The true statement about trend lines include the following: B. The distance from the points to the line should be as small as possible.
What is a trend line?In Mathematics and Statistics, a trend line is sometimes referred to as a line of best fit and it can be defined as a statistical tool which is commonly used in conjunction with a scatter plot, in order to determine whether or not there's any form of correlation (either positive or negative) between a given data.
Generally speaking, the line of best fit or trend line should be very close to the data points as much as possible. This ultimately implies that, a characteristics of a trend line is that the distance from each of the data points to the line must be as small as possible i.e closer to the line.
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2. Evaluate
45 x ( - 4 + 1 )
Answer:
-135
Step-by-step explanation:
45 x ( -4 + 1 )
BODMAS -> Bracket of Division Multiplication Addition Subtraction
=> 45 x -3
=> -135
Use the following information to answer the question.
The Smiths want to buy a 9 ft. by 12 ft. carpet and center it in a 15 ft. by 20 ft. room.
What is the area of the carpet?
__________sq. ft.
The area of the carpet is 108 sq. ft.
To find the area of the carpet, we first need to multiply the length and width of the carpet. Therefore, 9 ft. x 12 ft. = 108 sq. ft.
The Smiths need to buy a 108 sq. ft. carpet to center it in their 15 ft. by 20 ft. room.
The area of the carpet is 108 sq. ft.
To find the area of the carpet, you need to multiply its length by its width. In this case, the dimensions of the carpet are 9 ft. by 12 ft.
Area = length × width
Area = 9 ft × 12 ft
The area of the 9 ft. by 12 ft. carpet that the Smiths want to buy and center in their 15 ft. by 20 ft. room is 108 sq. ft.
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A function f has Maclaurin series given by 1+x^2/2!+x^4/4!+x^6/6!+...+x^2n/(2n)!. Which of the following is an expression for f(x)?
a) cosx
b) e^x-sinx
c) e^x+sinx
d) 1/2 (e^x+e^-x)
e) e^x^2
The Maclaurin series expansion of a function f is the Taylor series expansion of the function about x=0. The expression for f(x) that corresponds to this Maclaurin series is: a) cosx
In other words, it is the power series representation of the function centered at x=0. The coefficients of the terms in the Maclaurin series expansion of a function f can be obtained using the formula:
an = f^(n)(0)/n!
where f^(n)(0) is the nth derivative of f evaluated at x=0.
Given the Maclaurin series expansion of a function f as 1+x^2/2!+x^4/4!+x^6/6!+...+x^2n/(2n)!, we can see that the nth coefficient an is given by x^(2n)/(2n)!.
Comparing this to the known Maclaurin series expansions of the given options, we see that the Maclaurin series expansion of option d) 1/2 (e^x+e^-x) matches the given Maclaurin series expansion of f(x).
Therefore, the expression for f(x) is 1/2 (e^x+e^-x).
A function f has a Maclaurin series given by 1+x^2/2!+x^4/4!+x^6/6!+...+x^2n/(2n)!. The expression for f(x) that corresponds to this Maclaurin series is:
a) cosx
The Maclaurin series for cos(x) is given by the sum of alternating even powers of x divided by their respective factorials, which matches the given series.
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Describe How y=5 and y=5x-4 are related to the lines on a graph
Step-by-step explanation:
The equation y=5 represents a horizontal line that passes through the y-axis at the point (0,5). This line has a constant y-value of 5, which means that no matter what x-value is plugged into the equation, the y-value will always be 5.On the other hand, the equation y=5x-4 represents a line with a slope of 5 and a y-intercept of -4. This line passes through the y-axis at the point (0,-4) and has a steepness of 5 units of y for every 1 unit of x.Therefore, these two equations are related in that they both represent lines on a graph, but the first equation is a horizontal line with a constant y-value of 5, while the second equation is a slanted line with a slope of 5 and a y-intercept of -4.PLEASE HELP WILL MARK BRAINLIEST
A researcher determined that the heights of male students in a
particular town are normally distributed with a mean of 63 inches and
a standard deviation of 1.5. Use the graph above to answer the
following questions:
67.5
a. What percentage of these students is taller than 66 inches?
b. If the data are based on 200 students, how many students are
between 60 and 64.5 inches tall? Explain.
