Basic Distributions We shall recall a few basic distributions, which are most often seen in applications. Normal distribution A random variable X is said to have a normal distribution if its probability density function is given by p(x)=σ2π​1​e−(x−μ)2/(2σ2), with μand σ>0 constant parameters, see Fig. 2.2(a). The mean and variance are given by E[X]=μ,Var[X]=σ2. If X has a normal distribution with mean μ and variance σ2, we shall write X∼N(μ,σ2) Exercise 2.10.1 Let α,β∈R. Show that if X is normal distributed, with X∼N(μ,σ2), then Y=αX+β is also normal distributed, with Y∼N(αμ+β,α2σ2)

The volume of the prism when Joe is packing the cubes will be 210cm³.

It should be noted that the volume of the prism given in this situation will be:

= Length × Width × Height

In this case, since Joe is packing 1-centimeter cubes into a prism. The volume will be:

= Length × Width × Height

= 5 × 6 × 7

= 210cm³

In conclusion, the volume will be 210cm³.

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The given cost function is C(x) = 0.01x³ - 1.2x² + 55x, which gives the cost, in thousands of dollars, to produce x thousand items.(a) Formula for the marginal cost:C'(x) = dC(x)/dxSo, C'(x) = (0.01x³ - 1.2x² + 55x)'C'(x) = 0.03x² - 2.4x + 55The formula for the marginal cost is C'(x) = 0.03x² - 2.4x + 55.(b) C'(0) gives the marginal cost when no items are produced.

C'(0) = 0.03(0)² - 2.4(0) + 55C'(0) = 55The units of the marginal cost are dollars per thousand items.(c) The graph of the marginal cost function is as follows. To find the minimum marginal cost and the production level for which the marginal cost is the smallest, we can check the lowest point on the graph. \(C(x)=0.01x^3-1.2x^2+55x\)Differentiating with respect to \(x\), we get\(C'(x)=0.03x^2-2.4x+55\).

Hence, we can set the derivative equal to zero\(\begin{aligned} C'(x) &= 0 \\ 0.03x^2-2.4x+55 &= 0 \end{aligned}\)Solving for \(x\), we get\(x = \frac{20}{3},\frac{275}{3}\)Thus, the production level for which the marginal cost is the smallest is \(\frac{20}{3}\) thousand units.

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The dimensions of the parking lot that maximize the area while using 500 feet of fence are x = 230 ft and y = 115 ft.

To maximize the area of the parking lot given the available fencing, we can use the concept of optimization. Let's denote the lengths of the sides of the parking lot as follows

x is Length of the side parallel to the building (where the gap is 40 ft)

y is Length of one of the sides perpendicular to the building (where the gaps are 15 ft)

From the given information, we know that we have 500 feet of fence available. The total amount of fence used will be the perimeter of the parking lot, which can be expressed as

Perimeter = x + 2y + 40

To maximize the area, we need to express the area of the parking lot in terms of x and y. The area is given by

Area = x × y

We are given the constraint that the total amount of fence available is 500 feet, so we can set up an equation

x + 2y + 40 = 500

We can rearrange this equation to solve for x

x = 500 - 2y - 40 x = 460 - 2y

Substituting this value of x into the area equation, we have:

Area = (460 - 2y) × y

Now, we have the area in terms of a single variable, y. To find the maximum area, we can take the derivative of the area equation with respect to y and set it equal to zero

d(Area)/dy = 460 - 4y = 0

Solving this equation, we find

y = 115

Substituting this value back into the equation for x

x = 460 - 2(115) = 230

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Answer:

Step-by-step explanation:

yeah

Answer:

It actually might be D or C

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

i just did a test over that and it said D

...

The unknown number is 13. We can find the solution in the following manner.

We can start by translating the given sentence into an equation:

10x - 4 = 126

Here, x represents the unknown number we're trying to find.

To solve for x, we need to isolate it on one side of the equation. We can do this by adding 4 to both sides, and then dividing both sides by 10:

10x - 4 + 4 = 126 + 4

10x = 130

x = 13

Therefore, the unknown number is 13.

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The probability of randomly selecting a cream filled

Chocolate is 1/4

Let E be the event of selecting cream filled chocolate.

Number of favourable outcome = 6

Total number of possible outcome = 24

Probability if selecting a cream filled chocolate = 6/24

= 1 / 4

Hence, the probability of randomly selecting a cream filled chocolate is 1/4

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Answer:

4 is the answer.

Step-by-step explanation:

4 is the lowest integer that satisfies both inequalities.

Expected cost = $180 + $720 = $900.

The second option is the better choice for the motorcycle owner in terms of expected cost.

To determine which policy option has the least expected cost, we need to calculate the expected cost of each option and compare them.

Let's first consider the option with a $500 premium and a $600 deductible. If the motorcycle is damaged, the cost of repairs will be $800, but the owner will have to pay the $600 deductible. So, the expected cost of this policy is:

Expected cost = (probability of damage) x (cost of repairs + deductible) + (probability of no damage) x (annual premium)

Expected cost = (0.2) x ($800 + $600) + (0.8) x ($500)

Expected cost = $560 + $400 = $960

Now, let's consider the option with a $900 premium and a $100 deductible. If the motorcycle is damaged, the owner will only have to pay the $100 deductible, but the annual premium is higher. So, the expected cost of this policy is:

Expected cost = (probability of damage) x (cost of repairs + deductible) + (probability of no damage) x (annual premium)

Expected cost = (0.2) x ($800 + $100) + (0.8) x ($900)

Expected cost = $180 + $720 = $900

Comparing the expected costs, we see that the second option with the $900 premium and $100 deductible has the least expected cost of $900.

Therefore, the second option is the better choice for the motorcycle owner in terms of expected cost.

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Answer:

2:51 i think

Step-by-step explanation:

To model the cost of renting an economy car for x days, you can use a linear equation. A linear equation can be represented in the form y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept. In this case, y represents the cost of renting the car, and x represents the number of days.

To find the equation of the line, we need to use the given information to find the slope and y-intercept. We know that the cost of renting the car increases by a certain amount for each additional day, so the slope will be the daily rate. We also know that the cost of renting the car for 1 day is $90, which means that $90 is the y-intercept.We can use the two points (1, 90) and (3, 170) to find the slope:Slope = (y2 - y1) / (x2 - x1)

Slope = (170 - 90) / (3 - 1)Slope = 80 / 2Slope = 40Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:y - y1 = m(x - x1)We can use the point (1, 90) as our reference point:y - 90 = 40(x - 1)Simplifying this equation gives y = 40x + 50Thus, the function to model the cost of renting an economy car for x days is given by the equation y = 40x + 50, where y represents the cost and x represents the number of days.

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In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.

In order to determine whether the differences between group means are statistically significant, ANOVA examines the differences between groups.

ANOVA, which stands for Analysis of Variance, is a statistical method used to compare the means of two or more groups.

It analyzes the variability between group means and within group variability to assess whether there are significant differences among the groups.

The main idea behind ANOVA is to compare the variation between groups with the variation within groups.

If the variation between groups is significantly larger than the variation within groups, it suggests that there are meaningful differences among the groups.

This implies that the differences between group means are statistically significant, indicating that the groups are not just randomly different.

ANOVA achieves this by calculating an F-statistic, which is the ratio of the variability between groups to the variability within groups.

If the F-statistic is large enough to exceed a critical value based on the chosen significance level, it indicates that the group means are significantly different.

Regarding the statement about a linear equation, it is incorrect.

In a linear equation, the value of Y when X is 0 is called the y-intercept, not the slope.

The slope refers to the rate of change of Y with respect to changes in X.

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Answer:

I think it would be a 20 percent

Step-by-step explanation:

because the 4 red is 40% the blue is another 40% then the green is only 20 I could be wrong though hope this helped

Answer:

-4.7

Step-by-step explanation:

Answer:

homie dont play

Step-by-step explanation:

Answer:

$4.161616 =

As a fraction

= $[(4 × 62500) + 10101]/62500

= $(260101/62500)

As a mixed number =

$\(4\frac{10101}{62500}\)

Step-by-step explanation:

Cost of making a computer component = $4.161616

= $4 + $0.161616

6 numbers after the decimal , hence

0.161616 × 1000000/1000000

= 161616/1000000

= 10101/62500

We are told in the question to write the repetiting decimal cost as a fraction and as a mixed number

$4 + $0.161616 = $4 + 10101/62500

As a fraction

= $[(4 × 62500) + 10101]/62500

=$260101/62500

As a mixed number = \($4\frac{10101}{62500}\)

Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.

This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.

Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.

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The similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

Let's order the numbers -3, 5, -10, and 16 as requested.

From least to greatest:

-10, -3, 5, 16

The ordered list from least to greatest is: -10, -3, 5, 16.

Now let's order the same numbers from closest to zero to farthest from zero:

-3, 5, -10, 16

The ordered list from closest to zero to farthest from zero is: -3, 5, -10, 16.

Regarding the similarity between the two lists, both lists contain the same set of numbers: -3, 5, -10, and 16. However, the ordering criteria are different in each case. In the first list, we order the numbers based on their magnitudes, whereas in the second list, we order them based on their distances from zero.

By comparing the two lists, we can observe that the ordering changes since the criteria differ. In the first list, the number -10 appears first because it has the smallest magnitude, while in the second list, -3 appears first because it is closest to zero.

Overall, the similarity lies in the fact that both lists contain the same set of numbers, but their order is determined by different criteria - one based on magnitude and the other based on distance from zero.

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Answer:

x ≈ 10.4

Step-by-step explanation:

BD is an angle bisector and divides the opposite side into segments that are proportional to the other two sides , that is

\(\frac{AD}{CD}\) = \(\frac{AB}{BC}\) ( substitute values )

\(\frac{x}{11}\) = \(\frac{18}{19}\) ( cross- multiply )

19x = 11 × 18 = 198 ( divide both sides by 19 )

x ≈ 10.4 ( to the nearest tenth )

Answer: did you make that up ??

Step-by-step explanation:

Answer:

A. Alternate interior

B. Transitive property

C. Converse alternate interior angles theorem.

The shortest range of dollar spending on textbooks in a year that includes 60% of all students is approximately $374 to $426.

To find the shortest range of dollar spending on textbooks that includes 60% of all students, we'll use the normal distribution properties. Given a mean (µ) of $400 and a standard deviation (σ) of $50, we need to find the range around the mean that covers 60% of the distribution.

Since the normal distribution is symmetrical, 60% of the area corresponds to 30% of the area in each tail. We'll use the z-score table to find the z-score corresponding to the 30% and 70% percentiles (since the table usually provides cumulative probabilities).

Looking up the z-score table, we find that a cumulative probability of 30% corresponds to a z-score of approximately -0.52, and a cumulative probability of 70% corresponds to a z-score of approximately 0.52.

Now, we'll use the z-score formula to find the corresponding dollar amounts:

X = µ + (z * σ)

For the lower end (z = -0.52):
X = 400 + (-0.52 * 50) ≈ 374

For the upper end (z = 0.52):
X = 400 + (0.52 * 50) ≈ 426

Thus, the shortest range of dollar spending on textbooks in a year that includes 60% of all students is approximately $374 to $426.

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The correlation coefficient is most directly related to the slope of the regression line. It measures the strength of the linear relationship between X and Y, while the slope of the regression line tells us how much Y changes for each unit change in X.

The correlation coefficient is a statistical concept that refers to the strength and direction of a linear relationship between two variables. It is a number that ranges from -1 to 1. A value of -1 indicates a perfect negative correlation, meaning that as one variable increases, the other decreases, while a value of 1 indicates a perfect positive correlation, meaning that as one variable increases, the other increases as well. A value of 0 indicates no correlation, meaning that there is no linear relationship between the two variables.

The correlation coefficient is most directly related to the slope of the regression line. The regression line is a line that best fits the data points in a scatterplot. It is used to estimate the value of one variable based on the value of another variable. The slope of the regression line is the change in Y for a unit change in X. It tells us how much Y changes for each unit change in X. The correlation coefficient measures the strength of the linear relationship between X and Y. If the correlation coefficient is positive, then the slope of the regression line is also positive, meaning that as X increases, Y also increases. If the correlation coefficient is negative, then the slope of the regression line is also negative, meaning that as X increases, Y decreases.

The mean of Y and the mean of X are not directly related to the correlation coefficient. The mean of Y is the average value of Y, while the mean of X is the average value of X. They are used to calculate the intercept of the regression line, which is the value of Y when X is 0. The regression constant is another name for the intercept of the regression line. It is also not directly related to the correlation coefficient.
The mean of Y, the mean of X, and the regression constant are not directly related to the correlation coefficient.

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The long run behavior of the function f(x)=5(2)x+1 is that it approaches 1 as x approaches negative infinity and it approaches infinity as x approaches positive infinity.

The long-term behavior of the function f(x)=5(2)x+1 can be discovered by examining how the function behaves as x gets closer to negative and positive infinity.

As x→−[infinity], f(x) = 5(2)^ -∞+1 = 5(0)+1 = 1

As x approaches negative infinity, the value of the function approaches 1.

As x→[infinity], f(x) = 5(2)^ ∞+1 = 5(∞)+1 = ∞

As x approaches positive infinity, the value of the function approaches infinity.

As a result, the function f(x)=5(2)x+1 behaves in the long run in such a way that it approaches 1 as x approaches negative infinity and infinity as x approaches positive infinity.

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A sampling distribution is a theoretical distribution that defines the possible sample statistics that may be calculated from a population.

The sample statistic is a function of sample data and provides an estimate of the population parameter, which is a characteristic of the population. The sampling distribution of sample means, for instance, is a theoretical distribution of sample means from all conceivable samples of a specific size that could be drawn from the population under investigation. It is described by its mean and standard deviation, which are calculated based on the population's true mean and variance. For example, if we consider the population of heights of adults in a specific city, the mean and variance of the height distribution for the population will be known to us. We may, however, select many possible samples of 30 people from this population, and the sample means that we can obtain for these samples will vary. These sample means' distribution is the sampling distribution of the sample mean.

The central limit theorem is used to derive the sampling distribution of sample means. It states that, for samples of a large enough size, the sampling distribution of sample means is approximately normal, regardless of the population's distribution.

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Answer:

4 bouquets

Step-by-step explanation:

She can make four bouquets, being that 4 is the greatest common factor of both 12 and 16

Answer:

t=c

Step-by-step explanation:

ty = xyzn

answer : Tn=7n+4

first find the common difference then use the formula Tn=a+(n-1)d

The costs incurred for ads, content creation, and employee salaries, as well as the profit margin are $4,840.00, $19,000.00, $4,254.00, $1,064.80,  $29,158.80.

To calculate the total invoice amount charged to the florist for the first month of the contract, we need to consider the costs incurred for ads, content creation, and employee salaries, as well as the profit margin.

1. Cost of Ads:

The cost per impression is $0.11, and there are 5,500 impressions per ad. Since there were 8 ads purchased, the total cost of ads can be calculated as follows:

Total cost of ads = Cost per impression × Impressions per ad × Number of ads

= $0.11 × 5,500 × 8

= $4,840.00

2. Content Creation Cost:

The content creation cost is given as $19,000.00.

3. Employee Salaries:

The weekly salary per employee is $1,063.50, and the month consists of 4 weeks. Since the number of employees engaged in posting and monitoring chat/comments is not provided, we will assume there is one employee. Therefore, the total employee salary for the month can be calculated as follows:

Total employee salary = Weekly salary × Number of weeks

= $1,063.50 × 4

= $4,254.00

4. Profit Margin:

The contract states that the firm will be reimbursed for the cost incurred per paid ad plus a 22.0% profit on cost. To calculate the profit, we need to find 22.0% of the total cost of ads.

Profit = 22.0% of Total cost of ads

= 22.0% of $4,840.00

= $1,064.80

Now, we can calculate the total invoice amount charged to the florist by summing up all the costs:

Total invoice amount = Cost of ads + Content creation cost + Employee salaries + Profit

= $4,840.00 + $19,000.00 + $4,254.00 + $1,064.80

= $29,158.80

Therefore, the total invoice amount charged to the florist for the first month of the contract is $29,158.80.

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44=2(3x−5)

Step 1: Simplify both sides of the equation.

44=2(3x−5)

44=(2)(3x)+(2)(−5)(Distribute)

44=6x+−10

44=6x−10

Step 2: Flip the equation.

6x−10=44

Step 3: Add 10 to both sides.

6x−10+10=44+10

6x=54

Step 4: Divide both sides by 6.

6x /6 = 54 /6

x=9

5.66

Step-by-step explanation:

44= 6x-10

44-10=6x

34=6x

34/6=x

5.66=x