Samantha measured the dimensions of a rectangular poster frame. It was 3/4 yard long and 1/2 yard wide. What is the area of the
2 answers:
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Answer:
a) We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.
b) If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
Step-by-step explanation:
For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinatios of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
In this problem, we have that:
The probability that a single radar station will detect an enemy plane is 0.65. This means that .
(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?
This is the value of n for which .
n = 1.
n = 2
n = 3
n = 4
We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?
The expected number of sucesses of a binomial variable is given by:
So when
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
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Answer:
see the attachment for a graph
Step-by-step explanation:
With the given point and slope, the equation of the line can be written in point-slope form:
y -k = m(x -h) . . . . . line with slope m through point (h, k)
y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)
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Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:
(-1 +2, 2 +1) = (1, 3).
You can draw your line through those two points.
