suppose the vertical distance between the points (0, a) and (0, b) is 5. if her wealth increased from $1,050 to $1,350, then a. britney's subjective measure of her well-being would increase by more than 5 units. b. britney would change from being a person who is not risk averse into a risk-averse person. c. britney would change from being a risk-averse person into a person who is not risk averse. d. britney's subjective measure of her well-being would increase by less than 5 units.

(a) Point estimate (mean difference): 2.2 tomatoes. (b) The standard deviation of differences: Approximately 3.47. (c) The test statistic: Approximately 1.38.

To perform a t-test for the population mean difference, follow these steps:

(a) Calculate the point estimate (mean difference): The point estimate is the mean difference between the yields of fertilizer A and fertilizer B.

Mean difference = (Sum of differences) / Number of pairs

Using the given data gives:

Mean difference = ((7-4) + (6-7) + (5-6) + (8-5) + (10-3)) / 5

Subtracting gives:

Mean difference = (3 - 1 - 1 + 3 + 7) / 5

Solving gives:

Mean difference = 11 / 5

Dividing gives:

Mean difference = 2.2

(b) Calculate the standard deviation of the differences:

To calculate the standard deviation of the differences, we need to calculate the squared differences, find their sum, divide by (n-1), and then take the square root.

Squared differences:[tex](3 - 2.2)^2, (-1 - 2.2)^2, (-1 - 2.2)^2, (3 - 2.2)^2, (7 - 2.2)^2[/tex]

Solving gives:

Sum of squared differences = (0.64 + 12.96 + 12.96 + 0.64 + 21.16)

Solving gives:

The sum of squared differences = 48.36

The standard deviation of the differences [tex]= \sqrt{48.36 / 4}[/tex]

Solving gives:

The standard deviation of the differences [tex]= \sqrt{2.09}[/tex]

Rounded to three decimal places

The standard deviation of the differences ≈ 3.47

c) Calculate the test statistic:

The test statistic (t) = (Point estimate - Null hypothesis value) / (Standard deviation /√(sample size))

Let's assume the null hypothesis is that there is no difference between the two fertilizers

(i.e., mean difference = 0).

[tex]t = (2.2 - 0) / (3.47 / \sqrt5)[/tex]

Substituting [tex]\sqrt 5 = 2.236[/tex]

t = 2.2 / (3.47 / 2.236)

Rounded to two decimal places

t ≈ 1.378

So, the test statistic is approximately 1.378.

The gardener can compare this test statistic to critical values from the t-distribution to determine whether the difference between the two fertilizers is statistically significant at a certain significance level. If the calculated test statistic is greater than the critical value, she ma

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​

By answering the presented question, we may conclude that In general, expressions it is often most convenient to choose numbers that are powers of ten. 

In mathematics, an expression is a collection of integers, variables, and complex mathematical (such as arithmetic, subtraction, multiplication, division, multiplications, and so on) that describes a quantity or value. Phrases can be simple, such as "3 + 4," or complicated, such as They may also contain functions like "sin(x)" or "log(y)". Expressions can be evaluated by swapping the variables with their values and performing the arithmetic operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Tavon may have chosen to multiply both sides of the equation by 10 because he wanted to remove the decimal point and work with integers. Then he can use his knowledge of integer multiplication and division to solve the equations more easily.

Tavon may have used a different number and removed the decimal point. For example, you could multiply both sides by 100 or 1000 instead of 10. However, you should carefully choose a number that is manageable and does not overcomplicate the problem. Multiplying by larger numbers complicates the calculations, and multiplying by smaller ones does not eliminate the decimal point entirely. In general, it is often most convenient to choose numbers that are powers of ten. 

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a. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{17}}$.

b. Yes, the sampling distribution of the sample mean is a normal distribution with a mean of $52000 and a standard error of $\frac{4800}{\sqrt{51}}$.

c. You would need to know that the population distribution of X, teacher salaries, is normal in order to answer the questions regarding any sample size.

d. Assuming a sample size of 51, the probability that the sampling error is within $1000 is approximately 0.84 or 84%.

e. Assuming a sample size of 51, the 90th percentile for the average teacher's salary is approximately $54488.

f. Assuming that teacher's salaries are normally distributed, the 90th percentile for an individual teacher's salary is approximately $56396.

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Answer:

4m + 6

Step-by-step explanation:

Since the length is twice as long your equation should look like this

2(2m + 3) = L

which would be 4m + 6 as the length of the rectangle

The missing value to find the length of BC is 9x.

The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.

The distance formula is given as:

distance = √((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values of the coordinates of B and C we have:

distance = √((7x - (-2x))² + (-1y - (-4y))²)

distance = √((9x)² + (3y)²)

distance = √(81x² + 9y²)

distance = 3√(9x² + y²)

Hence, the missing value to find the length of BC is 9x.

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Eve now completes a percent   mile in about 67% less time than she did previously.

In essence, percentages are fractions with a denominator of 100. The cent symbol (%) is placed next to a number to indicate that it is a percentage. As an illustration, if you answered 75 of 100 questions correctly on an examination (75/100), then would have received a score of 75% percent drop (original value − new value) / initial value x 100%).

Let's use "t1" for yesterday's time and "t2" for today.

t1 = 15 minutes, t2 = 5 minutes.

Using the equation, we obtain:

percentage decrease equals (t1 - t2) / (t1 x 100%) percentage decrease equals (15 - 5) / (15 x 100%) percentage decrease equals 10 / (15 x 100%) percentage decrease equals 0.666... x 100% percentage decrease equals 67%

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Therefore, the length of the diagonal of the rectangle is approximately 193.57 cm or 49.43 cm, depending on which value of x is used.

Perimeter is the total distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the lengths of its four sides.

Here,

(i) Let the length of the rectangle be y cm.

Then, the perimeter of the rectangle is given by:

2(x + y) = 112

x + y = 56

y = 56 - x

(ii) The area of the rectangle is given by:

Area = length x breadth

597 = yx

Substituting y = 56 - x, we get:

597 = x(56 - x)

597 = 56x - x²

x² - 56x + 597 = 0

(iii) Using the quadratic formula,

x = (-(-56) ± √((-56)² - 4(1)(597))) / (2(1))

x = (56 ± √(3136 - 2388)) / 2

x = (56 ± √(748)) / 2

x = (56 ± 2√(187)) / 2

x = 28 ± √(187)

Therefore, the two solutions are x = 28 + √(187) and x = 28 - √(187).

(iv) The length of the rectangle is y = 56 - x.

Using Pythagoras theorem, the length of the diagonal of the rectangle is given by:

d² = y² + x²

d² = (56 - x)² + x²

d² = 3136 - 112x + 2x²

d = √(3136 - 112x + 2x²)

Substituting the value of x from part (iii) into the above equation, we get:

d = √(3136 - 112(28 ± √(187)) + 2(28 ± √(187))²)

d = √(3136 - 3136 ± 112√(187) + 56 ± 56√(187) + 2(187))

d = √(37400 ± 168√(187))

d ≈ 193.57 cm (rounded to 2 decimal places) or d ≈ 49.43 cm (rounded to 2 decimal places)

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Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.

Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.

We can write quadradic equation as [tex]y=1+x^2[/tex]

Where y is number οf dοts and x is step number.

Then if x=0 and y=1

If x = 1 and y = 2

If x = 2 and y = 5

If x = 3 and y = 10

Hence Patten B fοllοws the quadratic realatiοnship.

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Answer:

To write the equation of a circle given its center and a point on the circle, we need to use the standard form of the equation of a circle, which is:

(x - h)^2 + (y - k)^2 = r^2

where (h, k) is the center of the circle and r is the radius.

Let's use point A as the point on the circle. We are given that the center of the circle is (4, -2) and point A is (6, 1). We can use the distance formula to find the radius of the circle:

r = √[(6 - 4)^2 + (1 - (-2))^2] = √[4^2 + 3^2] = 5

Now we can substitute the center and radius into the standard form equation:

(x - 4)^2 + (y + 2)^2 = 5^2

Simplifying and expanding the right-hand side, we get:

Therefore, the equation of the circle is (x - 4)^2 + (y + 2)^2 = 25 and we used point A to find it.

Answer:

x = -1

Step-by-step explanation:

The axis of symmetry is a line that divides the two sides of a parabola through the vertex.

Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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If Idil drove 12 miles in 1/5an hour on average, then she drove at an average speed of 60 miles per hour.

To calculate the average speed of Idil's car in miles per hour, we need to divide the distance she drove (12 miles) by the time it took her to drive that distance (1/5 hour):

Average speed = distance ÷ time

Average speed = 12 miles ÷ (1/5) hour

To divide by a fraction, we can multiply by its reciprocal, so:

Average speed = 12 miles × 5/1 hour

Average speed = 60 miles per hour

Therefore, Idil drove at an average speed of 60 miles per hour.

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The probability of getting the complete set of cards in Box 5 is 3/64.

To calculate the probability of getting the complete set of cards in Box 5, we have to consider the probability of getting each of the 4 cards in the previous 4 boxes.

For the first box,

The probability of getting any one of the 4 cards is 1,

since there are no previous boxes to consider.

For the second box,

The probability of getting a card that is not already in our possession is 3/4 (since there is one card already collected).

For the third box,

The probability of getting a card that is not already in our possession is 2/4 (since there are now two cards already collected).

For the fourth box,

The probability of getting a card that is not already in our possession is 1/4 (since there are now three cards already collected).

Multiplying these probabilities together, we get,

⇒ 1 x 3/4 x 2/4 x 1/4 = 3/64

So the probability of getting the complete set of cards in Box 5 is 3/64.

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Answer:

D. 24 ft

Step-by-step explanation:

Congruent means equal. Since ABCD and PQRS are congruent they are the same.

Answer:

D

Step-by-step explanation:

Answer:

20.864

Step-by-step explanation:

8.15 x 4 is 32.6. I used a calculator but what I would do if I were solving on paper would be to double it, and then double it again.

Then, we divide 32.6 by five to get 6.52. I did this with a calculator, but if I were solving on paper, I would divide by 10 (move decimal point), and then double it.

Finally, we muliply 6.52 by 3.2. I did this with a calculator and got 20.864, but if I was doing this on paper, I would just solve using standard form!

Let me know if this helped by hitting brainliest! If you have any questions, comment and I'll get back to you ASAP.

You can use the distributive property of multiplication over addition and the fact that 18 is thrice of 6.

The given expression is equivalent to

Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.

[tex]a(b+c)=a\times b+a\times c[/tex]

(remember that many times, when using letters or symbols, we hide multiplication and write two things which are multiplied, close to each other. As in [tex]2\times x=2x[/tex])

The given expression is [tex]6g-18h[/tex]

We know that we can write

[tex]6=2\times3[/tex]

[tex]18=2\times9=3\times6[/tex]

Thus,

[tex]6g-18h=6\times g-6\times 3h=6(g-3h)=-6(-g+3h)[/tex]

[tex]6g-18h=2\times 3g-2\times 9h=2(3g-9h)=-2(-3g+9h)[/tex]

[tex]6g-18h=3\times 2g-3\times 6h=3(2g-6h)=-3(-2g+9h)[/tex]

All of the above forms are obtained from the same expression without altering its value but only forms, so their simplified forms are same so they are equivalent expressions.

Thus,

The given expression is equivalent to

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Answer:C & D

Step-by-step explanation:

The percentage of the teenagers who purchased something with their parents' money can be calculated from the two-way frequency table. About 38.64% of the teenagers purchased something with their parents' money.

There were a total of 88 teenagers who were surveyed by Alexis. 38 of them completed the purchase, and out of these 38 teenagers, 34 of them used their parents' money. So, the percentage of teenagers who purchased something with their parents' money can be calculated as follows:

Percent of teenagers who purchased something with their [tex]parents' money = \frac{Frequency of completed purchase}{Total Number of teenagers surveyed} *100[/tex]

Percent of teenagers who purchased something with their parents' money = [tex]\frac{34}{88} * 100%[/tex]%

Therefore percent of teenagers who purchased something with their parents' money = 38.64%

Therefore, about 38.64% of the teenagers purchased something with their parents' money.

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The scale factor is 2 and center dilation is reduced.

The scale factor is a ratio that describes how much a figure has been enlarged or reduced. It is calculated by dividing the length of the corresponding sides of the original and dilated figures. If the scale factor is greater than 1, then the figure is enlarged, and if it is less than 1, then the figure is reduced.

To find the scale factor in an IXL dilations problem, you need to compare the corresponding sides of the original and dilated figures.

If the original figure has a side length of 4 units, and the dilated figure has a corresponding side length of 8 units, then the scale factor is 8/4=2. This means that the dilated figure is twice as large as the original figure.

The center of dilation is the point about which the figure is enlarged or reduced. It is the fixed point that remains unchanged during the dilation process.

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Answer:

[tex]\frac{11}{8}[/tex]

Step-by-step explanation:

3(2k+3)=6-(3k-5)

6k +9=6-3k+5

6k+3k=6+5

8k=11

k=[tex]\frac{11}{8}[/tex]

Answer: I think it is k=2/9

Step-by-step explanation:

There are four presentation methods to choose from. These include reciprocal training, traditional classroom instruction, audiovisual training, and distance learning. The multiple selection question format asks which presentation methods are included.

What is a presentation method?

A presentation method refers to a way to deliver information to a group of individuals. Presentation methods are often used to teach concepts, inform, or persuade the audience. Various presentation methods are available for different types of information, such as traditional classroom instruction, audiovisual training, and distance learning. These methods vary in how information is presented and how participants engage with the material.Presentation methods that are available Reciprocal Training, Reciprocal Training, often known as reciprocal teaching, is a technique that involves individuals exchanging roles as teachers and learners. This method has been shown to be effective in developing students' comprehension of academic material.Traditional Classroom Instruction, Traditional classroom instruction, also known as classroom instruction, is a technique that has been used for centuries. A teacher is in front of a group of students, who are expected to engage with the material and participate in activities.Audiovisual Training Audiovisual training refers to the use of video, audio, and other visual aids in the delivery of instruction. This approach is thought to be more engaging and memorable than other teaching methods.Distance Learning Distance learning, or online learning, is a form of education that is delivered via the internet. This allows individuals to learn from any location, as long as they have access to the internet. This type of education is often more cost-effective than traditional classroom instruction.Therefore, all of the above presentation methods are effective.

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The required distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

To solve this problem, we can use the Pythagorean theorem to find the distance the ship traveled from its starting point to its destination.

We can see that the ship traveled 35 miles east and 28 miles south, forming a right triangle. The distance from the starting point to the destination is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can find the length of the hypotenuse:

[tex]$\begin{align*}\text{distance} &= \sqrt{35^2 + 28^2}\&= \sqrt{1225 + 784}\&= \sqrt{2009}\&\approx 44.8 \text{ miles}\end{align*}[/tex]

Therefore, the distance the ship traveled from its starting point to its destination is approximately 44.8 miles.

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Answer:

three times

Step-by-step explanation:

As per the given question, we have to identify the premises and conclusions of different passages in the text of Aristotle's Nicomachean Ethics. It is a philosophical text that explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. Here are the premises and conclusions of some of the passages:

Passage 1:

Premises: (P) All human beings have a natural desire for knowledge. (C) Therefore, philosophy is an important pursuit for all human beings.

Conclusion: Philosophy is an essential activity for all people because all humans have an innate desire for knowledge.

Passage 2:

Premises: (P) Virtues are habits that are formed by repeatedly practicing virtuous actions. (C) Therefore, becoming a virtuous person requires a lot of practice.

Conclusion: Being virtuous requires lots of practice because virtues are habits that are formed through repeated actions.

Passage 3:

Premises: (P) Moral virtues are acquired by habituation. (C) Therefore, becoming virtuous requires practicing virtuous actions.

Conclusion: One becomes virtuous by practicing virtuous actions because moral virtues are acquired through habituation.

Passage 4:

Premises: (P) Happiness is the highest good that humans can achieve. (C) Therefore, all human actions aim at achieving happiness.

Conclusion: All human actions are aimed at achieving happiness because happiness is the highest good that humans can attain.

Passage 5:

Premises: (P) All humans have a natural desire to be happy. (C) Therefore, achieving happiness is the ultimate goal of all human actions.

Conclusion: The ultimate goal of all human actions is to achieve happiness because all humans have a natural desire to be happy.

In summary, the text of Aristotle's Nicomachean Ethics explains the ethical theory and how to live a good life. It is based on the concept of eudaimonia, which is translated as happiness or human flourishing. The premises and conclusions of different passages have been identified in the given question, and we have explained them in detail.

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Therefore, there are 336 different groups of software packages that can be selected from the 8 different software packages offered during the Computer Daze special promotion.

There are 8 different software packages to choose from during the Computer Daze special promotion. Since the customer purchasing a computer and printer is given a choice of 3 free software packages, this means that there are 336 different groups of software packages that can be selected.

To calculate this, the total number of possibilities can be found by using the formula nPr,

where n is the total number of choices, and r is the number of items chosen. This can be written as 8P3. 8P3 is equal to[tex]8x7x6 = 336.[/tex]

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There are 495 ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.

Given that, we need to find the number of ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.

We can use combinations to solve this problem.

The number of ways to choose 8 employees from 12 for the day shift is:

C(12,8)

= 12! / ( 12 - 8 )! × 8!

= 495

Similarly, the number of ways to choose 4 employees from the remaining 4 for the night shift is:

C(4,4) = 1

= 4! / ( 4 - 4 )! × 4!

= 4!/4!

= 1

Therefore, the total number of ways to make the assignment is:

495 × 1 = 495

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The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).

What are parallel lines?

In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.

If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:

slope = (y2 - y1) / (x2 - x1)

slope = (-5 - 7) / (8 - (-2))

slope = -12 / 10

slope = -6 / 5

So, the equations of the two parallel lines are:

y - 7 = (-6 / 5)(x + 2) --- equation 1

y + 5 = (-6 / 5)(x - 8) --- equation 2

To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).

So, after the rotation, the new coordinates of the two points will be:

(-(-2), -7) = (2, -7) --- for point (-2, 7)

(-(8), -(-5)) = (-8, 5) --- for point (8, -5)

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Answer:

Use the quadratic formula to solve. Show work describe solution.

Step-by-step explanation:

The quadratic formula is used to find the solutions (or roots) of a quadratic equation in the form ax^2 + bx + c = 0, where a, b, and c are constants.

The quadratic formula is:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

To use the quadratic formula, we need to plug in the values of a, b, and c from the given equation and solve for x.

For example, let's say we have the equation 2x^2 + 5x - 3 = 0.

Here, a = 2, b = 5, and c = -3.

Plugging these values into the quadratic formula, we get:

x = (-5 ± sqrt(5^2 - 4(2)(-3))) / 2(2)

Simplifying the expression inside the square root:

x = (-5 ± sqrt(49)) / 4

x = (-5 ± 7) / 4

We get two solutions:

x = (-5 + 7) / 4 = 1/2

x = (-5 - 7) / 4 = -3

So the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.

These solutions represent the points where the quadratic curve intersects the x-axis. They can also be used to factor the quadratic equation or graph the quadratic function.

In the given elementary matrix, the corresponding elementary row operation is multiplication of the second row of a given matrix with a scalar of 5. The given matrix is an elementary matrix because it can be obtained by multiplying an identity matrix by an elementary matrix. The inverse of the given matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix.

The given elementary matrix is:
[1 0 0]
[0 0 5]
[0 1 0]

The corresponding elementary row operation for this matrix is multiplication of the second row of a given matrix with a scalar of 5. This means that if we have a matrix A and we multiply the second row of A with a scalar of 5, we get a new matrix B which is represented by the above elementary matrix.

The inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

The inverse of a given elementary matrix can be obtained by applying the inverse of the corresponding elementary row operation to an identity matrix. In this case, the inverse of the given elementary matrix can be obtained by multiplying a scalar of 1/5 to the second row of the identity matrix. This gives us the above inverse matrix.

Therefore, the corresponding elementary row operation for the given matrix is multiplication of the second row of a given matrix with a scalar of 5 and the inverse of the given matrix is:
[1 0 0]
[0 1/5 0]
[0 0 1]

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To find the point on the given plane that is closest to the given point (5,6,2), we can use Lagrange multipliers.

Let f be the function that represents the plane x-y+z=3 and let g be the function that represents the point (5,6,2). Then, the point on the plane closest to (5,6,2) is the point that minimizes g=x2+y2+z2. We can use the method of Lagrange multipliers to solve this problem.

Let lambda be the Lagrange multiplier. Then, we need to solve the system of equations given by:
x2+y2+z2-2x-2y-2z=0x-y+z-3=0

By solving this system of equations, we obtain the point 13/14x=7/7y=11/7z=5/7, which is the closest point on the plane to the given point (5,6,2).

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