A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed.

Answers

Answer 1

Answer:

For a vending machine having Service time is 20 seconds per cup and customers arrive at a mean rate of 64 per hour, then average number of customers waiting in a line is 0.10

Number of customer in a queue means those who are waiting for a server.

Given the following information:

Mean arrival rate of customer, μ=64 customers per hour

Service time is 20 seconds per cup that is 1 customer per 20 seconds

λ=180 customers per hour

Average number of customers waiting in a line, $L_q=(\lambda ^2)/(2\mu (\mu -\lambda))$

On substituting the values,

$L_q=(60^2)/(2* 180(180-64))\nL_q=0.098\approx 0.10$

Thus, average number of customers waiting in a line is 0.10

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Complete question:

A vending machine dispenses hot chocolate or coffee. Service time is 20 seconds per cup and is constant. Customers arrive at a mean rate of 64 per hour, and this rate is Poisson-distributed. Determine the average number of customers waiting in line.

Answer 2

Answer:

Final answer:

This problem engages queueing theory in mathematics, specifically it involves a vending machine with constant service time and Poisson-distributed customer arrival rate. The system is analyzed to be stable as the service rate surpasses the arrival rate.

Explanation:

This problem is a classic case of queueing theory in mathematics, particularly relevant in Probability and Statistics. Our case involves a vending machine that has a constant service time of 20 seconds per cup of hot chocolate or coffee. The mean customer arrival rate is presented as 64 per hour, described as being Poisson-distributed.

To start, consider the service rate. With the service time being a constant 20 seconds per cup, this translates to 3 cups being served per minute or 180 cups per hour. This value becomes our service rate µ. For the arrival rate or lambda (λ), the rate was given as 64 customers per hour.

In this particular queuing system, the service rate is higher than the arrival rate. This means that the system is stable, and queues are not expected to be overly long because customers are being served at a faster rate than they are arriving.

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2.02 Graded Assignment: Graphing Exponential Equationssum consumer mathwill give brainliest1. We mentioned how the price of movie tickets has increased over time with inflation in Unit 6. Let’s let the equation y = 0.50(1.06)x represent the price of movie tickets for the years after 1950.Using this equation, find the price for 2022, 2023 and 2024

Answers

Answer:

2022: 33.19

2023: 35.18

2024: 37.29

Explanation:

The given equation to find the ticket price is

$y=0.5(1.06)^x$

Where x is the number of years after 1950.

So, to find the price for 2022, 2023 and 2024, we need to replace x by 72, 73 and 74 respectively because

2022 - 1950 = 72

2023 - 1950 = 73

2024 - 1950 = 74

Then, the price for each year is

$\begin{gathered} 2022\colon y=0.5(1.06)^(72) \n y=0.5(66.37) \n y=33.19 \n 2023\colon y=0.5(1.06)^(73) \n y=0.5(70.36) \n y=35.18 \n 2024\colon y=0.5(1.06)^(74) \n y=0.5(74.58) \n y=37.29 \end{gathered}$

A researcher wants to determine if birthweights of children born to U.S. mothers is affected in any way when large megadoses of caffeine are consumed routinely by the mother during pregnancy. It is known that the birthweights are normally distributed with mean 7.5 pounds and standard deviation 1 pound. When drawing a sample of size 40 from such a population, and computing the mean birthweight in the sample, use the Central Limit Theorem to find the 2.5-th percentile of the distribution of sample means.

Answers

Answer:

7.19

Step-by-step explanation:

The sum of three consecutive odd integers is -381

Answers

Given that the numbers are consecutive:
let the first number be x, the second number will be x+1, the third number be x+2
thus the sum of the numbers will be:
x+(x+1)+(x+2)=-381
3x+3=-381
3x=-381-3
3x=-384
x=-128
thus the first number is -128, the second number is -127 and the third number is -126

WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FASTEST!

Answers

Answer:

speed i answerd first U.U

Step-by-step explanation:

Which scatter plot could have a trend line whose equation is y = x + 15?

Answers

Answer:

I'm going to say it's the third one (bottom left) because it's the only one that has points scattered in the same vicinity as the graph when I plugged in that equation. The line showed was linear and had many points including (0,15), (1, 16), and (2, 17).

Use simple linear regression analysis to find the parameters for the line that minimizes MSE for this time series. Do not round your interim computations and round your final answers to three decimal places. For subtractive or negative numbers use a minus sign. (Example: -300) y-intercept, b0 = Slope, b1 = MSE = One of OSH’s goals is to cut the percentage of U.S. adults who were users of tobacco to 12% or less within nine years of the last year of these data. Does your regression model from part (b) suggest that OSH is on target to meet this goal?

Answers

Answer:

a)The data shows a downward trend pattern

Step-by-step explanation:

See attached images

Final answer:

In simple linear regression, the parameters for the line that minimizes the MSE can be found. To determine if a regression model suggests a goal is being met, compare predicted values to the goal value.

Explanation:

In simple linear regression analysis, the parameters for the line that minimizes the Mean Squared Error (MSE) can be found. The y-intercept (b0) and slope (b1) of the line can be calculated using the data. To determine if the regression model suggests that a goal is being met, you would compare the predicted values from the regression model to the goal value. If the predicted values are less than or equal to the goal value, then the goal is being met.

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