a suburban specialty restaurant has developed a single drive-thru window. customers order, pay, and pick up their food at the same window. arrivals follow a poisson distribution while service times follow an exponential distribution. if the average number of arrivals is 6 per hour and the service rate is 2 every 15 minutes, what is the average number of customers waiting in line behind the person being served? a. 3.00 b. 0.5 c. 2.25 d. 30.0 e. 0.75
Answers
Using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.
What is exponential distribution?The Poisson point process, or a process in which events occur continuously and independently at a constant average rate, uses an exponential distribution to represent the probability distribution of the time between occurrences.
Statistics and probability theory both make use of this distribution.
So, we know that:
6 arrivals on average are made per hour (Poisson distribution).
It provides two services every fifteen minutes (exponential distribution).
Waiting line behind the person being served:
(15 / 6 * 2) + 1
(15 / 12) + 1
1.25 + 1
2.25
Therefore, using the Poisson distribution and the exponential distribution, on average, there are (C) 2.25 consumers in line behind the person serving.
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Related Questions
What is the reciprocal of 14/19?
Answers
Answer:
1 5/14
Step-by-step explanation:
Flip it around: 19/14
Turn 19/14 into a mixed number which is:
1 5/14
Answer:
the reciprocal of 14/19 is 19/14 (also can be written as 1.3571)
Step-by-step explanation:
reciprocal of a fraction is the opposite, your numerator becomes the denominator and the denominator becomes the numerator.
the fraction is flipped.
After a pizza party there are 4 2/3 pizzas left over. If the pizzas are divided so that party goers can take home 1/6 of a pizza, how many guests can take home pizza? *
1 point
8 guests
26 guests
28 guests
33 guests
Answers
Answer:
26 guests
Step-by-step explanation:
Find f[g(x)] and g[f(x)] for the given functions. 3 f(x) = -x³ +3, g(x) = 4x+7 (Simplify your answer. Do not factor.) (Simplify your answer. Do not factor.) f[g(x)] = g[f(x)] =
Answers
The value of f[g(x)] is - 64x³ - 336x² - 588x - 340 and the value of g[f(x)] is -4x³ + 19
The functions are as follows; f(x) = -x³ +3 and g(x) = 4x+7
The value of f[g(x)] is obtained by replacing every x in f(x) with the value of g(x) as given below
f[g(x)] = f(4x + 7) = - (4x + 7)³ + 3
When we expand (4x + 7)³, it gives us 64x³ + 336x² + 588x + 343
Then
f[g(x)] = - 64x³ - 336x² - 588x - 340
Similarly, g[f(x)] is obtained by replacing every x in g(x) with the value of f(x) as shown below;
g[f(x)] = g(-x³ + 3) = 4(-x³ + 3) + 7g
[f(x)] = -4x³ + 19
Therefore,
f[g(x)] = - 64x³ - 336x² - 588x - 340
g[f(x)] = -4x³ + 19
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Mrs. Sloan draws two figures on the board.
Allen says that figure Z is dilated te form
figure Z using a scale factor of 3 and point X
as the center of dilation. What mistake did
Allen make? What is the correct scale factor?
Explain your reasoning.
Answers
A dilated shape will either be enlarged or compressed.
Allen did not make any mistake, and the scale factor is 3.
The dimension of the smaller rectangle (figure Z) is:
3 units by 4 units
The corresponding dimension of the bigger rectangle (figure Z') is:
9 units by 12 units
The scale factor (k) is calculated by dividing the dimensions of Z' by Z.
So, we have:
\(k = \frac{9}{3}\)
\(k = 3\)
or
\(k = \frac{12}{4}\)
\(k = 3\)
Notice that both values of k are the same (i.e. 3)
This means that the scale factor is 3
Also figure Z and Z' share the same center of origin at point X
This means that the center of dilation from Z to Z' is X
Hence,
Allen made no mistake, and she is correct about the scale factor.
