Let X₁ and X₂ be independent normal random variables, distributed as N(μ₁,0²) and N(μ2,0²), respectively. Find the means, variances, the covariance and the correlation coefficient of the random variables u=2x1-x2 and v= 3x1 + x2

Answer:

2+4=6

20+40=60

200+400=600

2,000+4,000=6,000

Step-by-step explanation:

The scale of measurement of the distance between any two locations is typically considered to be interval or ratio scale.

The interval scale represents measurements where the intervals or differences between values are meaningful and consistent. In the case of distance, the intervals between different distances are consistent and can be measured in a standardized unit (e.g., meters, kilometers, miles).

If the measurements of distance also have a meaningful and non-arbitrary zero point, such as absolute zero representing no distance, then the scale would be considered a ratio scale. However, it is important to note that the choice of scale may vary depending on the specific context and purpose of the measurement.

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Answer:

the answer is is is is is is is is .............. 194,000

Answer:

77%

Step-by-step explanation:

462/600=x/100

46200=600x

46200/600=77

x=77

77%

The linear correlation coefficient unknown population is denoted by the statistic r and correlation strength is denoted by the parameter p, respectively.

As a result, correlations are generally portrayed by the two integers r and p. A number of +1 denotes a fully linearly positive correlation, while a number of -1 denotes a fully linearly negative connection. The correlation coefficient has a range of -1 to +1. The linear correlation becomes weaker as r approaches closer to zero.

The sample correlation coefficient evaluates the scatter plot points and a linear regression line constructed from those points (r). The correlation coefficient, denoted as r, ranges in value from -1 to 1. A p-value is a measure of statistical significance.

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Answer:

−45.6

−228/5

Step-by-step explanation:

Convert to a mixed number by placing the numbers to the right of the decimal over

10

Reduce the fraction. Then, convert the mixed number to an improper fraction by multiplying the denominator by the whole number and adding the numerator to get the new numerator. Place this new numerator over the original denominator.

Answer:

-45 and three-fifths

Step-by-step explanation:

\(=\left(-16-0.6\times 13+1\right)\times 2\)

\(0.6 \times 13 = 7.8\)

\(=2\left(1-16-7.8\right)\)

\(-16-7.8+1\)

\(-22.8\)

\(2\left(-22.8\right)\)

\(-22.8\times 2\)

\(=-45.6\)

\(= \frac{3}{5} \\= -45\:\frac{3}{5}\)

Optional: How we converted 0.6 to 3/5

\(= 0.6\)

\(\frac{0.6}{1} \times \frac{10}{10} = \frac{6}{10}\)

\(\frac{6\div 2}{10\div 2}\)

\(= \frac{3}{5}\)

Hope this helps!

Converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters. By definition conversion of units means the conversion between different units and measurements of the same quantity done by the process of multiplication or division. In maths, conversion is the process of changing the value of one form to another for example inches to millimeters, or liters to gallons. Units are used for measuring length, measuring weight, measuring capacity, measuring temperature, and measuring speed.

If we want to calculate how many Grams are 1000 Milligrams we have to multiply 1000 by 1 and divide the product by 1000. So for 1000, we have (1000 × 1) ÷ 1000 = 1000 ÷ 1000 = 1 Gram.

So finally 1000 mg = 1 g

Thus, converting 1,000 mg to 1 gram would require moving the decimal place zero places to the left.

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Answer:

Step-by-step explanation:

2x² - 8x - 24 = 0

2x² - 12x + 4x - 4*6 = 0

2x(x-6) + 4(x - 6) = 0

(x - 6)(2x + 4) = 0

The department's sales per square foot are $51.16 per square foot.

Division is the process of dividing a number by a given number.

Given that, the supermarket had sales last week of $15349, and the area of the department is 300 square feet.

The sales per square foot are:

(total sales)/ (total area)

= 15349/300

= 51.16

Hence, the department's sales per square foot are $51.16 per square foot.

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Answer:

9x+6

Step-by-step explanation:

I think by equivalent, you mean solve it.

5x+(x+6)+3x

5x+x+6+3x, open the parenthesis

9x+6, add up the like terms

Answer:

4:3

Step-by-step explanation:

Legit just simplified it.The original ratio is 24:18. First found the greatest common multiple (GCF) and divided both by it. In this case it was 6. So 24/6 = 4 and 18/6 = 3. Now your newly simplified ratio of apples to pears is 4:3.

The t test statistic for the bank's claim that wait times are not longer than five minutes is 4.29.

T - test statistic

T test statistic refer an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related.

Given,

Wait times for customers once they enter the bank. wait time is defined as the time between when a customer enters the bank until they reach a teller. a random sample of customers are recorded and their wait times in minutes are as follows: (4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79).

Here we need to determine the t test statistic for the bank's claim that wait times are not longer than five minutes.

In order to find the t test statistic, we have to calculated the average for the given waiting time,

Here the given wait times are:

(4.21, 5.55, 3.02, 5.13, 4.77, 2.34, 3.54, 3.20, 4.50, 6.10, 0.38, 5.12, 6.46, 6.19, 3.79).

In this list there are 15 members timings are presented.

Therefore, the average is calculated as,

=> (4.21 + 5.55 + 3.02 + 5.13 + 4.77 + 2.34 + 3.54 + 3.20 + 4.50 + 6.10 + 0.38 + 5.12 +  6.46 + 6.1 + 3.79) /15

=> 64.3/15

=> 4.29.

Therefore, the t test statistic for the bank's claim that wait times are not longer than five minutes is 4.29.

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Based on the IQR values, we conclude that Bus 18 is more consistent than Bus 47, as it has smaller IQR. This means the travel times of students on Bus 18 are more tightly clustered around the median, and are fewer outliers in data.

A line plot is a type of graph that displays data as points or dots along a number line. Each dot or point represents a single data value, and the number line shows the range of the data. Line plots are useful for displaying small to moderate-sized data sets and for identifying the central tendency and variability of the data.

To determine which bus is the most consistent, we need to look at the variability of data. The most appropriate measure of variability for this purpose is the interquartile range (IQR), which is the range of the middle 50% of the data.

From the given data, we can calculate the IQR for both buses as follows:

For Bus 18:

Lower quartile (Q1) = 8

Upper quartile (Q3) = 24

IQR = Q3 - Q1 = 24 - 8 = 16

For Bus 47:

Lower quartile (Q1) = 10

Upper quartile (Q3) = 34

IQR = Q3 - Q1 = 34 - 10 = 24

The range, which is the difference between the maximum and minimum values, is not as appropriate a measure of variability for this purpose, as it is heavily influenced by outliers. Therefore, we cannot use the range to determine the consistency of the data for either bus.

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The correct sequence of project phases is Definition - Planning  - Performance. The correct answer is B.

This is the typical order of project phases in a traditional project management approach. It starts with the definition phase, where the project's goals, the scope, and the requirements are established.

Then comes the planning phase, where the project plan is developed, including the allocation of resources, scheduling, and budgeting.

Finally, the performance phase begins, during which the project activities are executed, monitored, and controlled to ensure the successful project completion.

Therefore the sequence of project phase is  Definition - Planning  - Performance The correct answer is B.

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Answer:

D

Step-by-step explanation:

They should both level out at the same height considering the volume of hydrochloric acid used.

Answer:

D

Step-by-step explanation:

The theoretical minimum number of workstations is 4, with each workstation performing tasks for 35 seconds.

The theoretical minimum number of workstations is calculated by dividing the total task time by the cycle time. In this case, the total task time is 150 seconds and the cycle time is 35 seconds, so the theoretical minimum number of workstations is:

150 seconds / 35 seconds = 4 workstations

Therefore, the theoretical minimum number of workstations is 4. This means that the tasks can be divided into 4 groups, each of which can be performed in 35 seconds.

In practice, there may be more than 4 workstations, but this is the minimum number required.

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(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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Answer:

true

Step-by-step explanation:

square root functions are just half of a parabola rotated 90° so depending on which half of the parabola (top has minimum and bottom has maximum) it is, it will have one, but it cannot have both since it is a continuous function after the max or min

Answer:

The answer is 105.

Step-by-step explanation:

Answer:

m= -1

Use: y = mx + b

We have 19 input variables, the calculation would be \(2^1^9\), resulting in 524,288 possible regression models.

If you are running a regression with 19 input variables and want to choose a model including a subset of those variables, there would be a total of 524,288 possible regression models that can be formed.

To determine the number of possible regression models, we need to consider the power set of the input variables. The power set of a set includes all possible subsets that can be formed from the original set, including the empty set and the set itself. In this case, the power set would represent all the possible combinations of including or excluding the 19 input variables in the regression model.

The number of elements in the power set can be calculated by raising 2 to the power of the number of input variables. Since we have 19 input variables, the calculation would be \(2^1^9\), resulting in 524,288 possible regression models.

It's important to note that while there are a large number of possible regression models, not all of them may be meaningful or useful in practice. Selecting the most appropriate subset of variables for a regression model typically involves considerations such as statistical significance, correlation analysis , domain knowledge, and model evaluation techniques to identify the most predictive and relevant variables for the specific problem at hand.

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Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation:

Answer:

Step-by-step explanation:

The slope-intercept form:

y = mx + b

Where m is the slope and b is the Y-intercept

m = 9,   b = 13

so:

y = 9x + 13

There would be no asterisks plotted, indicating no outliers, as none of the observations (20, 24, and 28) fall below the lower fence or above the upper fence. The correct answer is b.

Based on the information, none of the observations 20, 24, and 28 can be classified as outliers since they are not below the lower fence or above the upper fence.

In a box plot, outliers are typically defined as observations that fall below the lower fence (Q1 - 1.5 * IQR) or above the upper fence (Q3 + 1.5 * IQR), where IQR is the interquartile range (Q3 - Q1).

Since the given data set does not contain any observations below the lower fence or above the upper fence, there would be no asterisks plotted to indicate outliers (option b is true). The three smallest observations (20, 24, and 28) are within the acceptable range and are part of the data set's distribution.

Therefore, the correct answer is b. There would be no asterisks plotted, indicating no outliers.

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The net change in the value of the function between x = 1 and x = 6 is 30.

To find the net change in the value of the function between the inputs of 1 and 6, we need to find the difference between the output values of the function at x = 1 and x = 6, and then take the absolute value of that difference.

First, we can find the output value of the function at x = 1:

f(1) = 6(1) - 5 = 1

Next, we can find the output value of the function at x = 6:

f(6) = 6(6) - 5 = 31

The net change in the value of the function between x = 1 and x = 6 is the absolute value of the difference between these two output values:

|f(6) - f(1)| = |31 - 1| = 30

Therefore, the net change in the value of the function between x = 1 and x = 6 is 30.

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we get the graph of the quadratic function by plotting the points on the graph paper.

We are given the quadratic function as:

f (x) = x²

We need to graph the function and find the values of the function for some given points of x.

For x = - 2, we get that:

f (x) = x²

f (- 2) = (- 2)²

f (- 2) = 4

For x = - 1, we get that:

f (x) = x²

f (- 1) = (- 1)²

f (- 1) = 1

For x = 0, we get that:

f (x) = x²

f (0) = (0)²

f (0) = 0

For x = 1, we get that:

f (x) = x²

f (1) = (1)²

f (1) = 1

For x = 2, we get that:

f (x) = x²

f (2) = (2)²

f (2) = 4

Plotting these points on the graph, we obtain the graph of the quadratic function.

Therefore, we get the graph of the quadratic function by plotting the points on the graph paper.

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Answer:

A

Step-by-step explanation:

sum of x divided by 5 and 2 means whatever is x divided by 5 and adding 2. (if that makes sense)

Answer:

2L+2W

Step-by-step explanation:

U JUST MOVE THE 2 TO THE L AND MOVE THE 2W TO THE OTHER SIDE. I THINK MY ANSWER IS RIGHT BUT MAYBE WAIT FOR ANOTHER PERSON

Confirmed Solution:

\(p=2l+2w\)

Hope this helps!

Answer:

To calculate the area of the triangle we need to know the length of the base and the height of the triangle.

Let us consider that the base is AB. The base length is the distance between points A and B.

       \(\boldsymbol{\sf{ d(AB)=\sqrt{(3-(-2))^2+(-2-(-1))^2}=\sqrt{25+1}=\sqrt{26}. }}\)

To calculate the length of the height we have to start by calculating the equation of the line that passes through the points A and B.

                    \(\boldsymbol{\sf{ \cfrac{x+2}{5}=\cfrac{y+1}{-1} \ \ \Longrightarrow \ \ y=-\cfrac{x}{5}-\cfrac{7}{5} }}\)

Now we calculate the perpendicular to the previous line that passes through point C. This will be the equation of the height of the triangle. The slope of this line is \(\bf{-\frac{1}{-1/5}=5 }\).

Then the perpendicular line is of the form y = 5x + n. Since this line passes through point C, we substitute the coordinates of the point on the line to find the independent term n=-7, so the perpendicular line is y=5x-7.

Let us now calculate the intersection point of the lines, for this we equalize both lines.

                               \(\boldsymbol{\sf{-\cfrac{x}{5}-\cfrac{7}{5}=5x-7 \ \ \Longrightarrow \ \ x=\cfrac{14}{13} .}}\)

Substituting in the perpendicular line we obtain \(\bf{y=-\frac{21}{13}}\) , then the intersection point is

                 \(\boldsymbol{\sf{P\left(\cfrac{14}{13},-\cfrac{21}{13}\right).}}\)

To calculate the length of the height, we need to find the distance between the points P and C.

             \(\boldsymbol{\sf{d(PC)=\sqrt{\left(2-\cfrac{14}{13}\right)^2+\left(3-\left(-\cfrac{21}{13}\right)\right)^2}=\sqrt{\cfrac{288}{13}} }}\)

We calculate the area of the triangle

                            \(\boldsymbol{\sf{Area=\cfrac{\sqrt{26}\cdot\sqrt{\cfrac{288}{13}}}{2}=12\ u^2 }}\)