Answer:
a) 2.5%
b) 190
Step-by-step explanation:
a) 2.35+0.15=2.5
b) (.34+.34+.135+.135)x200=
.95x200=190
Which graph represents a function?
"
Answer:
the 1rst one.
Step-by-step explanation:
because the other ones represent vertical curves which is impossible.
10. Last year, Jodi invested $10,000, part at 8% annual interest and the rest at 6% annual interest. If she received
$760 in interest at the end of the year, how much did she invest at each rate?
The amount Judi invested at each rate, using simple interest are;
The amount Jodi invested at 8% = $8,000
The amount Jodi invested at 6% = $2,000
What is a simple interest?A simple interest is the amount obtained from the product of a principal and an interest rate.
The amount Jodi invested at 8% last year = Part of $10,000
The amount she invested at 6% = The rest of the $10,000 amount
The amount she received as interest at the end of the year = $760
Let x represent the amount Jodi invested at 6%, we get;
(10000 - x) × 8% + x × 6% = 760
Therefore; 800 - 0.08·x + 0.06·x = 760
800 - 0.02·x = 760
0.02·x = 800 - 760 = 40
x = 40/0.02 = 2000
The amount Jodi invests at 6%, x = $2,000
The amount she invested at 8% = $10,000 - $2,000 = $8,000
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A standard deck of cards has two colors; black (B) and red (R). A card is picked randomly and replaced. Then another card is picked from the deck. Which tree diagram shows the sample space?
The answer to the question is 32/52 = 8/13.
There are 52 cards in a deck in total.
Of those 52 cards, there are four different suits (diamonds, hearts, clubs, spades).
There are 13 cards in each of the different suits. Also, there are 3 face cards in each of the different suits (therefore, there are 12 face cards in total).
Diamonds and Hearts are red cards (there are 26 total red cards) and
Clubs and Spades are black cards (there are 26 total black cards).
There are 26 black cards and 12 face cards in total.
However, of those 26 black cards, there are 6 face cards. That means there are
26+12-6 = 32 cards in total that are either a black card or a face card, but not both.
That means the answer to the question is 32/52 = 8/13.
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Which angle has a measurement of 80°? (1 point)
a
a protractor showing an angle with one side lined up with the base line and one side going right through the fifth tick mark past one hundred five degrees
b
a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past seventy degrees
c
a protractor showing an angle with one side lined up with the base line and one side going right through the fifth tick mark past one hundred thirty five degrees
d
a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past one hundred ten degrees
We can see here that the angle has a measurement of 80° is: D. a protractor showing an angle with one side lined up with the base line and one side going right through the tenth tick mark past one hundred ten degrees
What is an angle?A geometric shape known as an angle is created when two rays meet at a location known as the vertex. An angle's measurement, which expresses the amount of rotation required to shift one of the rays to meet the other ray, is frequently expressed in degrees or radians.
Acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (more than 90 degrees but less than 180 degrees), straight angles (exactly 180 degrees), reflex angles (greater than 180 degrees but less than 360 degrees), and full angles (exactly 360 degrees) are the several classifications of angles based on their measurement.
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what is the difference between the mean and median
Answer:
The mean is an average general view of the data while median is the value which divides a distribution into two equal parts showing where 50% of the data lies.
Answer:
Shown below.
Step-by-step explanation:
The mean and median are both ways to describe the center of a set of numbers.
What is the mean and how do you find it?The mean is the average of all the numbers in the set. To find the mean, you add up all the numbers and divide by how many there are.
What is the median and how do you find it?The median is the middle number in a set of numbers when they are arranged in order from smallest to largest. If there are two numbers in the middle, then the answer is simply whatever is between them.
(Ex. if the numbers were 3 and 4, the median will be 3.5.)
So, what's the difference?The biggest difference between the mean and median is that the mean is affected by outliers, which are values that are much larger or smaller than the other values in a set of data. If there are outliers in a data set, the mean will be affected more than the median.
HELP
I DONT REMEBEE LEARNING THIS
The set containing the zeros of the graphed function h(x) is given as follows:
{-1, 2}.
How to obtain the zeros of a function?The zeros of a function are the values of the input x for which the output y of the function assumes a value of y.
Hence, on the graph of a function, the zeros of a function are the values of x for which the graph either touches or crosses the x-axis.
From the graph, the zeros are given as follows:
x = -1 and x = 2.
Meaning that the set is {-1, 2}, and the first option is correct.
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Find the interval in which y = x squared + 4 is increasing.
Step-by-step explanation:
This is a bowl shaped parabola with axis of symmetry x = 0
From - inf to 0 it is DEcreasing
from 0 to + inf it is INcreasing
104
103
Simplify.
× 10⁹ = 10[?]
To solve, we'll work left to right.
First, we have division. When we are dividing terms with exponents, given that the base is the same, then we need to subtract the exponents.
10^4 / 10^3 = 10^1
Next, we have multiplication. When we are multiplying terms with exponents, given that the base is the same, then we need to add the exponents.
10^1 x 10^9 = 10^10
Answer: 10^10
Hope this helps!
the total enclosure around a playground at a daycare is to be 800 square feet. one side of the playground is bordered by the school building while the three remaining sides will be enclosed with fencing. find the dimensions that minimize the length of fencing needed
The dimensions that minimize the length of fencing needed are approximately 28.28 feet by 28.28 feet, creating a square-shaped playground.
To minimize the length of fencing needed for the enclosure, we need to find the dimensions that maximize the area of the playground. Since one side of the playground is already bordered by the school building, we can focus on the remaining three sides.
Let's assume the length of the playground parallel to the school building is L, and the width perpendicular to the school building is W. The area of the playground can be expressed as A = L * W.
Given that the total area of the enclosure is 800 square feet, we have the constraint L * W = 800.
To minimize the length of fencing needed, we want to maximize the area A. This occurs when the length and width are as close as possible to each other. In other words, we want to find the dimensions that form a square shape.
In a square, the length and width are equal, so we can solve the constraint equation L * L = 800.
Taking the square root of both sides, we find L = √800 ≈ 28.28 feet.
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a nationwide survey finds that 20% of people like baseball. of those people that like baseball, 50% also like tennis. of the surveyed people that like tennis, what is the minimum percent that could like baseball?
We need to use a bit of math and logic. First, we know that 20 percent of people surveyed like baseball. We also know that 50% of those who like baseball also like tennis. This means that out of the total surveyed population, 10% (50% of 20%) like both baseball and tennis.
Next, we need to find out the minimum percent of people who like tennis that could also like baseball. To do this, we need to consider the fact that there could be some people who like tennis but not baseball, and we want to find the lowest possible percentage of people who like both sports.
Let's say that x% of people surveyed like tennis but not baseball. This means that (100-x)% of people who like tennis also like baseball. We want to find the minimum value of (100-x)% that would still satisfy the conditions given in the problem.
We know that 10% of people surveyed like both baseball and tennis. This means that (100-x)% of people who like tennis but not baseball is equal to 90%.
Using a bit of algebra, we can solve for x:
(100-x)% * 90% = 10%
Simplifying this equation, we get:
(100-x)% = 10%/90%
(100-x)% = 11.11%
Therefore, the minimum percent of surveyed people who like tennis that could also like baseball is 11.11%.
In summary, of the surveyed people that like tennis, the minimum percent that could like baseball is 11.11%. This is found by considering the fact that 50% of people who like baseball also like tennis, and finding the minimum percentage of people who like tennis but not baseball that would still allow for the 10% of people who like both sports.
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What happens if a subgroup in the background info has less than 50 members?
The background info has less than 50 members, it may lead to insufficient data for making statistic significant conclusions. It's important to have a larger sample size for reliable results and accurate analysis.
A subgroup in the background information has less than 50 members, it may be more difficult to draw statistically significant conclusions or generalize findings to a larger population. This is because the smaller the sample size, the larger the margin of error and the less reliable the data may be. It is still possible to conduct research on small subgroups and draw valid conclusions if appropriate methods are used.
Researchers may need to use alternative statistical analyses or consider qualitative methods to explore the subgroup in more detail. Ultimately, the validity of the findings will depend on the quality of the data collected and the methods used to analyze it.
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an exotic fish is placed in a rectangular aquarium that has a length of 75cm and a width of 35 cm. if the water level rises 2 cm when the fish is placed in the aquarium, what is the volume of the fish?
The volume of the fish is 5250 cubic centimeters (cm³).
To find the volume of the fish, we need to determine the change in water level when the fish is placed in the aquarium. The change in water level represents the volume of the fish.
The aquarium has a length of 75 cm and a width of 35 cm. The fish causes the water level to rise by 2 cm.
The volume of the fish can be calculated using the formula for the volume of a rectangular prism:
Volume = Length * Width * Height
In this case, the length is 75 cm, the width is 35 cm, and the height is the change in water level, which is 2 cm.
Substituting these values into the formula, we have:
Volume of fish = 75 cm * 35 cm * 2 cm
Volume of fish = 5250 cm³
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customers arrive at a travel agency at a mean rate of 11 per hour. assuming that the number of arrivals per hour has a poisson distribution, give the probability that strictly more than 5 customers arrive in a given hour. translation: x has a poisson distribution with mean 11. what is p (x > 5)?
The probability that strictly more than 5 customers arrive in a given hour is approximately 0.8335 (or 83.35%).
Let's denote the random variable representing the number of customers arriving in an hour as X, which follows a Poisson distribution with a mean of 11.
To calculate P(X > 5), we need to sum the probabilities of X being greater than 5 for all possible values of X greater than 5.
P(X > 5) = 1 - P(X ≤ 5)
Using the Poisson distribution formula, we can calculate the cumulative probability of X being less than or equal to 5:
P(X ≤ 5) = Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 5
Substituting the mean λ = 11 into the formula, we get:
P(X ≤ 5) = Σ [e^(-11) * (11^k) / k!] for k = 0 to 5
P(X ≤ 5) ≈ 0.1665
Finally, calculating P(X > 5) using the complement rule:
P(X > 5) = 1 - P(X ≤ 5)
P(X > 5) ≈ 1 - 0.1665
P(X > 5) ≈ 0.8335
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in the cost equation tc = f + vx, x is best described as the:
The cost equation is used to estimate total costs associated with a given level of activity or output, where f is the fixed cost and v is the variable cost per unit of activity. The variable cost component (vx) changes in proportion to the level of activity or output (x), whereas the fixed cost component (f) remains constant regardless of the level of activity.
In the cost equation tc = f + vx, x is best described as the level of activity or the quantity of the input variable. The cost equation is a mathematical representation of the relationship between the total cost of production and the level of activity or the quantity of the input variable. The variable x represents the number of units produced or the amount of resources used in the production process, which can be measured in terms of labor hours, machine hours, or any other relevant unit of measure. The variable v represents the variable cost per unit of activity, and f represents the fixed cost of production.
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Mr. Jacobs is going to make a histogram of the test scores from the last math test he gave. He plans to first organize the data into a stem-and-leaf plot and then make the histogram from the stem-and-leaf plot. The test scores are listed below.
79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87, 85
How many bars will his histogram have?
4
6
3
5
The answer could be that Mr. Jacobs's histogram will have 4 bars.
The test scores are listed below;
79, 82, 65, 61, 94, 97, 84, 77, 89, 91, 90, 83, 99, 71, 68, 77, 87 and, 85
We have that the range of the data is from 61 to 99. To create the bars for the histogram, we need to divide this range into intervals.
In that case, the intervals would be:
60-69
70-79
80-89
90-99
thus, the histogram would have 4 bars.
Therefore, Mr. Jacobs's histogram will have 4 bars.
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Answer: that would be 4
Step-by-step explanation: there would be 3 numbers in the 60-69 range, 4 numbers that fall into the 70-79 range, 6 numbers that fall into the 80-89 range, and 5 numbers that fall into the 90-99 range. The interval with more data than any other is the 80-89 range, therefore, making it the mode interval. i hope this helps
Halp me this question
Answer: The third option, 26 plus 22 plus ___ = 52
Step-by-step explanation:
In a simple linear regression problem, the correlation coefficient r and the slope b1:
a. must be equal to each other.
b. must have the same sign.
c. must have opposite signs.
d. are not related.
In a simple linear regression problem, the correlation coefficient r and the slope b1 are related to each other, but they do not necessarily have the same sign. Therefore, option (b) and (c) are incorrect.
The correlation coefficient r measures the strength and direction of the linear relationship between two variables, while the slope b1 represents the change in the dependent variable (y) for a one-unit change in the independent variable (x).
The relationship between r and b1 is given by the equation:
r = b1 * (sY/sX)
where sY is the standard deviation of the dependent variable (y), and sX is the standard deviation of the independent variable (x).
From this equation, we can see that r and b1 have the same sign if the standard deviations sY and sX have the same sign. However, if the standard deviations have opposite signs, then r and b1 will have opposite signs.
Therefore, the correct answer is (d) the correlation coefficient r and the slope b1 are related but are not necessarily equal or have the same sign.
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$700 is deposited in an account with 5% interest rate, compounded continuously. What is the balance after 12 years?
Step-by-step explanation:
Continuous compounding formula
FV = PV e^(rt) PV = $ 700 r = .05 t = 12
FV = future value = $ 700 e^(.05 * 12) = $ 1275.48
Juan purchased a tool set for $1980 on the installment plan. He made a 10% down payment ans agreed to pay $116 per month
Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.
Juan purchased a tool set for $1,980 using an installment plan.
1. Down payment: Juan made a 10% down payment on the $1,980 tool set. To calculate this, multiply the total cost by the down payment percentage:
$1,980 * 0.10 = $198
2. Remaining balance: Subtract the down payment from the total cost to find the remaining balance:
$1,980 - $198 = $1,782
3. Monthly payments: Juan agreed to pay $116 per month to cover the remaining balance. To determine the number of months needed to pay off the balance, divide the remaining balance by the monthly payment:
$1,782 / $116 ≈ 15.36
Since Juan can't make partial payments, he will need to make 16 monthly payments to fully pay off the balance.
4. In conclusion, Juan made a 10% down payment of $198 on a $1,980 tool set, leaving a remaining balance of $1,782. He will make 16 monthly payments of $116 to cover the remaining balance.
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n(A × B) = pq.
what does the n mean in this equation
this equation is related to the cartesian product and is the formula
n(A × B) = pq = 2 x 3 = 6. In the given equation n(A × B) = pq, the n refers to the cardinality or the number of elements present in the Cartesian product A × B.
Here, A and B are sets, and the Cartesian product A × B is the set of all ordered pairs (a, b), where a is an element of set A and b is an element of set B. The cardinality of a set is the number of elements it contains.
So, n(A × B) means the number of ordered pairs present in the Cartesian product A × B. The value of n can be calculated by multiplying the number of elements in set A with the number of elements in set B.
Therefore, n(A × B) = pq, where p is the number of elements in set A and q is the number of elements in set B.To explain further, consider the example of two sets, A = {1, 2} and B = {3, 4, 5}.
The Cartesian product A × B would be {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}. Here, the number of ordered pairs in the Cartesian product is 6, which is equal to n(A × B).
The number of elements in set A is 2 (p = 2) and the number of elements in set B is 3 (q = 3). Therefore, n(A × B) = pq = 2 x 3 = 6.
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IG IDEAS MATH
#3 i
Solve the formula for h.
The area A of a trapezoid with height hand bases b. and b, is given by the formula A =
h =
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-h(b₁ + b₂).
The area of the trapezoid is solved and height h = 2A / ( a₁ + b₁ )
Given some information, the formula for a trapezoid's area is:
Area = (1/2) (base₁ + base₂) height
where base₁ and base₂ are the lengths of the parallel sides of the trapezoid, and height is the perpendicular distance between the parallel sides.
So, to calculate the area of a trapezoid, you need to know the lengths of the two bases and the height.
Let's say base1 = b1, base2 = b2, and height = h.
Then, the formula for the area becomes:
Area = (1/2) x (b1 + b2) x h
b = longer base of trapezium
h = height of trapezium
Now , on solving for height of trapezium , we get
A = ( ( a₁ + b₁ ) h₁ ) / 2
Multiply by 2 on :
2A = ( a₁ + b₁ ) h
Divide by ( a + b ) :
h = 2A / ( a₁ + b₁ )
Hence , the height is h = 2A / ( a₁ + b₁ )
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In the figure above, quadrilateral UVWX is a parallelogram.
Part a) What are the values of p, UV, and VW? Write the number only.
Part b) What property of a parallelogram did you use to solve? Show your work and explain your reasoning.
Answer:
For the given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
Step-by-step explanation:
A quadrilateral having two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides consist of equal length, and the opposing angles are of equal size. Also, the interior angles that are additional to the transversal on the same side. 360 degrees is the total of all interior angles.
The opposing sides are equal and parallel. Angles on either side are equivalent. All of the angles will be at right angles if any one of them is a right angle.
We know that the opposite sides of a parallelogram are parallel and equal making this:
8p + 6 = 9p – 2
6 + 2 = 9p – 8p
8 = p
Now, the value of side is:
UV = 8(8) + 6 = 70
The value of side VW is:
VW = 5(8) – 6 = 34
The given quadrilateral the value of p is 8, UV = 70 and VW = 34. The property of parallelogram used is the opposite sides are parallel and equal.
Express each of the following as a rational number 3/7+(-2/9)+7/9
Answer:
=62/63
=[tex]\frac{62}{63}[/tex]
Step-by-step explanation:
Convert everything to a denominator 63
=[tex]=\frac{3*9}{63} +-\frac{2*7}{63} +\frac{7*7}{63}[/tex]
=[tex]\frac{27}{63} +\frac{-14}{63} +\frac{49}{63}\\[/tex]
Add up the numerators
= [tex]\frac{62}{63}[/tex]
in a small fast food restaurant, on average, 10 customers come per hour. the restaurant can serve 12 customers per hour. on average, a customer spends 14 minutes in the restaurant. what is the average length of the line?
Therefore, the estimated average length of the line is 3 customers.
We can approach this problem by using the M/M/1 queueing model, which assumes a Poisson arrival process, an exponential service time distribution, and a single server.
In this case, the arrival rate (lambda) is 10 customers per hour, the service rate (mu) is 5 customers per hour (since the average servicem time is 14 minutes or 0.2333 hours), and there is one server.
The utilization factor (rho) is given by rho = lambda / mu = 10 / 5 = 2, which is greater than 1. This means that the system is not stable, and the queue will grow indefinitely.
To find the average length of the line, we can use Little's Law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time spent in the system:
L = lambda * W
where L is the average number of customers in the system, lambda is the arrival rate, and W is the average time spent in the system.
In this case, since the system is not stable, we cannot use Little's Law directly. However, we can still estimate the average length of the line as follows:
Let's assume that the queue is at its steady-state when there are N customers in the system (i.e., being served plus waiting in the line). Then, the average length of the line (Lq) is:
Lq = N - 1
since one customer is being served and the remaining N-1 customers are waiting in the line.
The steady-state condition requires that the arrival rate equals the departure rate, which is the service rate in this case. Therefore, we can use the following formula to estimate N:
N = lambda / (mu - lambda)
Plugging in the values, we get:
N = 10 / (5 - 10) = -2
This negative value indicates that the system is not stable, and there are more customers arriving than the system can handle. However, we can still estimate the average length of the line as:
Lq = |N - 1| = |-2 - 1| = 3
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Complete this area model to divide. 9,516 ÷ 4
Answer:
2379
Step-by-step explanation:
