Assuming that a router that can be modeled as an M/M/1 queuing system with a mean arrival rate of 500 packets/second and a mean service rate of 1000 packets/second, what is the probability of packet loss if the number of packets in residence is limited to 10

Answer:

6/5, 7/6

Step-by-step explanation:

The nth term is (n+1)/n

2/1, 3/2, 4/3, 5/4

Put n as 5 and 6.

(5+1)/5

= 6/5

(6+1)/6

= 7/6

Answer:

The period is of [tex]\frac{\pi}{3}[/tex] units.

The horizontal shift is of 30 units to the left.

Step-by-step explanation:

The secant function has the following general format:

[tex]y = A\sec{(Bx + C)}[/tex]

A represents the vertical shift.

C represents the horizontal shift. If C is positive, the shift is to the right. If it is negative, it is to the left.

The period is [tex]P = \frac{2\pi}{B}[/tex]

In this question:

[tex]y = 7\sec{6x - 30}[/tex]

So [tex]B = 6, C = -30[/tex]

Then [tex]P = \frac{2\pi}{6} = \frac{\pi}{3}[/tex]

The period is of [tex]\frac{\pi}{3}[/tex] units.

The horizontal shift is of 30 units to the left.

Complete Question

The complete question is shown on the first and second uploaded image

Answer:

The  marginal density function of Y is  [tex]f(y)= \frac{e^{\frac{-y}{10} }}{10}[/tex]

The distribution is exponential distribution

and the expected value is[tex]E[Y] = 10[/tex]

Step-by-step explanation:

From the question we are told that the function is  

       [tex]f(x,y) = \frac{e^{-\frac{y}{10} }}{10y} \ \ \ 0< y <x<2y[/tex]

Now the marginal density function of Y i.e f(y) is mathematically evaluated by obtaining the probability density function of y as follows

           [tex]= \int\limits^{2y}_{y} { \frac{e^{\frac{-y}{10} }}{10y} } \, dx[/tex]

            [tex]= \frac{e^{\frac{-y}{10} }}{10y} * (2y - y )[/tex]

          [tex]= \frac{e^{\frac{-y}{10} }}{10}[/tex]

The distribution of the function above is exponential distribution with a rate parameter equals to  

            [tex]\lambda = \frac{1}{10}[/tex]

  The mean DOT estimate E{Y} is mathematically evaluated as

           [tex]E[Y] = \frac{1}{\lambda}[/tex]

    substituting value

            [tex]E[Y] = \frac{1}{\frac{1}{10} }[/tex]

             [tex]E[Y] =10[/tex]

Answer:

2) 43

4) 65

Step-by-step explanation:

The first and third quartile of the data can be found by calculating the median of the first and second halves of the data.  For example, the first quartile of the data can be calculated thus:

40,41,43,50,56

41,43,50

43

and the third quartile thus:

62,63,65,78,97

63,65,78

65

Hope it helps <3

Answer:

A) 43

B) 65

Step-by-step explanation:

A) First Quartile = [tex](N+1)\frac{1}{4}[/tex]

Where N is the number of observations

=> 1st Quartile = (11+1)(1/4)

=> 1st Quartile = (12)(1/4)

=> 1st Quartile = 3rd number

B) Third Quartile = [tex](N+1)\frac{3}{4}[/tex]

=> 3rd Quartile = (11+1)(3/4)

=> 3rd Quartile = (12)(3/4)

=> 3rd Quartile = 3*3

=> 3rd Quatile = 9th number

Answer:

a) Test statistic = 1.960

b) The critical values include -2.50 and 2.50.

The critical regions of rejection are thus

t < -2.50 or t > 2.50

c) The sketch of the curve is presented in the attached image to this solution. The shaded parents indicate the rejection regions.

d) The t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.

Step-by-step explanation:

a) Test statistic is computed using the expression

t = (x - μ₀)/σₓ

x = Sample mean = 104.2

μ₀ = the standard we are comparing Against

σₓ = standard error of the mean = (σ/√n)

σ = 9.6

n = Sample size = 24

σₓ = (9.6/√24) =

t = (0.425 - 0.35) ÷ 0.07816

t = 1.9595917942 = 1.960

b) To obtain these critical values, we first find the degree of freedom

Degree of freedom = n - 1 = 24 - 1 = 23

The critical values for significance level of 0.01 and degree of freedom of 23 is given as

t(0.01, 23) = 2.50

So, since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include

t < -2.50 and t > 2.50

c) since the test is two-tailled (we are testing in both directions; greater than or less than), the regions of rejection include

t < -2.50 and t > 2.50

The t-distribution curve is very similar to the normal distribution curve. The t-distribution curve is also a bell shaped curve, but it is heavier at the limits indicating that the t-distribution favours outliers more than the normal distribution.

