1. The server utilization is 500%.
2. The average response time in the system cannot be accurately calculated due to an overloaded and unstable system.
3. The average waiting time in the queue cannot be accurately calculated due to an overloaded and unstable system.
Q1. How do we calculate server utilization?The server utilization can be calculated by dividing the request processing rate by the request arrival rate. In this case, the server utilization would be:
Server Utilization = Request Processing Rate / Request Arrival Rate
= 20 req/s / 4 req/s
= 5/1
= 5
Therefore, the server utilization is 5 or 500% (since it exceeds 100%).
Q2. How do we calculate average response time?To calculate the average response time in the system, we need to consider the queuing delay (waiting time in the queue) and the service time (time taken to process a request). In the M/M/1 queue model, the average response time is the sum of the average queuing delay and the average service time.
Average Service Time = 1 / Request Processing Rate
= 1 / 20 req/s
= 0.05 s
The M/M/1 queue model has a known formula for the average queuing delay, which is:
Average Queuing Delay = (Server Utilization²) / (1 - Server Utilization) * Average Service Time
= (5²) / (1 - 5) * 0.05 s
= 25 / -4 * 0.05 s
= -1.25 s
Since the queuing delay cannot be negative, it suggests that the server is overloaded, and the system is unstable. In this case, the average response time cannot be calculated accurately using the M/M/1 model.
Q3. How do we calculate average waiting time?Similarly, to calculate the average waiting time in the queue, we can use the formula for the average queuing delay mentioned above:
Average Waiting Time = (Server Utilization²) / (1 - Server Utilization) * Average Service Time
= (5²) / (1 - 5) * 0.05 s
= -1.25 s
Again, due to the negative value, it suggests an overloaded and unstable system, so the average waiting time cannot be accurately calculated using the M/M/1 model.
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Use the properties of exponents to simplify the following expressions
1. 5³⋅5⁴
5⁷
5¹²
5⁻¹
5
2. (2⁸)²
2¹⁶
2⁶
2¹⁰
2⁴
3. Anything raised to a power of zero is always:
0
itself
1
negative
4. n²⋅n⁴⋅n⁵
n²²
n¹³
n⁴⁰
n¹¹
5. 8⁷ ⁄ 8²
8⁵
8¹⁴
8⁹
1⁵
6. 3⁻⁴
3^4
-3^4
1 ⁄ 3^4
1 ⁄ 12
7. 7⁰
0
7
-7
1
8. Fill in the blank with the correct exponent to make the statement true.
3^16 = (3^8)(3^_ )
2
4
8
1
9.Which is equivalent to 5 x 5 x 5 x 5
5^3
4^5
5^4
5^5
10. Which is equivalent to 3^4Respuesta necesaria. Opción única.
27
81
9
12
Answer:
Below in bold
Step-.by-step explanation:
1. 5 ^(3+4) = 5^7.
2. 2^(8*2) = 2^16.
3. 1.
4. n^11
5. 8^(7-2) = 8^5.
6. 1 / 3^4.
7. 7.
8. 8.
9. 5^4.
10. 81.
What property is -2x–6+4=-2? (see image)
The piecewise function h(x) is shown on the graph.
On a coordinate plane, a piecewise function has 2 lines. The first line has a closed circle at (negative 4, negative 4) and goes up to an open circle at (negative 1, 2). The second line has a closed circle at (negative 1, 3), continues horizontally to (1, 3), and then goes down to a closed circle at (4, 0).
What is the value of h(3)?
–2
–1
1
2
Step-by-step explanation/Answer:
The value for h(3) is 1.
Coordinate (3,1)
The value on h(3) is located in the last part of the piecewise function, which starts at (1,3) until (4,0). To know the exact image of h(3), we can find the function that belongs to that piece of line, and then calculated the asked value.
So, to calculate the equation, we first have to find the slope with its definition, and then we'll use the point-slope formula to find the equation:
Therefore, the coordinates is (3,1), that is, the value for h(3) is 1.
Answer:
option c
Step-by-step explanation:
edge 2022
factor 11k^4 − 88k^3 + 77k^2
Answer:
11k^2 (k - 7)(k - 1)
Step-by-step explanation:
The highest common factor is
11k^2
Using the distributive property we get at least 2 factors.
11k^2 ( k^2 - 8k + 7)
The second factor reduces yet again.
11k^2 (k - 7)(k - 1)
Answer:
11k^2(k−7)(k−1)
Step-by-step explanation:
11k^4 − 88k^3 + 77k^2
Factor out 11.
11(k^4-8k^3+7k^2)
Consider k^4-8k^3+7k^2. Factor out k^2.
k^2(k^2−8k+7)
Consider k^2 −8k+7. Factor the expression by grouping. First, the expression needs to be rewritten as k^2+ak+bk+7. To find a and b, set up a system to be solved.
a+b=−8
ab=1×7=7
Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system solution.
a=−7
b=−1
Rewrite k^2−8k+7 as (k^2−7k)+(−k+7).
(k^2−7k)+(−k+7)
Factor out k in the first and −1 in the second group.
k(k−7)−(k−7)
Factor out common term k−7 by using distributive property.
(k−7)(k−1)
Rewrite the complete factored expression.
11k^2(k−7)(k−1)
The students in Mr. Tran’s class want to raise $905.94 for new basketball equipment for the school. So far, they have earned a total of $732.78. How much money do they still need to earn?
A.
$173.16
B.
$233.24
C.
$636.84
D.
$1,638.72
if its right I give you something
Answer:
A 173.16
Step-by-step explanation:
905.94 - 732.78 = 17316
help me.............
Answer:
Step-by-step explanation:
In order to simplify we do the following...
[tex]5y + \frac{5}{14} + 9n + \frac{2}{14} + 2y - 3n = (5y +2y) +(\frac{5}{14}+ \frac{2}{14}) + (9n - 3n) = 7y + \frac{1}{2} + 6n[/tex]
Answer:
This expression can be simplified to 7y + 6n + 1/2
Step-by-step explanation:
You can find this by grouping like terms and adding them together. Starting with the expression we're given:
5y + 5/14 + 9n + 2/14 + 2y - 3n
Let's make it easier by grouping like terms:
(5y + 2y) + (9n - 3n) + (5/14 + 2/14)
Now we'll add them together:
7y + 6n + 7/14
And finally, we can simplify that fraction by factoring 7 out of both the numerator and denominator:
7y + 6n + 1/2
And now we have the final answer.
Mae Ling earns a weekly salary of $345 plus a 7.0% commission on sales at a gift shop. How much would she make in a work week If she stood $4,300 worth of merchandise?
She would make $________?
Answer:
She would make $646.00
6.On Saturday, Jane likes to work out, eat, and read a book. She will either lift weights, run, or hike. Then she will choose 1 of the 6 restaurants near her home, and read either Harry Potter, Catcher in the Rye, or Girl on the Train. How many different ways can she spend her Saturday?
Answer:
Number of different ways can she spend her Saturday = 54
Step-by-step explanation:
Jane has to do three types of things - Work out , Eat and Read a book
In Work out -
She either lift weights, run, or hike
In Eating -
She will choose 1 of the 6 restaurants near her home
In Reading -
Read either Harry Potter, Catcher in the Rye, or Girl on the Train
Number of ways in which she can work put = ³C₁ = [tex]\frac{3!}{1! (3-1)!} = \frac{3!}{2!} = 3[/tex]
Number of ways in which she can eat = ⁶C₁ = [tex]\frac{6!}{1! (6-1)!} = \frac{6!}{5!} = 6[/tex]
Number of ways in which she can read = ³C₁ = [tex]\frac{3!}{1! (3-1)!} = \frac{3!}{2!} = 3[/tex]
So, Total number of ways = 3×6×3 = 54
Please help me this is due asap!
Answer:
Step-by-step explanation:
Did not see any questions I think you make a mistake you did not put the question.
Enrique has $50 in his lunch account and spends $5 per day from the account. Maya has $46 in her lunch account and spends $4 per day from the account. Which equations model the situation?
50 – 5x = y and 46 – 4x = y
5x + 50 = y and 4x + 46 = y
5x – 50 = y and 4x – 46 = y
5 – 50x = y and 4 – 46x = y
Answer:
50 – 5x = y and 46 – 4x = y, is your answer
The radius of a circle is 4 centimeters.what is the area
A bag contains 4 Snickers bars and 1 Twix bar, and the outcome is drawing a Twix bar. Does the phrase that describes the probability of drawing a Twix bar
A.
No, because there are still only two possible outcomes.
B.
No, because it is still less likely to have an outcome of drawing a Twix.
C.
Yes, because there are still only two possible outcomes.
D.
Yes, because it is still less likely to have an outcome of drawing a Twix.
Answer:
Yes because there are still only two possible outcomes
Step-by-step explanation:
I think it’s this one cause I’m on it too
1, 1/2, 1/4, 1/8, ... What's the pattern rule and the next three numbers? Please someone help me!
Answer:
1/14 ,1/22 ,1/32
Step-by-step explanation:
pattern is according to 2 table
1/2, 1/4, 1/8 the denominators difference is 2 table
2×1=2 difference between 2&4 is 2
2×2=4 difference between 4&8 is 4
2×3=6 8+6=14
2×4=8 14+8=22
2×5=10 22+10=32
hope you've understood
Apply the distributive property to simplify the expression 7(11-7).
Answer:
28
Step-by-step explanation:
The Distributive property uses the number outside the parenthesis and combines it (using multiplication) with the ones inside.
So, the number 7 will be multiplied with the numbers inside the parenthesis.
7(11-7)
7 × 11 = 77
7 × -7 = -49 (It will just be the same way you multiply but with a added negative sign.)
77-49=
28
please help ! 2.5 : 12.5 reduce the following into ratio of whole number.??
What are the zeros of f(x) = x2 - x - 30?
O A. x = 10 and x = -3
O B. x = 6 and x = -5
O C. x= -10 and x = 3
O D. x= -6 and x = 5
Answer:
B
Step-by-step explanation:
the x intercepts of this graph are -5 and 6
An olive farmer has 7,426 olives to put into jars. It takes 47 olives to fill each jar. How many jars will the farmer be able to fill with olives?
Answer:
Step-by-step explanation:
divide 7,426 by 47 on a calculator, that’s the answer of how many jars you’ll need
is 250% of 41 less than 100, greater than 100 but less than 150, or greater than 150?
El alcance de tangente
Answer: ¿Qué significa alcance tangente? ¡Lo busqué y no dice nada!
Step-by-step explanation:
help me for brainlistt
Answer:
120 ft squared
Step-by-step explanation:
First you find the areas of all the triangle surfaces and add them up
1/2 * b * h = 21
21 *4 = 84
Find the area of the square base and add the 2 values up
6^2 = 36
36+84 = 120
I need help pleaseee):
Answer:
Step-by-step explanation:
Factorise : x³ + x - 3x² -3
Answer:
(x²+1)(x-3)
Step-by-step explanation:
Factorize x³ + x - 3x² -3
x³-3x²+x-3
Factorize
x²(x-3)+1(x-3)
= (x²+1)(x-3)
Hence the factorized form is (x²+1)(x-3)
can someone please help me with this:)
Answer: c
Step-by-step explanation:
HELP I NEED HELP ASAP
The function f(t)=1,500,000(0.885)^t models the population of a small country after t years. Which statement is true?
A. The population is growing at a rate of 88.5%
B. The population is declining at a rate of 11.5%
C. The population is declining at a rate of 88.5%
D. The population is growing at a rate of 11.5%
Answer:
B. The population is declining at a rate of 11.5%
Step-by-step explanation:
if your graph the equation you will clearly see that it is declining and if you don't know how to graph the equation then go to the demos calculator, its an app & website, super easy to use. most people would assume the answer would be one of the 88.5% just because it's in the original equation but the .885 in the equation doesn't represent the rate of change there for the answer is 11.5%.
please help me , I'm so confused ...
Answer:
E
Step-by-step explanation:
The fractions have the same denominator so all you have to do is add the numerator, retain the denominator, and add the whole number.
What is the measure of Angles are not necessarily drawn to scale.
Answer: 31
Step-by-step explanation:
59 is vertically opposite to 59 in the bottom right angles of the triangle so that angle is also 59
Then the angle in the bottom left is 90/ right angle
90+59=149
180-149=31
PLZ ANSWER !!!!!!
An eagle is flying at an altitude of 280 feet. The angle of depression from the eagle to a mouse on the ground is 15º. What is the direct line distance from the eagle to the mouse? Round answer to the nearest thousandth.
Answer:
289.877 ft
Step-by-step explanation:
You can draw the eagle and mouse by using a right triangle. You know that the height of the triangle will be 280 feet and the distance between eagle and mouse should be the hypotenuse. Since we know the angle and one side of the triangle, we can use trignometry (cosine(angle)=adjacent/hypotenuse). Plug in your values and solve for the hypotenuse.
Will mark brainliest for whoever answers
Answer:
i think g(x) is not the inverse function of f(x). HOPE THIS HELPS!
Step-by-step explanation:
How do you set up factor by grouping for the
polynomial:
V(x) is a function.
True or false??
Answer:
TRUE AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA