Answer:
0.96 = 96% probability that at least one of them detect an enemy attack.
Step-by-step explanation:
For each radar, there are only two possible outcomes. Either it detects the attack, or it does not. The missiles are operated independently, which means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
In which
is the number of different combinations of x objects from a set of n elements, given by the following formula.
![C_{n,x} = \frac{n!}{x!(n-x)!}](https://tex.z-dn.net/?f=C_%7Bn%2Cx%7D%20%3D%20%5Cfrac%7Bn%21%7D%7Bx%21%28n-x%29%21%7D)
And p is the probability of X happening.
Assume that a particular detection system has a 0.80 probability of detecting a missile attack.
This means that ![p = 0.8](https://tex.z-dn.net/?f=p%20%3D%200.8)
If two military radars are installed in two different areas and they operate independently, the probability that at least one of them detect an enemy attack is
This is
when
. So
![P(X \geq 1) = 1 - P(X = 0)](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29)
In which
![P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28X%20%3D%20x%29%20%3D%20C_%7Bn%2Cx%7D.p%5E%7Bx%7D.%281-p%29%5E%7Bn-x%7D)
![P(X = 0) = C_{2,0}.(0.8)^{0}.(0.2)^{2} = 0.04](https://tex.z-dn.net/?f=P%28X%20%3D%200%29%20%3D%20C_%7B2%2C0%7D.%280.8%29%5E%7B0%7D.%280.2%29%5E%7B2%7D%20%3D%200.04)
![P(X \geq 1) = 1 - P(X = 0) = 1 - 0.04 = 0.96](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%201%29%20%3D%201%20-%20P%28X%20%3D%200%29%20%3D%201%20-%200.04%20%3D%200.96)
0.96 = 96% probability that at least one of them detect an enemy attack.
Answer: y intercept (0|0)
x intercept (0|0)
Step-by-step explanation:
Y intercept means x=0
y=3*0
y=0. So the point is (0|0)
X intercept means y=0
0=3x
X=0. So the point is also (0|0)
<u>Given</u>:
The given equation is ![q+\log _{2}(6)=2 q+2](https://tex.z-dn.net/?f=q%2B%5Clog%20_%7B2%7D%286%29%3D2%20q%2B2)
We need to determine the approximate value of q.
<u>Value of q:</u>
To determine the value of q, let us solve the equation for q.
Hence, Subtracting
on both sides of the equation, we get;
![q=2 q+2-\log _{2}(6)](https://tex.z-dn.net/?f=q%3D2%20q%2B2-%5Clog%20_%7B2%7D%286%29)
Subtracting both sides of the equation by 2q, we have;
![-q=2-\log _{2}(6)](https://tex.z-dn.net/?f=-q%3D2-%5Clog%20_%7B2%7D%286%29)
Dividing both sides of the equation by -1, we have;
![q=\log _{2}(6)-2](https://tex.z-dn.net/?f=q%3D%5Clog%20_%7B2%7D%286%29-2)
Now, substituting the value of
, we have;
![q=2.585-2](https://tex.z-dn.net/?f=q%3D2.585-2)
Subtracting the values, we get;
![q=0.585](https://tex.z-dn.net/?f=q%3D0.585)
Thus, the approximate value of q is 0.585
Hence, Option C is the correct answer.
2+4+6+8 = "i=1" "n=4" Σ 2i