Answer: a) P(x=0) = 0.0907, b) P(x≥10) = 0.7986
Step-by-step explanation: the probability mass function of a possion probability distribution is given as
P(x=r) = (e^-λ)×(λ^r) /r!
Where λ = fixed rate at which the event is occurring and each event is independent of each other = 2.4
a) P(x= at least one) = P(x≥1)
P(x≥1) = 1 - P(x<1)
But P(x<1) = P(x=0) { we can not continue to negative values because our values of x can only take positive values of integer}
Hence, P(x≥1) = 1 - P(x=0)
P(x=0) = e^-2.4 * 2.4^0/(0!)
P(x=0) = 0.0907×1/1
P(x=0) = 0.0907
b) if the average number of hits in 1 minutes is 2.4 then for 5 minutes we have 2.4×5 = 12.
Hence λ = 12.
P(x= at least 10) =P(x≥10) = 1 - P(x≤9)
P(x≤9) will be gotten using a cumulative possion probability distribution table whose area is to the left of the distribution.
From the table P(x≤9) = 0.2014.
P(x≥10) = 1 - 0.20140
P(x≥10) = 0.7986
Answer:
I Didn't see nothing
Step-by-step explanation:
So I can't help you
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
Answer:
2 sqrt(5) =x
Step-by-step explanation:
We can use the Pythagorean theorem since this is a right triangle
a^2 + b^2 = c^2
2^2 +4^2 = x^2
4+16 = x^2
20 = x^2
Take the square root of each side
sqrt(20) = sqrt(x^2)
sqrt(4*5) = x
sqrt(4) sqrt(5) =x
2 sqrt(5) =x
Answer:
Step-by-step explanation:
answer to the question:
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