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3 years ago

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

Mathematics

1 answer:

Lubov Fominskaja [6]3 years ago

8 0

Answer:

a) 20 second

b) 20 second

c) 1 minute

Step-by-step explanation:

Let X be the exponential random variable arising from the Poisson process with the rate λ = 3 counts per minute. Its cdf is then given by:

F(x) = I - e^-3x, x >= 0

Calculate the mean and the standard deviation of the random variable X as follows:

Е(X) =I/λ =I/3=20 second

std (x) =√1/λ^2=1/3=20 second

For the part c), write down the equation:

0.95 = P(X < x) = F(x) = I - e^-3x

and solve the equation for x to obtain:

x = -1/3 In 0.05 = 0.9985 ≅ 1 minute

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Tyler filled up his bathtub, took a bath, and then drained the tub. The function

TiliK225 [7]

Answer:

B(0) = 0 depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0

B(1) represents the function one minutes after filling began.

B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.

Step-by-step explanation:

The function gives depth of water in inches 7 minutes after filling began

A.) B(0)=0

The statement B(0) = 0 means the depth in inches 0 minutes after filling began is 0 ; that is at time = 0 ; depth = 0

B.) B(1)

B(1) represents the function one minutes after filling began.

C.B(9)=11

B(9) = 11 depicts that the depth in inches if water 9 minutes after filling began is 11.

4 0

3 years ago

Jonah is going to the store to buy candles. Small candles cost $2.50 and large candles cost $7.00. He needs to buy at least 20 c

artcher [175]

The system of linear inequalities are:

$a + b \geq 20\\\\2.50a + 7b\leq 80$

Solution:

Let "a" be the number of small candles bought

Let "b" be the number of large candles bought

He needs to buy at least 20 candles

Therefore, number of small candles and number of large candles bought must be at least 20

Thus, we frame a inequality as:

$a + b \geq 20$

"at least" means greater than or equal to

Here, we used "greater or equal to" symbol because, he can buy 20 candles or more than 20 candles also

From given,

Cost of 1 small candle = $ 2.50

Cost of 1 large candle = $ 7

He can spend no more than 80 dollars

Which means, he spend maximum 80 dollars or less than 80 dollars also

So we have to use "less than or equal to" symbol

Thus, we frame a inequality as:

Number of small candles bought x Cost of 1 small candle + number of large candles bought x Cost of 1 large candle $\leq$ 80

$a \times 2.50 + b \times 7 \leq 80\\\\2.50a + 7b\leq 80$

Thus the system of linear inequalities are:

$a + b \geq 20\\\\2.50a + 7b\leq 80$

3 0

3 years ago

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 500

ryzh [129]

Answer:

-$2.32

Step-by-step explanation:

Give that

The selling price per ticket is $9

And the number of tickets sold is 500

So,

There is one grand prize, three $300 second prize, and eleven $40 third prizes

We need to find out the expected value of the profit

$= \frac{1}{500} \times 2000 + \frac{3}{500} \times 300 + \frac{11}{500} \times 40\\\\$

= 4 + 1.8 + 0.88

= 6.68

Now the expected profit is

= $6.68 - $9

= -$2.32

6 0

2 years ago

Please Help Me I really need Accurate answer Can anyone help me?

DanielleElmas [232]

Answer:

mathematics make our brain fast and sharp

6 0

3 years ago

Given that is directly proportional to (p-1)2 and p is always positive, find the

Arturiano [62]

Answer:

p = 10.8

Step-by-step explanation:

Given that p is directly proportional to (p-1)² and p is always positive, then;

q = k (p-1)²

If q = 30 and p = 7

30 = k(7-1)²

30 = 6²k

30 = 36k

5 = 6k

k = 5/6

To get p when q = 80

q =k (p-1)²

80 = 5/6((p-1)²

480 = 5(p-1)²

480/5 = (p-1)²

(p-1)² = 96

p-1 = √96

p-1 = 9.8

p = 9.8 + 1

p = 10.8

B) 6

Ch 10.82

4 0

3 years ago