Answer:
100 - 16 = 84, and 84 divided by 12 is 7. She needs to buy 7 more boxes of granola bars for her students.
Step-by-step explanation:
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.
The greatest common fact is 6.
18 ÷ 6 = 3
24 ÷ 6 = 4
In simplest form, 18/24 = 3/4
It's hard to tell from the way the question is written.
-- If he has 5 pennies, then it doesn't matter how many he lost.
He has five of them.
-- If he has 5 pennies after he lost three of them, then there are
eight now, just like there were before, but he only has 5 of them.
-- If he had 5 pennies before he lost three, then there are still
5 pennies, but he only has two of them.
The function for x=3 is 1