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soldier1979 [14.2K]
3 years ago
15

Suppose that the log-ons to a computer network follow a Poisson process with an average of 3 counts per minute. (a) What is the

mean time between counts (in minutes)? (Round yours answers to 3 decimal places.) (b) What is the standard deviation between counts (in minutes)? (Round yours answers to 3 decimal places.) (c) If it is an average of 3 counts per minute, find the value of such that . (Round yours answers to 4 decimal places.)
Mathematics
1 answer:
vampirchik [111]3 years ago
6 0

Answer: a) 0.333, b) 0.333 and c) 0.9986.

Step-by-step explanation:

Since we have given that

Average = 3 counts per minute = λ

a) What is the mean time between counts ?

Since it follows a Poisson Process, So,

E[x]=\dfrac{1}{\lambda}=\dfrac{1}{3}=0.333

(b) What is the standard deviation between counts ?

\sigma=\dfrac{1}{3}=0.333

(c) If it is an average of 3 counts per minute, find the value of such that .

If the average = 3 counts per minute.

Then, P(X

Hence, a) 0.333, b) 0.333 and c) 0.9986.

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a merchant is selling wind chimes from a booth at a flea market. he rents his space for $125 per day. the profit from each wind
Oksi-84 [34.3K]
Rents his place for $125 per day and his goal has to be in 5 days. Lets use 125 times 5 days then each chime sold is $12 and we need the number of chimes sold so we use "x" as our variable. Equation 125(5) + 12x = 3500. Hope this helps.
7 0
3 years ago
Can someone plzzz help me with this math practice paper
weeeeeb [17]

Answer:

45 degrees for 8

135 degrees for 9

48 for 10

Yes a square is a rectangle

Next ones.

Sut = 21 becuase x=5

7

Step-by-step explanation:

Last one:

x^2 + 8 = 3x + 36

      - 8          -  8

x^2        = 3x + 28

     -3x       -3x

x^2 - 3x =     28

(x · x) - 3x = 28.        

This was were a little guess work was used,

I found that any number lower than 7 is less than 28 when pluged into x and any above is higher.

Hence x = 7

So

x^2 + 8 = 7^2 + 8

7 x 7 = 49.    49 + 8 = 57.

and

3x+36 = 7 x 3 + 36

7x3 = 21. 21 + 36 = 57.

Both lines are equal so x is indeed 7.

The RSTU rectangle

3x+6 = 5x-4

    +4        +4

3x+10 = 5x

-3x        -3x

10 = 2x

10/2 = 5

5 = x or x = 5

plug it in now

3 x 5 = 15. 15 + 6 = 21

and

5 x 5 = 25. 25 - 4 = 21

so x = 5

8-10

QRS = 45 degrees because bisects the square with a diagonal line from corner to corner

PTQ is a 135 degrees because it is wider than a 90 degrees angle and meets both upper corner from the middle of the square making it 135 degrees.

SQ = 48 because RT = 24 and RT is half the length of SQ meaning its length would be 48

Or

SQ= 24 degrees because RT = 24 and if RT was to continue on the line it is on it will reach the length of SQ.

3 0
3 years ago
A diver descends 130 feet below the surface over 35 minutes. what was his average rate of descent
attashe74 [19]

I believe you would do the feet ,130, divided by the minutes ,35, to get how many feet per minute. It would get you a never ending decimal of 3.714285. So  every minute he would drop about 4 feet. You will have to put it how it says to for what your answering is. If it says round to the whole number then he would drop 4 feet, but I hope this helps you in any way :)

4 0
2 years ago
Why must one leg of a triangle that the Pythagorean triple represents need an even-numbered length?
pashok25 [27]

Most of the square numbers are even.so if we need to find root over we need an even number to convert it to perfect square.

See the example below

  • P=3
  • B=4
  • H=5

\\ \ast\bull\rm\longmapsto H^2=P^2+B^2

\\ \ast\bull\rm\longmapsto H^2=3^2+4^2

\\ \ast\bull\rm\longmapsto H^2=9+16

\\ \ast\bull\rm\longmapsto H^2=25

\\ \ast\bull\rm\longmapsto H=\sqrt{25}

\\ \ast\bull\rm\longmapsto H=5

Some other triplets are

  • (6,8,10)
  • (5,12,13)
  • (8,15,17)
6 0
2 years ago
Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that
juin [17]

Answer:

The Taylor series of f(x) around the point a, can be written as:

f(x) = f(a) + \frac{df}{dx}(a)*(x -a) + (1/2!)\frac{d^2f}{dx^2}(a)*(x - a)^2 + .....

Here we have:

f(x) = 4*cos(x)

a = 7*pi

then, let's calculate each part:

f(a) = 4*cos(7*pi) = -4

df/dx = -4*sin(x)

(df/dx)(a) = -4*sin(7*pi) = 0

(d^2f)/(dx^2) = -4*cos(x)

(d^2f)/(dx^2)(a) = -4*cos(7*pi) = 4

Here we already can see two things:

the odd derivatives will have a sin(x) function that is zero when evaluated in x = 7*pi, and we also can see that the sign will alternate between consecutive terms.

so we only will work with the even powers of the series:

f(x) = -4 + (1/2!)*4*(x - 7*pi)^2 - (1/4!)*4*(x - 7*pi)^4 + ....

So we can write it as:

f(x) = ∑fₙ

Such that the n-th term can written as:

fn = (-1)^{2n + 1}*4*(x - 7*pi)^{2n}

6 0
2 years ago
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