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Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (0, 11), and a co-vertex at (4, 0). HELP ASAP
Answers
Answer:
Step-by-step explanation:
If you plot those points on a coordinate plane, you'll see that the distance from the origin up the y-axis to the point is greater than is the distance from the origin down the x-axis to the other point. That means 3 things to us: 1. the greater distance is a and the shorter is b; 2. the point (0, 11) is the vertex while the point (4, 0) is the co-vertex; and 3. this is a vertically stretched ellipse. A vertically stretched ellipse has an equation
\(\frac{(x-h)^2}{b^2} +\frac{(y-k)^2}{a^2} =1\) where h and k are the coordinates of the center, a is the greater distance (between the center and the vertex), and b is the smaller distance (between the center and the co-vertex). Here's what we have then thus far:
h = 0
k = 0
a = 11
b = 4
Filling in our equation then looks like this:
\(\frac{(x-0)^2}{4^2} +\frac{(y-0)^2}{11^2} =1\) and simplifying:
\(\frac{x^2}{16} +\frac{y^2}{121} =1\). It appears that the last answer is the one you want, although when I teach this to my precalc students, I do not encourage them to move the x and y terms around as that answer appears to have done. But addition is also commutative so I'm sure it's acceptable (I just think it looks strange that way).
The equation of ellipse is \(\dfrac{y^2}{121}+\dfrac{x^2}{16}=1\) option D is correct.
Important information:
The center of the ellipse is the origin.Vertex at (0,11).Co-vertex at (4,0)Ellipse:The standard form of an ellipse is:
\(\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1\)
Where, \((0,a)\) is vertex and \((0,b)\) is vertex.
Substitute \(a=11,b=4\) in the above equation.
\(\dfrac{x^2}{(4)^2}+\dfrac{y^2}{(11)^2}=1\)
\(\dfrac{x^2}{16}+\dfrac{y^2}{121}=1\)
\(\dfrac{y^2}{121}+\dfrac{x^2}{16}=1\)
Therefore, the correct option is D.
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During a session, a senate had a total of 112 Democrats and Republicans. There were 4 fewer Democrats than Republicans. How many members of each party were there?
Answers
Answer:
There are 54 Republicans, and 58 Democrats
Step-by-step explanation:
See the attached image
Dell Eatery employs one worker whose job it is to load apple pies on outgoing company cars. Cars arrive at the loading gate at an average of 48 per day, or 6 per hour, according to a Poisson distribution. The worker loads them at a rate of 8 per hour, following approximately the exponential distribution in service times. a. Determine the operating characteristics of this loading gate problem. [6 Marks] b. What is the probability that there will be more than six cars either being loaded or waiting? [2 Marks] Formulae L= μ−λ
λ
W= μ−λ
1
L q
W q
rho
P 0
= μ(μ−λ)
λ 2
= μ(μ−λ)
λ
= μ
λ
=1− μ
λ
P n>k
=( μ
λ
) k+1
Answers
The required probability is 0.4408.
The operating characteristics of the loading gate problem are:
L = λ/ (μ - λ)
W = 1/ (μ - λ)
Lq = λ^2 / μ (μ - λ)
Wq = λ / μ (μ - λ)
ρ = λ / μ
P0 = 1 - λ / μ
Where, L represents the average number of cars either being loaded or waiting.
W represents the average time a car spends either being loaded or waiting.
Lq represents the average number of cars waiting.
Wq represents the average waiting time of a car.
ρ represents the utilization factor.
ρ = λ / μ represents the ratio of time the worker spends loading cars to the total time the system is busy.
P0 represents the probability that the system is empty.
