Using mathematical notation similar to that used for Nowlin Plastics, give a mathematical model for calculating profit. (Write your answer in terms of the following variables q = Production Volume (quantity produced), R = Revenue Per Unit, FC = the Fixed Costs of Production, MC = Material Cost per Unit, LC = Labor Cost per Unit, and P(q) = Total Profit for producing (and selling) q units.)
P(q) =

Answer:

Step-by-step explanation:

4) A photograph costs $20, so the cost of x photographs is 20x.

Similarly, the cost of y prints is $25.

So the total cost is 20x+25y, and this has to be less than or equal to 400, so C.

5) just plug each pair in.

For example for the first option, x=5 and y=10, and since 20(5)+25(10)=100+250. which is less than or equal to 400, it works.

Answer:

(20, -2)

Step-by-step explanation:

Given the coordinate vectors p=(4,3) and q=(-2,7),

4p - 2q  = 4(4, 3)- 2(-2, 7)

4p - 2q  = (16, 12) - (-4, 14)

4p - 2q  = (16+4, 12-14)

4p - 2q  =(20, -2)

hence the required vector is (20, -2)

The probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.

We can use the central limit theorem to approximate the distribution of the sample mean. According to the central limit theorem, if the sample size is sufficiently large, the distribution of the sample mean will be approximately normal with a mean of 30,641 and a standard deviation of sqrt(variance/sample size).

So, we have:

mean = 30,641

variance = 14,561,860

sample size = 242

standard deviation = sqrt(variance/sample size) = sqrt(14,561,860/242) = 635.14

Now, we need to calculate the z-score corresponding to a sample mean of 31,358 miles:

z = (sample mean - population mean) / (standard deviation / sqrt(sample size))

= (31,358 - 30,641) / (635.14 / sqrt(242))

= 2.43

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than 2.43. The probability is approximately 0.9925.

Therefore, the probability that the sample mean would be less than 31,358 miles in a sample of 242 tires if the manager is correct is 0.9925 (or 99.25%).

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An event that is defined as impossible has a probability of zero. However, it is important to note that an event with an empirically approximated probability of zero does not necessarily mean it is impossible.

Empirical results are based on observations and data, which may be limited in scope or subject to measurement errors. Therefore, a probability approximation of zero based on empirical results does not provide absolute certainty that the event is impossible.

In probability theory, an event that is classified as impossible is one that has a probability of zero. This means that the event cannot occur under any circumstances. For example, if you roll a fair six-sided die and the event is defined as rolling a seven, which is not possible, then the probability of rolling a seven is zero.

On the other hand, when empirical results are used to approximate probabilities, it is crucial to consider the limitations of the data and the possibility of measurement errors. If an event has been observed to have a probability of zero based on empirical data, it means that it has not been observed to occur within the scope of the data collected.

However, it does not definitively prove that the event is impossible. There might be factors or conditions beyond the scope of the data that could lead to the occurrence of the event. Therefore, while an empirical approximation of zero probability suggests extreme unlikelihood, it does not guarantee that the event is impossible.

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A sampling distribution refers to a distribution of statistics, such as the mean or proportion, that is derived from a large number of random samples. It provides valuable insights into the behavior.

A sampling distribution is a distribution of statistics, such as the mean or proportion, that are derived from a large number of random samples. It represents the variability and patterns that arise from taking repeated samples from a population.

In statistical analysis, it is often not feasible or practical to collect data from an entire population. Instead, we rely on taking samples to make inferences about the population. The sampling distribution allows us to understand how the statistics of interest vary from sample to sample and provides valuable information about the accuracy and precision of our estimates.

By analyzing the sampling distribution, we can assess the reliability of our sample statistics and make inferences about the population parameters. It helps us understand the spread and central tendency of the statistics, and it guides us in drawing conclusions and making predictions based on the collected sample data.

In summary, a sampling distribution represents the distribution of statistics derived from multiple random samples and provides insights into the behavior and properties of these statistics in relation to the population.

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A sampling distribution refers to a distribution of statistics, such as the mean, that are derived from a large number of random samples taken from the same population. It represents the possible values that the statistic can take on when the same sampling procedure is used repeatedly.

