28x%20%5Cge%203%29%20%3D%20P%28x%20%3D%203%29%20%2B%20P%28x%20%3D%204%29%20%2B%20P%28x%20%3D%205%29)
![P(x = 3) = ^5C_3 * (0.35)^3 * (1 - 0.35)^{5-3}](https://tex.z-dn.net/?f=P%28x%20%3D%203%29%20%3D%20%5E5C_3%20%2A%20%280.35%29%5E3%20%2A%20%281%20-%200.35%29%5E%7B5-3%7D)
![P(x = 3) = ^5C_3 * (0.35)^3 * (1 - 0.35)^2](https://tex.z-dn.net/?f=P%28x%20%3D%203%29%20%3D%20%5E5C_3%20%2A%20%280.35%29%5E3%20%2A%20%281%20-%200.35%29%5E2)
![P(x = 3) = 10 * (0.35)^3 * (0.65)^2](https://tex.z-dn.net/?f=P%28x%20%3D%203%29%20%3D%2010%20%2A%20%280.35%29%5E3%20%2A%20%280.65%29%5E2)
![P(x = 3) = 0.1811](https://tex.z-dn.net/?f=P%28x%20%3D%203%29%20%3D%200.1811)
![P(x = 4) = ^5C_4 * (0.35)^4 * (1 - 0.35)^{5-4}](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%20%5E5C_4%20%2A%20%280.35%29%5E4%20%2A%20%281%20-%200.35%29%5E%7B5-4%7D)
![P(x = 4) = 5 * (0.35)^4 * (1 - 0.35)^1](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%205%20%2A%20%280.35%29%5E4%20%2A%20%281%20-%200.35%29%5E1)
![P(x = 4) = 5 * (0.35)^4 * (0.65)](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%205%20%2A%20%280.35%29%5E4%20%2A%20%280.65%29)
![P(x = 4) = 0.0488](https://tex.z-dn.net/?f=P%28x%20%3D%204%29%20%3D%200.0488)
![P(x = 5) = ^5C_5 * (0.35)^5 * (1 - 0.35)^{5-5}](https://tex.z-dn.net/?f=P%28x%20%3D%205%29%20%3D%20%5E5C_5%20%2A%20%280.35%29%5E5%20%2A%20%281%20-%200.35%29%5E%7B5-5%7D)
![P(x = 5) = 1 * (0.35)^5 * (1 - 0.35)^0](https://tex.z-dn.net/?f=P%28x%20%3D%205%29%20%3D%201%20%2A%20%280.35%29%5E5%20%2A%20%281%20-%200.35%29%5E0)
![P(x = 5) = 1 * (0.35)^5 * (0.65)^0](https://tex.z-dn.net/?f=P%28x%20%3D%205%29%20%3D%201%20%2A%20%280.35%29%5E5%20%2A%20%280.65%29%5E0)
![P(x = 5) = 1 * (0.35)^5 * 1](https://tex.z-dn.net/?f=P%28x%20%3D%205%29%20%3D%201%20%2A%20%280.35%29%5E5%20%2A%201)
![P(x = 5) = 0.0053](https://tex.z-dn.net/?f=P%28x%20%3D%205%29%20%3D%200.0053)
So:
![P(x \ge 3) = P(x = 3) + P(x = 4) + P(x = 5)](https://tex.z-dn.net/?f=P%28x%20%5Cge%203%29%20%3D%20P%28x%20%3D%203%29%20%2B%20P%28x%20%3D%204%29%20%2B%20P%28x%20%3D%205%29)
![P(x \le 3) = 0.1811 + 0.0488 + 0.0053](https://tex.z-dn.net/?f=P%28x%20%5Cle%203%29%20%3D%200.1811%20%2B%200.0488%20%2B%200.0053)
![P(x \le 3) = 0.2352](https://tex.z-dn.net/?f=P%28x%20%5Cle%203%29%20%3D%200.2352)
Answer:
1. 469 2. 171 3. 36 4. 0 5. 60