The Frisco Roughriders need help with determining which of the following queuing systems is better for their new food vending area. They have the option of installing a two server system that has less automation or a new one server system in which drinks are automatically filled. They have 1 person per minute show up. The service rate for the automated system is 100 customers per hour and each server for the 2 server is 40 customers per hour. They have a few key metrics that they are trying to determine and need your help in deciding which system to install:
a. probability that no one is in line
b. total number of people in the system
c. total wait time in the system

The number of  individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5% is at least 246.

To determine the sample size needed for a 90% confidence interval with a margin of error no more than 5%, we can use the formula:

n = (\(z^{2}\) * p * q) / \(E^{2}\)

where:
n = sample size
z = z-score for the desired confidence level (in this case, 1.645 for 90%)
p = proportion of individuals who believe global warming is not a problem (0.8)
q = 1 - p (0.2)
E = margin of error (0.05)

Plugging in these values, we get:

n = (\(1.645^{2}\)* 0.8 * 0.2) / \(0.05^{2}\)
n ≈ 246

Therefore, at least 246 individuals will need to be sampled to have a 90% confidence interval with a margin of error no more than 5%. The answer is at least 246.

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Answer:

3/4 divided by 9 (break it down) = 1/12

The correct representation of the inequality is -6x + 15 < 10 - 5x and an open circle is at 5 and a bold line starts at 5 and is pointing to the right.

In mathematical concept, an inequality is a representation of an order linking two numbers or algebraic expressions together. These orders are called inequality signs such as greater than (>), less than (<), greater than or equal to(≥), or less than or equal to(≤). Either questions or theorems can be used to express inequality problems, and both can be solved using methods similar to those used to solve equations.

From the given information, we are given the inequality:

= -3(2x - 5) < 5(2 -x)

Open brackets, we get:

= -6x + 15 < 10 - 5x

Subtract 15 from both sides, we have:

= -6x + 15 - 15 < 10 - 5x - 15

= -6x < -5x - 5

Add 5 to both sides

= -6x + 5 < -5x - 5 + 5

= -6x + 5 < -5x

= -x < - 5

= x < 5

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Answer:

8.06 ounces

Step-by-step explanation:

Ounces of wool of the sweater = percent of wool in the sweater x weight of the sweater

65% x 12.4 ounces

0.65 x 12.4 = 8.06 ounces

Answer:

umm

Step-by-step explanation:

Answer:

n=900

Step-by-step explanation:

n/4= 225, so multiply by 4 to get n=900 (hopefully I understand the question correctly, if not, please let me know.)

Answer:

Step-by-step explanation:

For all shapes, the surface area will go up by a factor of 9 (3^2). This is true of spheres, cones, cubes, pyramids, torusses, everything.

The surface area of any body is proportional to the square of any linear dimension. Triple a linear dimension and you get a 9 fold increase in surface area. This is as true for pretzels as it is for spheres and cubes.

The resulting control chart will help identify any points that fall outside the control limits, indicating potential anomalies or special causes of variation in the idle time ratio.

To construct the control chart for the idle time ratio based on three standard deviations, we need to follow several steps:

Step 1: Calculate the average idle time ratio.

To calculate the idle time ratio, we divide the idle time (in minutes) by the total effective working time (in minutes). In this case, the total effective working time per day is 8 hours or 480 minutes. Calculate the idle time ratio for each day using the formula:

Idle Time Ratio = Idle Time / Total Effective Working Time

Day 1: 40 / 480 = 0.083

Day 2: 35 / 480 = 0.073

...

Day 25: 28 / 480 = 0.058

Step 2: Calculate the average idle time ratio.

Sum up all the idle time ratios and divide by the number of days to find the average idle time ratio:

Average Idle Time Ratio = (Sum of Idle Time Ratios) / (Number of Days)

Step 3: Calculate the standard deviation.

Calculate the standard deviation of the idle time ratio using the formula:

Standard Deviation = sqrt((Sum of (Idle Time Ratio - Average Idle Time Ratio)^2) / (Number of Days))

Step 4: Calculate the control limits.

The upper control limit (UCL) is the average idle time ratio plus three times the standard deviation, and the lower control limit (LCL) is the average idle time ratio minus three times the standard deviation.

UCL = Average Idle Time Ratio + 3 * Standard Deviation

LCL = Average Idle Time Ratio - 3 * Standard Deviation

Step 5: Plot the control chart.

Plot the idle time ratio data on a graph, along with the UCL and LCL calculated in Step 4. Each data point represents the idle time ratio for a specific day.

The resulting control chart will help identify any points that fall outside the control limits, indicating potential anomalies or special causes of variation in the idle time ratio.

Note: Since the calculations involve a large number of values and the table provided is not suitable for easy calculation, I recommend using a spreadsheet or statistical software to perform the calculations and create the control chart.

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If you are allocated 1 TB data to use on your phone, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.

1 Terabyte (TB) = 1,000 Gigabytes (GB

So, 1 TB = 1,000 GB

So, the total data available is 1,000 GB/month

Then, to find how many years it will take until you run out of your quota of 1 GB/month consumption, divide the total data available by the monthly consumption:

1,000 GB/month ÷ 1 GB/month = 1,000 months

To convert months to years, divide by 12:1,000 months ÷ 12 months/year ≈ 83.33 years

Therefore, it will take you 83.33 years until you run out of your quota of 1 GB/month consumption.

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Thus, the probability are Zero represents the impossibility.

1/2 equals probable and unlikely

1 = event happens.

Because we don't know how something will turn out, we might talk about the probability of one outcome or the potential for several outcomes.

Typically, the likelihood is stated as the proportion of favourable events to all other potential outcomes in the sample space.

The probability of an event is calculated using the formula P(E) = (Number of favourable outcomes) (Sample space).

Given that probability can only be a number between 0 and 1,

The zeroth value is the impossible.

so there is a 50% chance for both likely and unlikely.

If 1, the event must take place.

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Answer:

2√ 3

Step-by-step explanation:

√ 48  −  √ 12

=> √ (2 x 2 x 2 x 2 x 3)  −  √ (2 x 2 x 3)

=> 2 x 2√ 3  −  2√3

=> 4√ 3  −  2√ 3

=> 2√ 3

The simplification of the given expression √48−√12 will be 2√3.

The component we may multiply by itself to obtain a given number is the number's square root. Squaring an integer is the reverse of finding its square root.

It is given that the expression is, √48  − √12

We have to simplify the given expression.

Another word for "solving a math difficulty" is "simplifying an equation." When you simplify an expression, your goal is to make it as simple as you can.

=√48 −√12

=> √ (2 x 2 x 2 x 2 x 3)  −  √ (2 x 2 x 3)

=> 2 x 2√ 3  −  2√3

=> 4√ 3  −  2√ 3

=> 2√ 3

Thus, the simplified form of the given expression √48−√12 will be 2√3.

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Answer:

RS = 6

Step-by-step explanation:

6x-2=3x+7

 +2     +2

6x   =3x+9

-3x     -3x

3x=9

x=3

3+3=6

This means that your parallelogram has an area of 204 square centimeters.

Thank you for your question. Based on the information provided, it seems that you have a parallelogram with a base of 17 centimeters and a height of 12 centimeters, while your friend also has a parallelogram with a base of 17 centimeters.

To find the area of a parallelogram, we use the formula:
Area = base x height
So for your parallelogram, the area would be:
Area = 17 cm x 12 cm = 204 cm^2

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Answer:

2 • (x - 2) • (3x + 1)

Step-by-step explanation:

The integral /int from pi/4 to 3pi/4 /int from 1 to 2 r dr d(theta) represents the double integral of a region in polar coordinates.

The region can be visualized as a sector of a circle in the polar plane, bounded by the angles pi/4 and 3pi/4, and by the radii 1 and 2. The first integral /int from 1 to 2 r dr integrates over the radial direction, while the second integral /int from pi/4 to 3pi/4 d(theta) integrates over the angular direction.

To evaluate the integral, we integrate the radial part first. Integrating r with respect to r yields (1/2)r^2. Plugging in the limits of integration, we get [(1/2)(2)^2] - [(1/2)(1)^2] = 2 - 1/2 = 3/2.

Next, we integrate the angular part. Integrating d(theta) with respect to theta gives theta. Evaluating the limits of integration, we have (3pi/4) - (pi/4) = pi/2.

Finally, multiplying the results of the radial and angular integrals, we have the value of the double integral as (3/2) * (pi/2) = 3pi/4. Thus, the integral evaluates to 3pi/4.

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By analyzing the population equation we can see that:

Here we have the population equation:

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*t}}\)

a) When does the growth rate start to decrease?

The rate of change will be:

\(p'(t) = 0.5*\frac{500}{(1 + 4.55e^{-0.5*t})^2}*4.55e^{-0.5*t}\)

Below, you can see the graph of it, and there you can see that for t > 0 the rate always decreases.

b) The initial population is what we get when we evaluate p(t) in t = 0

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*0}} = \frac{500}{1 + 4.55} = 91\)

c) What is the maximum population?

It is 500 (asymptotically), which is the value that we get when we take the limit of t to infinity.

d) The population after 2 years is given by:

\(p(t) = \frac{500}{1 + 4.55e^{-0.5*2}} = 187\)

So after two years, there will be 187 birds.

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The value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.

To find the value of $\#(\&4)$, we first need to evaluate $\&4$. Using the given definition of $\&x$, we have:

$$\&4 = 4 + 5 = 9$$

Now, we can substitute this value into the definition of $\#x$:

$$\#(\&4) = \#9 = 9^2 = 81$$

Therefore, the value of $\#(\&4)$ is 81. We first evaluated $\&4$ using the definition given, which gave us the value 9. Then, we substituted this value into the definition of $\#x$ to find the final answer of 81.
To find the value of #(&4), let's first compute &4.

According to the definition, &x = x + 5. So, &4 = 4 + 5 = 9.

Now we need to find the value of #9. The definition of #x is x², which means #9 = 9² = 81.

Therefore, the value of #(&4) is 81.

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The trigonometric values for a right triangle can be obtained through the measurements of the different sides,

this can be found in a triangle like this,

then, identify the measurements in the given triangle

then,

According to the given question we have The equivalent logarithmic equation to 5.2 – = h is ln(e 5.2) = 5.2, and the value of h is approximately 0.0067.

The logarithmic equivalent of e 5.2 is ln(e 5.2). 5.2 – = h as an equivalent logarithmic equation can be solved using the properties of logarithms.

In order to solve this, first we need to take the natural logarithm of both sides. ln(5.2–) =

ln(h)ln(e 5.2) can be evaluated by using the properties of logarithms as follows: ln(e 5.2) = 5.2 (because ln(e) = 1)

Thus, the logarithmic equivalent of e 5.2 is ln(e 5.2) = 5.2.

Furthermore, the value of ln(5.2–) can be found by using the property of logarithms that ln(a–) = -ln(a).

Therefore, ln(5.2–) = -ln(5.2).We can then substitute the value of ln(e 5.2) and ln(5.2–)

to obtain the final logarithmic equation: -ln(5.2) = ln(h) -5.2 = ln(h)Finally, we can exponentiate both sides to solve for h:

eh = e-5.2h = e-5.2 ≈ 0.0067

Therefore, the equivalent logarithmic equation to 5.2 – = h is ln(e 5.2) = 5.2, and the value of h is approximately 0.0067.

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Answer:

hope it helps

Step-by-step explanation:

I hope u can understand

Answer:

18 units

Step-by-step explanation:

since the y- coordinates are equal then the 2 points lie on a horizontal line and the distance (d) between them is the absolute value of the x- coordinates, that is

d = | - 4 - 14 | = | - 18 | = 18

or

d = |  14 - (- 4) | = | 14 + 4 | =   18  = 18

Answer:

y = x -1

Step-by-step explanation:

parallel lines have the same gradient therefore = x.

y intercept of second is -1

Answer:

Its the same line y = x + 1.

Step-by-step explanation:

The slope of the line = slope of y = x + 1 which is 1.

Using the point-slope form of a line:

y - y1 = m(x - x1) and substituting the given values:

y - (-1)) = 1(x - (-2))

y + 1 = x + 2

y = x + 1

ANSWER and EXPLANATION

The slope of a graph is defined as the rate of change of the graph.

It is the rate at which the y values change with respect to the x values.

It can be calculated by dividing the rise of the graph by the run.

That is:

Based on the given data, it seems that both the polysilicon doping level and anneal temperature can affect the base current.

To visually interpret the data, we can create a scatter plot with the polysilicon doping level on the x-axis and the base current on the y-axis, with different colors or symbols representing the different anneal temperatures. We can also create a similar plot with the anneal temperature on the x-axis and the base current on the y-axis, with different colors or symbols representing the different polysilicon doping levels.

To analyze the model, we can examine the residuals to see if they are randomly distributed around zero, indicating that the model is a good fit for the data. If the residuals show a pattern, it may suggest that the model is not a good fit.

Assuming a linear model, we can estimate the parameters using regression analysis. The model could be of the form:

Base current = β0 + β1(doping level) + β2(anneal temperature) + ε

where β0 is the intercept, β1 is the coefficient for doping level, β2 is the coefficient for anneal temperature, and ε is the error term.

Once we have estimated the parameters, we can plot the response surface to see how the base current changes as a function of both the doping level and annealing temperature. This will give us a better understanding of the relationship between these variables and the response variable.

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According to the given information, 46% of people believe that there is life on other planets. A scientist, who disagrees with this finding, conducted a survey of 120 randomly selected individuals and found that 48 of them believed in life on other planets. To determine if there is sufficient evidence to conclude that the percentage differs from 48 at a significance level (α) of 0.10, a hypothesis test is needed.

The null hypothesis (H0) states that the percentage is equal to 48%, while the alternative hypothesis (H1) states that the percentage differs from 48%. In this case, the sample proportion (p) is 48/120 = 0.4, and the hypothesized proportion (p0) is 0.48.

To perform the hypothesis test, we need to calculate the test statistic (z) and compare it to the critical values. The test statistic can be calculated using the formula z = (p - p0) / √(p0 * (1 - p0) / n), where n is the sample size. After calculating the test statistic, we compare it to the critical values corresponding to α = 0.10.

If the test statistic falls within the critical region, we reject the null hypothesis and conclude that there is sufficient evidence to claim that the percentage differs from 48%. If it falls outside the critical region, we fail to reject the null hypothesis and cannot conclude that the percentage differs from 48% based on this sample.

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Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.

The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.

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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the

highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure

of variation.

The measure of variation that is affected most by a few extreme scores is the standard deviation.

The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared

deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.

On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.

The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.

The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.

The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme

enough to change the position of the middle value.

The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less

pronounced than on the standard deviation.

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Step-by-step explanation:

Hey there!

Your answer is Option A.

Check all:

A. y = 6x-2

Comparing the equation with y = mx+b, we get;

m= 6

and b= -2

B. y= 6x+2

Comparing the equation with y= mx+b, we get;

m = 6

b= 2

C. y = 2x+6

Comparing the equation with y= mx+b, we get;

m= 2

b = 6

D. y= -2x-6

Comparing the equation with y= mx+b, we get;

m= -2

b= -6

Therefore, Option A is correct answer.

Hope it helps...