The probability that there will be more than six cars either being loaded or waiting is to be determined. That is,
P (n > 6) = 1 - P (n ≤ 6)
Now, the probability of having less than or equal to six cars in the system at a given time,
P (n ≤ 6) = Σn = 0^6 [λ^n / n! * (μ - λ)^n]
Putting the values of λ and μ, we get,
P (n ≤ 6) = Σn = 0^6 [(6/ 48)^n / n! * (8/ 48)^n]
P (n ≤ 6) = [(6/ 48)^0 / 0! * (8/ 48)^0] + [(6/ 48)^1 / 1! * (8/ 48)^1] + [(6/ 48)^2 / 2! * (8/ 48)^2] + [(6/ 48)^3 / 3! * (8/ 48)^3] + [(6/ 48)^4 / 4! * (8/ 48)^4] + [(6/ 48)^5 / 5! * (8/ 48)^5] + [(6/ 48)^6 / 6! * (8/ 48)^6]P (n ≤ 6) = 0.5592
Now, P (n > 6) = 1 - P (n ≤ 6) = 1 - 0.5592 = 0.4408
Therefore, the required probability is 0.4408.
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Find the value of X.
Answers
Answer:
x=2
Step-by-step explanation:
\(2^{3x+1}+52=180^o\)
\(2^{3x+1}+52-52=180-52\)
\(2^{3x+1}=128\)
\(3x+1=7\)
\(x=2\)
tell me the correct answer and i will give you brainliest!!!
Li is making beaded necklaces. For each necklace, she uses 31 spacers, plus 8 beads per inch of necklace length. Write an equation to find how many beads Li needs for each necklace, where x is the length, in inches, of the necklace.
Answers
Answer:
x x 8= y
Step-by-step explanation:
Please help me 123 or 4
Answers
Answer:
3
Step-by-step explanation:
because divide Pt from both sides to get r=i/(pt)
5. A contractor estimates that he will need 18 sheets of drywall, he actually
uses 14 sheets of drywall. To the nearest percent, what is the percent
error?
Answers
Answer:
Percent error is approx. 22%
Step-by-step explanation:
So to do this you need to know the formula for percent error, which is
percent error = l measured - theoretical / theoretical l * 100%
With this just plug in 18 (real) and 14 (measured).
percent error = l 14 - 18 / 18 l * 100%
percent error = l -4 / 18 l *100%
percent error = l -2/9 l *100%
You then do absolute value because the percent error must be positive not negative! So -2/9 becomes 2/9. You then divide 2/9 to get approx. 0.22... and you muliply by 100% to get 22%.
0.3(4 − x) = x − 1.4?
Answers
Answer:
x is equal to 2
Step-by-step explanation:
simplify the equation
distribute the 0.3
0.3*4-0.3x=x-1.4
1.2-0.3x=x-1.4
get x by itself on one side
1.2+1.4=x+0.3x
simplify
2.6=1.3x
2=x
For each function, find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function.The formula for converting from Celsius to Fahrenheit temperatures is F=9/5 C+32 .
b. Use the inverse to find the Celsius temperature that corresponds to 25⁰F .
Answers
The formula for converting from Celsius to Fahrenheit temperatures is F = 9/5 C + 32 then the inverse function is one-to-one.
What is the inverse formula?The inverse function returns the original value for which the output of a function was given. When it comes to functions, f and g are inverse, with f(g(x)) = g(f(x)) = x. A function that is made up of its inverse returns the original value.
The formula for converting from Celsius to Fahrenheit temperatures is
F = 9/5 C + 32.
Let the Fahrenheit temperatures is F = 9/5 C + 32
Subtract 32 from both sides:
F - 32 = 9/5 C + 32 - 32
F − 32 = 9/5 C
Multiply both sides by 5:
5(F − 32) = 9C
Divide both sides by 9:
5/9 (F − 32) = C or C = 5/9 (F − 32)
For 27° F
⇒ C = 5/9 (27 - 32)
⇒ C = 5/9 (-5)
⇒ C = -25/9
⇒ -2.78 C° 2.dp.
Yes, the inverse is a one-to-one function.
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Four students received the following grades on their math quizzes. Which student could use the mode to show that she is doing better than the other three students?
Ashlee 70, 94, 90, 70, 94,
Belen 79, 79, 100, 95, 99,
Molly 66, 73, 98, 88, 98,
Sofia 88, 94, 96, 99, 80
Please answer right away.
Answers
Answer:
I guess Sofia is doing better than the other three students
Answer:Molly
Step-by-step explanation:
Molly can use her mode to show that she is doing better than the other three students.