The sketch of the curve is presented in the attached image with the shaded regions indicating the rejection region.

d) Since the t-statistic obtained (1.96), lies within the acceptance region (-2.50 ≤ x ≤ 2.50), we fail to reject the null hypothesis.

Hope this Helps!!!

Answer:

x = 2.2

Step-by-step explanation:

-0.45x + 0.33 = -0.66

Subtract .33 from each side

-0.45x + 0.33-.33 = -0.66-.33

-.45x = -.99

Divide each side by -.45

-.45x./-.45 = -.99/-.45

x = 11/5

x = 2.2

Answer:

So each strawberry is 4 calories

Step-by-step explanation:

First find the slope of the line

Two points on the line are

(0,0) and (3,12)

m = (y2-y1)/(x2-x1)

    = (12-0)/(3-0)

     = 12/3

      = 4

So each strawberry is 4 calories

Answer:

E. The parameter is μmale - μfemale and the statistic is xmale - xfemale.

Step-by-step explanation:

The sample statistic is a piece of information about the individuals or objects that were selected from a given population. The sample is just a fraction of the total population. Since it is a herculean task studying an entire population, the sample forms a manageable size that allows us to have an insight into the entire population. The sample statistics are now the piece of information about the sample being studied such as the average, mean, median, or mode.  The sample statistics have to be as specific as possible of the factors being measured. In the question, we would have to obtain the mean of both the male and female genders. This gives us an insight into the population under study.

The parameter, on the other hand, is a description of the entire population being studied. For example, we might want to determine the population mean. That is the factor we seek to measure. It is represented by the sign mu (μ).  

Answer

[tex]bc - 4b + 3c - 12[/tex]

solution,

[tex](b + 3)(c - 4) \\ = b(c - 4) + 3(c - 4) \\ = bc - 4b + 3c - 12[/tex]

hope it helps..

Answer:

[tex]bc - 4b + 3c - 12[/tex] apply de disruptive property by multiplying each term of b+3 by each term of c -4

Answer: (d) 88/ 2π

Step-by-step explanation:

Perimeter = 88m

Perimeter of a circle = 2πr

88 = 2π x r

r = 88 / 2π

Answer:

88/2π​ = r

Step-by-step explanation:

The circumference is 88 m

The circumference is given by

C = 2*pi*r

88 = 2 * pi *r

Divide each side by 2 pi

88 / 2pi = 2 * pi *r / 2 * pi

88 / 2 pi = r

Answer:

-6+2i

Step-by-step explanation:

f(2i)=2i^2+2i-4

2i^2 is -2 because i^2 is-1, times 2 is -2.

Therefore, the equation becomes -2+2i-4, leaving the answer of -6+2i.

Answer:

50%

Step-by-step explanation:

Answer:

[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]

Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]

If we apply natural log on both sides we got:

[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]

And solving for t we got:

[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]

So then would takes about 14.26 hours in order to have  95% of the lead to decay

Step-by-step explanation:

For this case we can define the variable of interest amount of Pb209 and for the half life would be given:

[tex] N(t) =N_o (\frac{1}{2})^{\frac{t}{t_{1/2}}}[/tex]

Where [tex]t_{1/2}= 3.3 hr[/tex] represent the half life and the intial amount would be [tex] N_o = 1[/tex]

And we want to find the time in order to have a 95% of decay so we can set up the following equation:

[tex] 0.05 = 1 (0.5)^{t/3.3}[/tex]

If we apply natural log on both sides we got:

[tex] ln(0.05) = \frac{t}{3.3} ln (0.5)[/tex]

And solving for t we got:

[tex] t= 3.3 *\frac{ln(0.05)}{ln(0.5)}= 14.26[/tex]

So then would takes about 14.26 hours in order to have  95% of the lead to decay

Answer:

P = £536.25

Her total pay for the week is £536.25

Step-by-step explanation:

The total pay can be written as;

P = t1(r1) + t2(r2)

Where;

t1 = normal time

r1 = normal time pay rate

t2 = overtime

r2 = overtime pay rate

Given;

t1 = 30 hours

t2 = 6 hours

r1 = £13.75

r2 = 1.5(r1) = 1.5(£13.75)

Substituting the given values into the equation 1;

P = 30(£13.75) + 6(1.5(£13.75))

P = £536.25

Her total pay for the week is £536.25

Answer:

We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:

[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]

[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]

And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria

Step-by-step explanation:

For this case we have the follwing info given:

[tex] \mu = 80.9[/tex] represent the mean

[tex]\sigma = 10.7[/tex] represent the deviation

We want to find the usual limits using the rule of thumb and for this case rule states that we have most of the values within 2 deviations from the mean so then we can find the usual limits like this:

[tex] \mu -2*\sigma = 80.9 -2*10.7= 59.5[/tex]

[tex] \mu +2*\sigma = 80.9 -2*10.7= 102.3[/tex]

And for this case a value of 142.3 is higher than the upper limti so then we can conclude that would be significantly high with the rule of thumb criteria

a) $36.

b) $44.

- I hope this helps.

Answer:

Step-by-step explanation:

Answer:

c(x,y)/(x²+y²)

Step-by-step explanation:

Since E​(x,y) = -∇V (x,y ) and V(x,y) =c ln (ro/√ x²+y²)

Let ro/√(x²+y²) = u and √(x²+y²) = v

dV/du = c/u = c√(x²+y²)/ro,

du/dv =  -ro/(x²+y²) = -ro/² and dv/dx = x/√(x²+y²)

Using the chain rule,

So dV/dx = dV/du × du/dv × dv/dx

= c√(x²+y²)/ro × -ro/(x²+y²) × x/√(x²+y²)

dV/dx = -cx/(x²+y²)

- dV/dx = -(-cx/(x²+y²)) = cx/(x²+y²)

Also, dv/dy = y/√(x²+y²)

Using the chain rule

dV/dy = dV/du × du/dv × dv/dy

= c√(x²+y²)/ro × -ro/(x²+y²) × y/√(x²+y²)

dV/dy = -cy/(x²+y²)

- dV/dy = -(-cy/(x²+y²)) = cy/(x²+y²)

E(x,y) = -∇V (x,y )

= -(dV/dx)i + [-(dV/dy)]j

= [cx/(x²+y²)]i +[ cy/(x²+y²)]j

= c(x,y)/(x²+y²)

Answer:

  x = 6

Step-by-step explanation:

Compare the given formula to the equations shown in the attachment. First of all, you see that all of the numbers are scaled by a factor of 4. Removing that gives ...

  [tex]r=\dfrac{6.6}{1+1.1\cos{\theta}}=\dfrac{1.1\cdot6}{1+1.1\cos{\theta}}[/tex]

This matches the formula for the hyperbola with e=1.1 and d=6, for a directrix of x = 6.

Answer:

a. A residual is how far off a point is from the expected value. For example, if I were to estimate the weight of my Southeastern Lubber Grasshopper, I would say it's maybe 5 ounces. But, in reality, it might be 4 ounces. So, the residual would be the reality minus the prediction, or 4 - 5, or -1 ounce.

b. The regression line is the line of predicted values for the points in the scatterplot. It tries to predict the points and make all the points be on the line.

Hope this helps!

Answer:

Step-by-step explanation:

Hello friend

The answer is 5:15 in 12 hour clock

Answer:

5:15 PM

Step-by-step explanation:

12:00 + 5:00

17:00 in 12 hour clock is 5:00 PM.

15 minutes + 5:00 PM

⇒ 5:15 PM

Answer: x < -18

Step-by-step explanation:

Simply multiply both sides by three to get x < -18

Step-by-step explanation:

x/3 < - 6

x < - 18

This should be the answer

Answer:

no supplement

Step-by-step explanation:

Supplementary angles add to 180 degrees

312 is greater than 180 degrees by itself, so it has no supplement

Answer:

f(10)=13

Step-by-step explanation:

f(x)=x/2+8

Let x = 10

f(10)=10/2 +8

      = 5 + 8

      = 13

Answer:

I hope this helps

Step-by-step explanation:

Answer:

not sure how to really answer this question.

Answer:

4.56,  4.65, 5.46, 5.64, 6.45, 6.54

Step-by-step explanation:

First we have to compare the first digits in each number as less is this digit as less is the number. So the least off all are

4.56 and 4.65

which of these two numbers is least ? Now we have to look to the 2-nd digits of these numbers:

they are 5 and 6 . 5<6 so 4.56<4.65

Lets select next numbers whicj first digit is 5. They are:

5.46 and 5.64. However the second digit of the number 5.64 -6 is bigger than the second digit of number 5.46 -4. That is why 5.46<5.64

Similarly 6.45< 6.54

Answer:

0.6517

Step-by-step explanation:

z = (x - μ)/σ

Z= standard score

x= observed value

μ= mean of the sample

σ= standard deviation of the sample

z = (x - μ)/σ  = (107.1 - 94 )/ 14 = 0.9357

probability that a randomly selected adult has an IQ greater than 107.1.  = P(Z > 0.935) =  0.6517

NB: the value is 0.6517 is pulled from the z table which can be found at the back of most math text.

Answer:

y=4x+9

Step-by-step explanation:

replace m with 4, which is the slope you gave, and

replace b with 9, the y-intercept you gave,

in the equation y=mx+b.

Answer:

largets area is 32 feet cubed

Step-by-step explanation:

8=4  foot 2 for each  side w and e and 32feet n and s  16 each side

Answer:

-12

Step-by-step explanation:

Edge 2021