The sampling distribution allows us to make inferences about the population parameter based on the statistics calculated from the samples. It is not the average deviation from the mean in a data set, a measure of whether or not a sample is truly random, or the process of allowing a few numbers to summarize many numbers. The sampling distribution shows the distribution of these sample means. It helps us understand how the sample means vary from sample to sample and gives us an idea of the range of values the population mean could take on. This information is useful in making inferences and drawing conclusions about the population based on the sample data. Imagine you have a population, let's say all the students in a school, and you want to know the average height of the students. It is practically impossible to measure the height of every student, so instead, you take a random sample of students and calculate the average height of that sample. If you repeat this process many times with different random samples, you will get a collection of sample means.

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The ideal amount of flour for 5 cakes is 40 cups of flour. The ratio of flour to cake for baking is 8 cups of flour for 2 cakes. This means for each cake, there should be 4 cups of flour. Therefore, for 5 cakes, it would be 5 multiplied by 4, which is equal to 40. This amount of flour should be enough to produce moist, light, and fluffy cakes.

If the baker uses more than 40 cups of flour, it could lead to overly dense and dry cakes, because the extra flour will absorb all the moisture and leave the cakes dry. On the other hand, using less than 40 cups of flour could lead to the cakes being too light and airy. Not having enough flour can lead to a dry and tough texture.

Therefore, the baker should use 40 cups of flour when making 5 cakes. Following the 8 cups of flour to 2 cakes ratio ensures that the cakes will have the perfect texture and consistency. This is why 40 cups of flour is the ideal amount for a baker to make 5 cakes.

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The link is in-secure....

Answer:

0.25

Step-by-step explanation:

Answer:

0.1, 0.21, 0.28, 0.35, 0.38, 0.49, 0.51, 0.54, 0.60, 0.62.

Answer:

25508

Step-by-step explanation:

Answer:

25508

Step-by-step explanation:

100 x 256 - 468 + 376

100 x 256 = 25600

25600-468= 25132

25132+376 = 25508

96% confidence interval for the population mean life of light bulbs produced by the electrical firm to be between 747.63 and 812.37 hours. This can be answered by the concept of standard deviation.

To calculate the confidence interval, we first need to determine the standard error of the mean, which can be calculated using the formula:

Standard Error of Mean = (Standard Deviation of Population) / sqrt(Sample Size)

In this case, the standard deviation of the population is given as 40 hours, and the sample size is 30. Thus, the standard error of the mean can be calculated as:

Standard Error of Mean = 40 / sqrt(30) = 7.32

Next, we need to find the critical value of t for a 96% confidence level with 29 degrees of freedom (n-1). Using a t-distribution table or calculator, we find this to be 2.048.

Using these values, we can calculate the confidence interval using the formula:

Confidence Interval = Sample Mean +/- (Critical Value * Standard Error of Mean)

Substituting the given values, we get:

Confidence Interval = 780 +/- (2.048 * 7.32) = 780 +/- 15.02

Therefore, the 96% confidence interval for the population mean life of light bulbs produced by the electrical firm is between 747.63 and 812.37 hours. This means we can be 96% confident that the true mean life of all light bulbs produced by the firm falls within this interval.

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The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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Answer:

y<1/2+2

Step-by-step explanation:

Answer:

I think the answer is A because I learned about slope last year

Answer: sorry my g i need the points lol

Step-by-step explanation: yes

Answer:

8

Step-by-step explanation:

No. of pieces of 1.75 hectares = 14 hectare ÷ 1.75 hectares = 8

Answer:

1/4

Step-by-step explanation:

f(x) = 2 * (1/2) ^x

Let x=3

f(3) = 2 * (1/2) ^3

     = 2 * ( 1/2) * 1/2) * (1/2)

     = 2 * 1/8

    = 2/8

    = 1/4

Answer:

I could be any number.

But it couldn't just be a 'b' it could be other letters. The letters is just a grown up way of saying a missing number. Its like saying:

10+b=11..

11-b=10..

therefore b=1

Does that make sense

It can also mean in the quadratic formula b

Step-by-step explanation:

In algebra, the variable "b" represents an unknown or variable number.

It is used to denote a quantity that can vary or take on different values. The purpose of using variables in algebraic equations is to generalize mathematical relationships and solve problems with unknown quantities. By assigning the letter "b" to a variable, we can manipulate and solve equations using algebraic operations, such as addition, subtraction, multiplication, and division.

The value of "b" can be determined through various methods, such as solving equations, simplifying expressions, or applying mathematical principles. The flexibility of variables like "b" allows us to solve a wide range of problems and analyze mathematical relationships without relying on specific numerical values.

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If you are trying to determine if an input variable may affect your key characteristic (output variable) by examining the

correlation between variables, you should use the tool: D. Scatter plot diagram. therefore, option D.Scatter plot

diagram is correct.

A scatter plot diagram is a graphical representation of the relationship between two variables. It can help you visualize

the correlation between the input and output variables, making it easier to determine if there is a potential cause-and-

effect relationship.

The tool that you should use to examine the correlation between variables is D. Scatter plot diagram.

A scatter plot diagram is a graphical representation that displays the relationship between two variables.

The x-axis represents the input variable, while the y-axis represents the output variable.

By plotting the data points on the scatter plot diagram, you can visually analyze the correlation between the variables.

If there is a strong positive or negative correlation between the variables, it suggests that the input variable may affect

the key characteristic (output variable).

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D. Scatter plot diagram is the tool that should be used to examine the correlation between variables to determine if an input variable may affect your key characteristic (output variable).

The scatter plot diagram is a graphical representation that displays the relationship between two variables, and it is commonly used to identify patterns, trends, and correlations between variables. By examining the scatter plot diagram, you can determine whether there is a positive, negative, or no correlation between the variables, which can help you to identify potential cause-and-effect relationships.
 To determine if an input variable may affect your key characteristic (output variable) by examining the correlation between variables, you should use:

A scatter plot diagram is a graphical tool that helps visualize the relationship between two variables, allowing you to identify any correlation between the input and output variables.

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The sum of the infinite geometric series 16 + 12 + 9 + ... is 64.

To find the sum of an infinite geometric series, you can use the formula:

sum =\(\frac a{(1 - r)}\)

where "a" is the first term in the series and "r" is the common ratio between terms.

In this case, the first term is 16 and the common ratio is 3/4, so the sum is:

sum \(= \frac{16}{(1 - \frac{3}4)} =\frac{16}{(\frac{1}4)} = 64\)

Therefore, the sum of the infinite geometric series 16 + 12 + 9 + ... is 64.

Note that this formula is only valid if the absolute value of the common ratio is less than 1. If the absolute value of the common ratio is 1 or greater, the series will either converge to a finite value or diverge to infinity, and the sum cannot be calculated using this formula.

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The probability of obtaining tails and the number 5 is 1/12

the probability of obtaining an even number is 1/2

P(heads and prime number)  1/4

Since the events are independent, the probability of obtaining tails and the number 5 is:

P(tails and 5) = P(tails) * P(5) = (1/2) * (1/6) = 1/12

The coin toss outcome is irrelevant, so the probability of obtaining an even number is:

P(even number) = 1/2

The probability of obtaining heads and a prime number is:

P(heads and prime number) = P(heads) * P(prime number) = (1/2) * (1/2) = 1/4

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Answer:

To three decimal places, The process capability index is 0.167

Step-by-step explanation:

We have to find the process capability index,

Upper specification = 16.5 ounces,

Lowe specification = 15.5 ounces

Mean = 16.0 ounces

Standard Deviation = S = 1 ounce

process capability index = (upper specification - lower specification)/6S

process capability index = (16.5 - 15.5)/6(1)

= 1/6

Process capability index = 1/6 = 0.16666667

To 3 decimal places, we get,

Process capability index = 0.167

The ratio of the number of molecules in a gas with a speed ten times greater than the root mean square speed to the number of molecules with a speed equal to the root mean square speed is not independent of temperature.

   The root mean square speed of gas molecules can be calculated using the formula:

   root mean square speed = √(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.

   Let's assume the number of molecules with a speed ten times greater than the root mean square speed is N₁, and the number of molecules with a speed equal to the root mean square speed is N₂.

   The ratio of these two numbers can be expressed as: N₁/N₂.

   At higher temperatures, the root mean square speed increases, which means the number of molecules with a speed ten times greater than the root mean square speed also increases.

   Therefore, as temperature increases, the ratio N₁/N₂ will increase as well.

   Similarly, at lower temperatures, the root mean square speed decreases, resulting in a decrease in the number of molecules with a speed ten times greater than the root mean square speed.

   Thus, the ratio N₁/N₂ is not independent of temperature; it varies with changes in temperature.

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Answer:

i ) $96120

ii ) Singular adult fee in 2012: $186.91

Step-by-step explanation:

( i )

To find the costs of all 560 peoples you:

Multiply the amount of people by the fee,

440 × 198 = $87120

120 × 120 = $9000

Add these go get the sum of member fees: $96120

( ii )

First calculate what 1% of the adult fee would be:

198 ÷ 100 = 1.98 = 1%

Then calculate what 0.1% of the fee:

1.98  ÷ 10 = 0.198 = 0.1%

Now multiply 5 by the value of 1% to get 5% :

5 × 1.98 = 9.9

Then multiply 6 by the  0.1% to get 0.6% :

0.198 × 6 = 1.188

Add these numbers together to get:

1.188 + 9.9 = $11.088 = 5.6%

Due to the fact this question is referring to money we will round this number 2 decimal places (as money does not exceed 2dp)

$11.09

We now subtract this from the 2013 fee to find out the 2012 fee

$198 - $11.09 = $186.91

$186.91 was the cost of a singular adult fee in 2012

Answer:

so sweethope you have an amazing day as well

Answer:

Sorry Good Afternoon, I also Love you and wishing you a great day and weekend.Bye

There are 160 possible area codes can be created with this format.

A process determining the number of possible arrangements in a collection of items in which the order of the selection does not matter is called combination.

Given that, When three-digit telephone area codes were first put in place in the United States and Canada, the first number could be any digit from 2 through 9, the second number could only be 0 or 1, and the third number could be any digit from 0 through 9.

So, according to question,

The first digit has about 8 options

The second digit has about 2 options

The third digit has about 10 options

Therefore, the total possible code = 8×2×10=160.

Hence, 160 possible codes are there.

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Answer:

y^2-7y+12

Step-by-step explanation:

muliply each unit of the first parentheses by the second

The point equidistant from the three sides of a triangle is its incentre.

The incenter is the centre of the largest circle that fits inside the triangle and is tangent to all three sides. It is called the incenter because it is equidistant from the interior angles of the triangle.

The incenter is a very important point in triangle geometry, and its position can be used to calculate various other measurements, such as the triangle's area and the lengths of its medians and angle bisectors.

In summary, the incenter is the answer to the question of the point equidistant from the three sides of a triangle.

Hence, the correct answer is C.

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Answer:

21

Step-by-step explanation:

We decompose prime factors of 48, 72, and 1008

48=2*2*2*2*3

72=2*2*2*3*3

1008=2*2*2*2*3*3*7

Let's compare 48, 72 with GOD(3) and LCM(1008), we can find that there must be at least 2 prime factors in the third number that is 3 and 7.

And let's find out the LCM of 48 and 72. Quite obvious the answer is 144.

Since the LCM should be the consequence of 144 multiplied by another prime factor.

Then let's try 144*7. Amazingly 144*7=1008. DONE!

The correct solution are,

(C) a=1, b=2, c=3.

The code segment does not work in the case where a > b, c > b, but a < c.

In this case, the value of 'low' is set to 'b' instead of 'a', which causes the code segment to print the incorrect value.

The values of a, b, and c that fall into this case are a=1, b=2, and c=3.

Let's trace through the code segment using a=1, b=2, and c=3:

Since a=1 and b=2, the first conditional statement (a > b && b > c) evaluates to false, so we skip the first 'if' block.

Since a=1 and c=3, the second conditional statement (a > b && c > b) evaluates to true, so we set 'low' to 'b'.

However, since we have an 'else' block following the second conditional statement, it will always be executed. So, 'low' is set to 'a' instead.

Finally, the code segment prints the sum of a + b + c - low, which is 1+2+3-1 = 5, which is incorrect.

The correct answer should be 1 + 3 = 4.

Therefore, the answer is (C) a=1, b=2, c=3.

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Answer:

6c^6

Step-by-step explanation:

ASSUMING you meant 15 * sqrt(0.16c^12)

the parentheses are important, and without them, I can't tell what exactly you mean is square-rooted and what is not

Answer: 6c^6

Step-by-step explanation: