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Dovator [93]
3 years ago
9

In analyzing hits by certain bombs in a war, an area was partitioned into 570 regions, each with an area of 0.75 km^ 2 . A total

of 535 bombs hit the combined area of 570 regions Assume that we want to find the probability that randomly selected region had exactly two hits the Poisson distribution formula

Mathematics
1 answer:
tangare [24]3 years ago
5 0

Answer:

0.1723 = 17.23% probability that randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\mu is the mean in the given interval.

535 bombs hit the combined area of 570 regions

This means that the mean number of hits per region is given by:

\mu = \frac{535}{570} = 0.9386

Find the probability that randomly selected region had exactly two hits

This is P(X = 2).

P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}

P(X = x) = \frac{e^{-\0.9386}*(0.9386)^{2}}{(2)!} = 0.1723

0.1723 = 17.23% probability that randomly selected region had exactly two hits.

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How many pairs (a, b), where a and b are positive integers, satisfy the equation a2−b2=105? PLS HELP
Vlad [161]

Answer:

  4

Step-by-step explanation:

The left side of the equation can be factored as the difference of squares:

  (a -b)(a +b) = 105

The right side of the equation can be factored to 4 different pairs of factors:

  105 = 1·105 = 3·35 = 5·21 = 7·15

For each of the factor pairs, we can match factors to get, for example, ...

  a -b = 1

  a +b = 105

The solution to this is a = (105 +1)/2 = 53, b = (105 -1)/2 = 52. Thus, we have ...

  (a, b) = (53, 52)

For the other factor pairs, the solutions are ...

  (a, b) = (19, 16), (13, 8), (11, 4)

There are a total of 4 positive integer solutions.

6 0
4 years ago
HELP WILL MARK BRAINLIEST IF GOTTEN RIGHT!!!!!!! PLS DONT ASNWER IF U DONT KNOW
Savatey [412]

Answer: 33 degrees

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8 0
3 years ago
Use the graph of f to describe the transformation that results in the graph of g. f(x) = log x; g(x) =
LuckyWell [14K]

Answer:

The function was expanded vertically by 5, and then translated vertically upwards 6 units.

Which is the third option in the list of possible answers.

Step-by-step explanation:

Recall that the types of transformations associated with:

A) a function multiplied by a positive factor larger than one consists on the function expanded vertically by that factor.;

B) a positive number added to the function consists on the vertical translation of the function upwards as many units as the number added.

Therefore, the function f(x) = log(x) being transformed into g(x)=5\,log(x)+6

consists of the initial function expanded vertically by 5, and then translated vertically upwards 6 units.

4 0
3 years ago
A walkway forms one diagonal of a square playground. The walkway is 22 m long. How long is a side of the​ playground?
nadya68 [22]
You can think of a square as two isosceles right angle triangles and use Pythagoras.

x^2 + x^2 = 22^2
x^2 + x^2 = 484
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x = 11√2

One side of the playground is 11√2 m long.
5 0
4 years ago
Sam is 5 years old. His older brother Tom, is three times as old as Sam. When Sam is 20, how old will Tom be?
GrogVix [38]

Answer:

60

Step-by-step explanation:

Sam is 5, Tom is 3 times as old, 5 times three is 15, so tom is 15, 20 is 4 times 5, so you take 15, and multiply it by 4, and that's your answer

6 0
3 years ago
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