Ashlee’s mode is 94, Belen’s mode is 79, Molly’s is 98, and Sofia doesn’t have a mode. The highest is Molly, so she should use her mode to show she is doing better.
The MD has placed an order for 15mg of albuterol and 0.5mg of atrovent to be given over one hour. The nebulizer you use has an output of 10ml oer hour when running at 4lmp. How much saline would you need to add to your medication to make it last the full hour?
Answers
The volume of the medication required, we subtract it from the nebulizer output to find the amount of saline needed.
To determine the amount of saline needed to make the medication last the full hour, we need to calculate the total volume of medication required and subtract it from the volume delivered by the nebulizer.
Given:
- Albuterol dose: 15 mg
- Atrovent dose: 0.5 mg
- Nebulizer output: 10 mL per hour
- Nebulizer flow rate: 4 LPM (liters per minute)
First, we need to convert the nebulizer flow rate to mL per hour:
4 LPM * 60 min = 240 mL per hour
Next, we calculate the total volume of medication required by adding the doses of albuterol and Atrovent:
Total medication volume = 15 mg + 0.5 mg
Now, we need to convert the total medication volume from milligrams to milliliters. To do this, we need to know the concentration of the medication (mg/mL) or the volume of the medication that corresponds to the given dose. Without this information, we cannot convert the dose to volume accurately.
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Find 4ac when a=3 and c+39
Answers
Answer:
468
Step-by-step explanation:
a=3 and c=39
4(3)(39)
468
i believe you accidently wrote c+39 instead of c=39 :)
Answer:
468
Step-by-step explanation:
Replace:
4(3)(39)
=468
HELP! need the answer!
Answers
Answer:
40
Step-by-step explanation:
20x2=40
Which expression has a value of 16 when n = 5? StartFraction 25 Over n EndFraction 7 30 minus 3 n 7 StartFraction 45 Over n EndFraction n cubed minus 114.
Answers
The value of the third expression \(\rm \dfrac{45}{n} + 7\) for n = 5 is 16 which is equivalent to 16.
What is an equivalent?The equivalent is the functions that are in different forms but are equal to the same value.
Given
The expressions are shown below.
\(\rm 1. \ \dfrac{25}{n} + 7\\\\2. \ 30 -3n\\\\3. \ 7+ \dfrac{45}{n}\\\\4. \ n^3 - 114\)
The expression is equivalent to 16 for n = 5.
1. For n = 5, the expression will be
\(\rm \dfrac{25}{n} + 7\\\\ \dfrac{25}{5} + 7\\\\5 + 7 \\12\)
The expression is not equivalent to 16.
2. For n = 5, the expression will be
\(\rm 30 - 3n\\30 - 3 * 5 \\30 - 15\\15\)
The expression is not equivalent to 16.
3. For n = 5, the expression will be
\(\rm \dfrac{45}{n} + 7\\\\ \dfrac{45}{5} + 7\\\\9 + 7 \\16\)
The expression is equivalent to 16.
4. For n = 5, the expression will be
\(\rm n^3 - 114 \\\\5^3 - 114 \\\\125 -114\\\\11\)
The expression is not equivalent to 16.
Thus, the third expression is equivalent to the 16.
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Answer:
The answer is C, \(7+\frac{45}{n}\)
Step-by-step explanation:
1. if n=5 then the expression would be rewritten as \(7 + \frac{45}{5}\)
2. 45 divide 5 is 9.
3. 9 + 7 =16 Therefore, your answer is C.Find each amount:
3.8% of 25
Answers
Answer:
0.95
Step-by-step explanation:
3.8 % of 25 is equal to 0.95.
To find 3.8 % of 25, we can calculate it using the following formula : Amount = ( Percentage / 100 ) * Base.
In this case, the percentage is 3.8 and the base is 25.
Using the formula , we have : Amount = ( 3.8 / 100 ) * 25.
First, we divide 3.8 by 100, which gives us 0.038. Then, we multiply 0.038 by 25 to find the amount.
Calculating, we have : Amount = 0.038 * 25 = 0.95.
Therefore, The value of 3.8 % of 25 is equal to 0.95.
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Ultrasound is one of many experimental treatments used for soft tissue injuries. In an experiment to gauge the efficacy of this treatment for knee injuries, seven subjects with recent knee injuries were enrolled in a trial. The range of motion (in degrees) of the joint was measured first. After a prescribed ultrasound treatment, the range of motion was measured again. Table 1 below contains the pre and post treatment responses from each of these subjects.
Table 1: Knee extensions (degrees) before and after ultrasound
Pre 57.5 28.0 29.7 65.1 44.0 51.7 39.4
Post 37.6 52.6 54.0 39.1 57.9 45.7 58.6
Diff A) In the table above, enter the differences (computed Pre - Post) in the empty cells.
B) Based on the sample, the average difference in the pre and post treatment responses is . (2 decimal places)
C) The margin of error for a 99% confidence interval for the true average difference in knee extension before versus after ultrasound treatment is 29.91. Using this margin of error , determine the lower and upper limits for the confidence interval.
Lower Limit: (2 decimal places)
Upper Limit: (2 decimal places)
D) Based on the results of this study, at = 0.01 we can conclude that :
Answers
A) The differences (computed Pre - Post) in the table are as follows:
Pre | Post | Diff
---------------------
57.5 | 37.6 | 19.9
28.0 | 52.6 | -24.6
29.7 | 54.0 | -24.3
65.1 | 39.1 | 26.0
44.0 | 57.9 | -13.9
51.7 | 45.7 | 6.0
39.4 | 58.6 | -19.2
B) The average difference in the pre and post treatment responses is calculated as the mean of the differences:
Average difference = (19.9 - 24.6 - 24.3 + 26.0 - 13.9 + 6.0 - 19.2) / 7 = -6.00 (rounded to 2 decimal places)
C) The margin of error for a 99% confidence interval is given as 29.91. Using this margin of error, the lower and upper limits for the confidence interval can be determined as:
Lower Limit = Average difference - Margin of error = -6.00 - 29.91 = -35.91 (rounded to 2 decimal places)
Upper Limit = Average difference + Margin of error = -6.00 + 29.91 = 23.91 (rounded to 2 decimal places)
D) Based on the results of this study, at α = 0.01 (0.01 significance level), we cannot make a conclusion about the true average difference in knee extension before versus after ultrasound treatment since the confidence interval includes zero.
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Find the quotient. The answer must be a proper fraction simplest form.
4 13 ÷ −3 16
Answers
Answer:
5 or 5/1
Step-by-step explanation:
did the math, this is the result. Not sure if it's right, correct me if I'm wrong
please answer
what is 2y^4 x 5y^3
Answers
it is the answer of your question
Step-by-step explanation:
STEP
1
:
Equation at the end of step 1
(2y4 • 5) • y3
STEP
2
:
Equation at the end of step 2
(2•5y4) • y3
STEP
3
:
Multiplying exponential expressions
3.1 y4 multiplied by y3 = y(4 + 3) = y7
Final result :
(2•5y7)
* Help!
* Need steps!
* Answer only if you know, thanks!
Answers
\(\text{Given that,}~3x-y = 12\\\\\\\dfrac{8^x}{2^y} =\dfrac{(2^3)^x}{2^y } = \dfrac{2^{3x}}{2^y} = 2^{3x-y} = 2^{12}\)
\(▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)
Let's solve ~
\( \sf3x - y = 12\)\( \sf3x = y + 12\)now, evaluate the value of given expression ~
\( \sf \dfrac{ {8}^{x} }{ {2}^{y} } \)\( \sf \dfrac{{(2 {}^{3} ) }^{x} }{ {2}^{y} } \)\( \sf \dfrac{2 {}^{3x} }{ {2}^{y} } \)Now, plug the value of 3x from the previous equation ~
\( \sf \dfrac{(2 ){}^{y + 12} }{ {2}^{y} }\)\( \sf2 {}^{ \ \cancel y + 12 - \cancel y} \)\( \sf{2}^{12} \)Therefore , the required expression is ~ 2¹²
The graph of the equation y = 4x + 2, what is the y when x = 1?
Answers
Answer: 6
Step-by-step explanation:
\(y=4(1)+2=6\)
substitute x for 1
4x1=4
4+2=6
a table or spreadsheet used to systematically evaluate options according to specific criteria is a ________.
Answers
A table or spreadsheet used to systematically evaluate options according to specific criteria is a decision matrix.
A decision matrix is a table or spreadsheet used to systematically evaluate options based on specific criteria. It is a tool commonly used in decision-making processes to objectively assess and compare different choices.
The decision matrix organizes the criteria in rows and the options in columns. Each cell in the matrix represents the evaluation or score of an option based on a particular criterion. The criteria can be weighted to reflect their relative importance in the decision-making process.
By filling out the decision matrix with scores or ratings for each option and criterion, a comprehensive evaluation can be performed. The matrix allows decision-makers to visualize and compare the performance of different options against the criteria, helping them make more informed and structured decisions.
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will mark branliest if correct:)
Answers
Answer:
If im not mistaking its b
Step-by-step explanation:
you gotta divide the nubers inside the box thing with then numbers outside it then multiply
Luisa’s restaurant bill comes to $75.50, and she leaves a 15% tip.
What is Luisa’s total before tax?
Answers
Answer:
$86.83
Step-by-step explanation:
Use the Simpson's rule to approximate ∫ 2.4 2f(x)dx for the following data
x f(x) f'(x)
2 0.6931 0.5
2.20.7885 0.4545
2.40.8755 0.4167
Answers
To approximate the integral ∫2.4 to 2 f(x) dx using Simpson's rule, we divide the interval [2, 2.4] into subintervals and approximate the integral within each subinterval using quadratic polynomials.
Given the data points (x, f(x)) = (2, 0.6931), (2.2, 0.7885), and (2.4, 0.8755), we can use Simpson's rule to approximate the integral.
Step 1: Determine the step size, h.
Since we have three data points, we can divide the interval [2, 2.4] into two subintervals, giving us a step size of h = (2.4 - 2) / 2 = 0.2.
Step 2: Calculate the approximations within each subinterval.
Using Simpson's rule, the integral within each subinterval is given by:
∫f(x)dx ≈ (h/3) * [f(x₀) + 4f(x₁) + f(x₂)]
where x₀, x₁, and x₂ are the data points within each subinterval.
For the first subinterval [2, 2.2]:
∫f(x)dx ≈ (0.2/3) * [f(2) + 4f(2.1) + f(2.2)]
≈ (0.2/3) * [0.6931 + 4(0.7885) + 0.8755]
For the second subinterval [2.2, 2.4]:
∫f(x)dx ≈ (0.2/3) * [f(2.2) + 4f(2.3) + f(2.4)]
≈ (0.2/3) * [0.7885 + 4(0.4545) + 0.8755]
Step 3: Sum up the approximations.
To obtain the approximation of the total integral, we sum up the approximations within each subinterval.
Approximation ≈ (∫f(x)dx in subinterval 1) + (∫f(x)dx in subinterval 2)
Calculating the values, we get the final approximation of the integral ∫2.4 to 2 f(x) dx using Simpson's rule.
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solve this equation
4f+2=6f-12
Answers
Let's try to understand how we can solve this equation
Given equation,4f+2=6f-12
Now we will take the terms on one side and constants on the other.
=> 2+12=6f-4f
=> 14=2f
=>7=f
So, the value of f would be 7. Remember that while bringing value to another side, the sign of that value changes. If it is a positive sign then it is going to be transformed into a negative one and vice versa.
What are the coordinates of the point?
A) 6, – 4)
B) (-6, – 4)
C) (6,4)
D) to (-4, 6)
Answers
Answer:
A) (6,-4)
Step-by-step explanation: