Michael knows 12 different routes to travel by car between Paris and Berlin. In how many ways can Michael drive from Paris to Berlin by one route and then return by a different route?​

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer: d. 3

Step-by-step explanation: 12 inches in a foot

Answer:

\(x=\dfrac{11}{4}\)

Step-by-step explanation:

Given:

\(9^{-\frac{1}{2}}=\dfrac{27^{\frac{1}{4}}}{3^{(x-1)}}\)

Rewrite 9 as 3² and 27 as 3³:

\(\implies (3^2)^{-\frac{1}{2}}=\dfrac{(3^3)^{\frac{1}{4}}}{3^{(x-1)}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{-1}=\dfrac{3^{\frac{3}{4}}}{3^{(x-1)}}\)

Multiply both sides by \(3^{(x-1)}\) :

\(\implies 3^{-1} \cdot 3^{(x-1)}=3^{\frac{3}{4}}\)

\(\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:\)

\(\implies 3^{(-1+x-1)}=3^{\frac{3}{4}}\)

\(\implies 3^{(x-2)}=3^{\frac{3}{4}}\)

\(\textsf{Apply exponent rule} \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x):\)

\(\implies x-2=\dfrac{3}{4}\)

\(\implies 4(x-2)=3\)

\(\implies 4x-8=3\)

\(\implies 4x=11\)

\(\implies x=\dfrac{11}{4}\)

Breanna was biking at a constant rate of 14 miles per hour.

A rate can be defined as the speed at which something happens or changes or the amount or number of times it happens or changes in a particular period.

The formula that describes the relationship between distance (d), rate (r), and time (t) is d = rt.

Now, we will solve for r. From d = rt. Our r will equals to:

= d/t.

Now we compute the rate at which Breanna was biking.

= 84 miles/6 hours

= 14.

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Answer:

A) 10-14

B) 45

C) 6.7%

Step-by-step explanation:

A) The interval that contain the most values can be gotten by looking at the histogram and selecting the interval with the highest frequency. Hence the interval 10-14 contains the most values because it has a frequency of 20.

B)The total number of swimmers is gotten by summing all the frequency of each individual lap. Hence:

Total swimmers on team = 10 + 12 + 20 + 0 + 3 = 45 swimmers

C) The percentage of swimmers who swam more than 14 laps = (number of swimmers that swam more than 14 laps/total swimmers) * 100%

The percentage of swimmers who swam more than 14 laps = [(0 + 3)/45] * 100% = (3/45) * 100% = 6.7%

Answer:

enlargement

Step-by-step explanation:

observe from the figure \(OK=x<x+5=7=OK'\)

since \(OK<OK'\), then the dilation is an enlargement.

Answer:

Step-by-step explanation:

defsfvbrfdv

Answer:

Around 170

Step-by-step explanation:

i think

The vector field F → = r a ( -y i → + x j → ) has no z-component and is independent of z, indicating that it lies entirely in the xy-plane and does not vary along the z-axis.

The vector field is given by:

F → = r a ( -y i → + x j → )

where \(r = \sqrt{(x^2 + y^2)}\) and a is a constant.

We can rewrite this vector field in terms of its components:

F → = ( r a ( -y ) , r a x )

To show that the vector field F → has no z-component and is independent of z, we can take the partial derivatives with respect to z:

∂ F x / ∂ z = 0

∂ F y / ∂ z = 0

Both partial derivatives are zero, which means that the vector field F → does not depend on z and has no z-component. Therefore, it is independent of z.

This indicates that the vector field F → lies entirely in the xy-plane and does not vary along the z-axis. Its magnitude and direction depend on the values of x and y, as determined by the expressions \(r = \sqrt{(x^2 + y^2)}\)) and the constant vector a.

In summary, the vector field F → = r a ( -y i → + x j → ) has no z-component and is independent of z, indicating that it lies entirely in the xy-plane and does not vary along the z-axis.

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The number of elements in the sample space for this experiment are 969 by combination formula.

In an experiment where a person eating at a cafeteria choose 3 out of the 19 vegetables on offer, the number of elements in the sample space is 969.

A sample space of an experiment is the set of all possible outcomes of a random experiment. So the number of elements in a sample space is the total number of possible outcomes of  the experiment.

Here the experiment is choosing 3 vegetables from a set of 19 vegetables offered. The total number of ways to choose 3 out of 19 distinct vegetables = \(^{19}C_{3}\)

= \(\frac{19!}{3!\times16!}\)

= 969

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the members of k are d and 4, while the members of l are all real numbers between 4 and 5 (inclusive).

In set-builder notation, {x | P(x)} represents the set of all elements x that satisfy the property P(x).

Using this notation, we have:

k = {x | x is an element of the set {d, 4}}

l = {x | x is a real number such that x is greater than or equal to 4 and less than or equal to 5}

what is  set-builder notation?

Set-builder notation is a way of specifying a set by describing the properties that its elements must satisfy.

In set-builder notation, we use braces { } to enclose a description of the elements of a set. The description consists of a variable, followed by a vertical bar "|" symbol (read as "such that" or "where"), and then a condition that the variable must satisfy.

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To construct a 98% confidence interval for B₁, we can use the t-distribution since the sample size is small (n = 12).

Given the sample mean (B₁ = 46), sample standard deviation (s = 5.7), and sum of squares (SSzz = 57), we can calculate the confidence interval.

The formula for a confidence interval is:

Confidence Interval = Sample Mean ± (Critical Value * Standard Error)

For a 98% confidence level and n = 12, the critical value is approximately 2.681 (obtained from a t-distribution table).

The standard error is calculated as the sample standard deviation divided by the square root of the sample size (s / √n).

Plugging in the values:

Standard Error = 5.7 / √12 ≈ 1.647

Confidence Interval = 46 ± (2.681 * 1.647)

Therefore, the 98% confidence interval for B₁ is approximately (42.21, 49.79).

In conclusion, we can be 98% confident that the true value of B₁ falls within the range of 42.21 to 49.79 based on the given sample data.

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The local school board should reject the null hypothesis since 0.000034 < 0.05.

There is sufficient evidence that the true proportion of households with school-aged children that would support starting the school year a week early is significantly different from the true proportion of households without school-aged children.

All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.

A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.

Thus, The local school board should reject the null hypothesis since 0.000034 < 0.05.

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Step-by-step explanation:

DECREASING 3.8% means  96.2 % is left each year   ( .962 in decimal)

1800 (.962) ^6  =~ 1427 population

Answer:

1389.6

explamation

1500 of 3.8% is 68.4

68.4*6=410.4

1800-410.4=139.6

Answer:

B. (5x - 4)(3x + 2)

Step-by-step explanation:

Factor the following:

\( \longrightarrow \) 15x² - 2x - 8

The coefficient of x² is 15 and the constant term is -8. The product of 15 and -8 is -120. The factors of -120 which sum to -2 are 10 and -12.

So,

\( \longrightarrow \) 15x² + (10 - 12)x - 8

\( \longrightarrow \) 15x² + 10x - 12x - 8

\( \longrightarrow \) 5x(3x + 2) - 4(3x + 2)

\( \longrightarrow \) (5x - 4)(3x + 2)

Bank B has a basic fee of $9.95 per month and a bill paying fee of $5.95 per month. It has a limit of 20 checks written per month, with a cost of $1 per bill beyond the limit. The total annual cost for Bank B is $174.40.

To compare the cost of online banking, Tim Worker needs to consider various factors, including the basic monthly fee, bill paying monthly fee, limits on the number of checks written, and cost per bill beyond the limit. The basic fee is the amount charged by the bank for providing access to online banking services.

The bill paying fee is charged for each payment made through the online bill pay service. The limit on the number of checks written is the maximum number of checks that can be written in a given month without incurring additional charges. The cost per bill beyond the limit is the amount charged for each bill payment made beyond the specified limit.

Bank B has a basic fee of $9.95 per month and a bill paying fee of $5.95 per month. It has a limit of 20 checks written per month, with a cost of $1 per bill beyond the limit. To calculate the annual cost for Bank B, we can multiply the basic fee and bill paying fee by 12 and add the cost of any additional bills beyond the limit, multiplied by the cost per bill and the number of months in a year.

The total annual cost for Bank B is $174.40, calculated as follows:

Basic fee = $9.95 * 12 = $119.40

Bill paying fee = $5.95 * 12 = $71.40

Cost of bills beyond limit = $1 * (35 - 20) * 12 = $180

Total cost = $119.40 + $71.40 + $180 = $371.80

However, since the cost per bill beyond the limit is capped at $20 per month, the actual cost is $9.95 * 12 + $5.95 * 12 + $20 * 12 = $174.40.

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Answer:

D. im answering for the purpose of the first person getting brainliest

Step-by-step explanation:

I can help you with the Java game exercise to build a snake game using a LinkedList. Here's a step-by-step guide to get you started:

Set up the project and GUI:

Create a new Java project in your preferred IDE.

Set up a graphical user interface (GUI) for the game using a suitable library such as Swing or JavaFX.

Create a Snake class:

Define a Snake class that represents the snake in the game.

Use a LinkedList data structure to store the coordinates of each segment of the snake's body.

Implement methods in the Snake class to move the snake, grow its length, and check for collisions.

Randomly generate numbers and letters:

Use the Random class from the java.util package to generate random numbers and letters.

Generate 10 random numbers between 0 and 9 (inclusive) and store them in a suitable data structure, such as an ArrayList.

Generate a random letter using the ASCII range for letters (e.g., 'A' to 'Z').

Set the initial location of numbers and letter:

Choose a suitable location on the game board for each number and letter.

Assign these randomly generated numbers and the letter to their respective locations.

Handle user input:

Implement event listeners or handlers to capture user input for controlling the snake's movement.

Map the user input to appropriate actions, such as changing the snake's direction.

Game loop and rendering:

Create a game loop that continuously updates the game state and renders the graphical elements on the screen.

Within the game loop, handle the movement of the snake, collision detection, and updating the game board.

Game over conditions:

Define conditions for game over, such as when the snake collides with itself or with the boundaries of the game board.

Display appropriate messages or actions when the game is over.

Testing and debugging:

Test your game thoroughly to ensure that it functions as expected.

Debug any errors or issues that arise during testing.

Remember to break down the problem into smaller tasks, implement and test each task separately, and gradually integrate them into the complete game. Feel free to ask specific questions if you encounter any issues along the way. Good luck with your game development!

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Answer:

5.40

Step-by-step explanation:

let X represent the price of a 18 minute phone call

X=18 ×1.80

6

= 5.40

Answer:

x = 5

Step-by-step explanation:

All 3 angles add up to 180.

5x+6 + 43 + 106 = 180

5x + 155 = 180

5x = 25

x = 5

Point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

A circle is a geometric shape defined as the set of all points in a plane that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

Center: The center is a fixed point in the plane from which all points on the circle are equidistant. It is denoted by the coordinates (h, k), where h represents the x-coordinate and k represents the y-coordinate of the center.

Radius: The radius is the distance between the center of the circle and any point on the circle. It is denoted by the letter "r". The radius is constant for all points on the circle.

Diameter: The diameter is a line segment passing through the center of the circle and with endpoints on the circle. It is twice the length of the radius, and it divides the circle into two equal halves.

In the xy-plane, the unit circle with center at the origin (0, 0) is defined by all the points that are at a distance of 1 unit from the origin.

Point A: (1, 0)

Point A lies on the x-axis and is 1 unit away from the origin. It represents a point on the unit circle.

Point B: (3/5, 4/5)

Point B lies on the unit circle but is not one of the standard points (such as (1, 0), (-1, 0), (0, 1), or (0, -1)). Instead, it represents a point on the unit circle with coordinates (3/5, 4/5). The x-coordinate of B is 3/5, and the y-coordinate is 4/5. The distance between point B and the origin (0, 0) is 1 unit, which satisfies the condition of being on the unit circle.

Therefore, point A (1, 0) and point B (3/5, 4/5) both lie on the unit circle with center at the origin.

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Answer:

B)20

Step-by-step explanation:

y=10 when x=2 and varies directly so y=5*x

when x=4 then y=5*x=5*4=20

Answer:

B. 7−10; 11−14; 15−18; 19−22

Step-by-step explanation:

Answer:

brackets, then Parenthesis then the FIRST Multiplication then the division and then math and sub and so on a so for

Step-by-step explanation:

In a standard normal distribution, the mean and the standard deviation are both 0 and 1, so  the correct answer to the given question is option b. 0 and 1.

Standard normal distribution: The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation

In a standard normal distribution, the correct answer to the given question is option b. 0 and 1. The standard normal distribution is a normal distribution curve where the values of the mean and standard deviation are 0 and 1 respectively

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Step-by-step explanation:

4x - 5y = 80

4x - 80 = 5y

y = 4x/5 - 16 = (4/5)x - 16

y-(axis-)intercept is the point of the function, where x = 0.

y = (4/5)×0 - 16 = -16

so, the point is (0, -16)

x-(axis-)intercept is the point of the function, where y = 0.

0 = (4/5)x - 16

16 = (4/5)x

80 = 4x

x = 20

so, the point is (20, 0)

we know that

The formula for combinations is

\(C=n!/[(n-r)!*r!]\)

where

\(n\) is the total number of objects you choose from

\(r\) is the number that you choose to arrange

in this problem

\(n=15\) students

\(r=4\) students

\(C=15!/[(15-4)!*4!]\) → \(C=15!/[11!*4!]\) → \((15*14*13*12*11!)/(11!*4*3*2*1)\)

\(C=(15*14*13*12)/(24)\) → \(C=1365\)

the answer is

1,365

Answer:

49.65-50.35

Step-by-step explanation:

0.7% of 50 is 0.35. We can find the range by first subtracting that from 50 which is 49.65, then adding it to get 50.35.