Write an equation that model the linear relationship in the table below
What is the slope
What is the y intercept
What is the equation of the line

Triangle ABC in quadrant 4 and polygon A' B' C' in quadrant 3 should be rotated 90 degrees clockwise in both directions.

In geometry, a transformation is a process that changes the position, scale, or orientation of a shape. Common transformations include translations, rotations, reflections, and dilations.

Transformations known as rotations involve turning a shape around a central fixed point known as the centre of rotation. The amount of rotation in degrees is determined by the angle of rotation, which can be either clockwise or anticlockwise.

The position of A' in relation to A denotes a clockwise rotation.

A clockwise rotation is further indicated by the fact that B' is situated beneath B.

The fact that C' is positioned to the right of C suggests that the rotation is also clockwise.

Since all of the relevant vertices of polygon A' B' C' are turned clockwise in relation to triangle ABC,

Therefore, the right answer is a 90° clockwise rotation.

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The corrcet statement is,

18%, percent of all students in the eighth grade at Lincoln Junior High School have pancakes as their favorite breakfast, but we cannot conclude anything about the percent of the population who have breakfast as their favorite meal.

Hence, Option B is true.

Given that;

Lincoln Junior High School asked all of their eighth grade students the question, “What is your favorite breakfast?

And, 18%, percent answered “pancakes.

Hence, We can conclude that;

18%, percent of all students in the eighth grade at Lincoln Junior High School have pancakes as their favorite breakfast,

But we cannot conclude anything about the percent of the population who have breakfast as their favorite meal.

Thus, Option B is true.

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The sides of ΔFED does AB in ΔABC correspond to:

AB --> EF  = (53°)

BC --> DE =  (37°)

AC --> DF=  (90°)

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

From the figure:

We have the following information:

ΔABC is similar to ΔFED.

WE have to find the which side in ΔFED does AB in ΔABC correspond to?

Now, According to the question:

ΔABC is similar to ΔFED.

So,

AB --> EF  = (53°)

BC --> DE =  (37°)

AC --> DF=  (90°)

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The value of the test statistic is -0.8 (rounded to three decimal places).

To determine whether the CAI method performs differently from the traditional method, we can use a one-sample t-test. The null hypothesis is that the mean time to receive a basic driving license with the CAI method is the same as the traditional method (i.e., μ = 8.2 hours). The alternative hypothesis is that the mean time is different from 8.2 hours (i.e., μ ≠ 8.2 hours).

The test statistic can be calculated as

t = (x - μ) / (s / √n)

where x is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.

Plugging in the values, we get:

t = (7.9 - 8.2) / (1.5 / √16)

t = -0.3 / 0.375

t = -0.8

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It will take approximately 16.90 (about 16 years 11 months) years for a $25,000 investment to triple when invested at 6.5% interest compounded continuously.

The formula for continuous compounding is given by:

A = P[tex]e^{(rt)}[/tex]

Where:

A = Final amount

P = Initial amount

r = Annual interest rate (as a decimal)

t = time in years

We need to solve for t when the final amount A is 3 times the initial amount P, i.e. A = 3P.

So, we have:

3P =  P[tex]e^{(rt)}[/tex]

Simplifying:

3 = [tex]e^{(rt)}[/tex]

Taking the natural logarithm of both sides:

ln(3) = rt

t = ln(3) / r

Substituting the given values:

t = ln(3) / 0.065

t ≈ 16.90 years

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The data type is quantitative data under the given condition that professor Donald creates a data set by combining student grades in his economics classes from the last 4 spring semesters.

Quantitative data is a type of data that deals with numbers and measurements. In the given case it deals with the attendance and the marks acquired by every individual in the course of 4 spring semesters.

Quantitative data is split  into two categories discrete and continuous.

Discrete variables are the ones that can only aquire one certain value, for instance  integers.

Continuous variables are the ones  that can aquire  any value within specified and certain range.

For the given case, the number of students who attended the class will fall under the example of discrete variables, while the scores on all components of the course as well as final grade would be examples of continuous variables.

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The true statement is "More Italians have brown or hazel eyes than blue or green eyes." (option a).

The given two-way table shows the row relative frequencies of two categorical variables, nationality, and eye color. The frequency count or relative frequency of each cell is denoted by the decimal numbers in the table.

To evaluate each statement, we need to compare the row relative frequencies of each nationality for the two eye colors. For example, statement A implies that the row relative frequency of Italian people with brown or hazel eyes is greater than the row relative frequency with blue or green eyes.

Looking at the given table, we can see that the row relative frequency of Italian people with brown or hazel eyes is 0.80, while the row relative frequency with blue or green eyes is 0.18.

Therefore, statement A must be true since the frequency count of Italian people with brown or hazel eyes is greater than the frequency count with blue or green eyes.

Therefore, the correct answer is A) More Italians have brown or hazel eyes than blue or green eyes.

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Answer:

Step-by-step explanation:

If you have 1,000,000 number cubes, each measuring one inch on a side, then the height of the tower you can build with them can be found by multiplying the number of cubes by the height of a single cube.

The height of a single cube is also one inch, since all sides are equal in length. Therefore, the height of the entire tower would be:

1,000,000 cubes × 1 inch/cube = 1,000,000 inches

To convert this to a more manageable unit, we can divide by the number of inches in a typical measure of length, such as a foot or a mile. For example:

1,000,000 inches ÷ 12 inches/foot ≈ 83,333.33 feet

This is a very tall tower, almost 16 miles high!

The distance between the landing pad ≈ 23.13 miles

The plane saw 2 landing pads in opposite direction . The angles of depression to pad A and pad B are 46° and 16°. The straight line distance from the helicopter to pad A is 5 miles .

The illustration forms a triangle with 2 half's of a right angle triangle.

Pad A right angle triangle

let us use this triangle to find the opposite sides which is the same for both right angle triangle formed .

tan 46° = opposite/adjacent

tan 46° = a/5

a = 5 tan 46°

a = 5 × 1.03553031379

a = 5.17765156895

a = 5. 2 miles

Pad B right angle triangle

Let us find the straight line distance from the helicopter to pad B.

The distance is the adjacent side of the triangle.

tan 16° = opposite/adjacent

tan 16° = 5.2/adjacent

adjacent = 5.2/0.28674538575

adjacent = 18.134555108

adjacent = 18.135

Straight line distance from the helicopter to pad B = 18.135 miles

The distance between the landing pad = 5 + 18.135 = 23.134555108  miles

The distance between the landing pads ≈ 23.13 miles

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a. A

b. C

A is a right triangle

C compared & matched : 2 angles in that triangle are the same number of degrees

The period of oscillation of the object is T/2. So, the correct option is T/2.

To determine the period of oscillation of the object when the elevator accelerates upward with acceleration 2g, we can use the formula for the period of a spring-mass system:
T = 2π√(m/k),
where T is the period, m is the mass of the object, and k is the spring constant.

When the elevator accelerates upward with acceleration 2g, the effective gravity acting on the object becomes:
g' = g + 2g = 3g.

Now, we can find the new period of oscillation (T') using the modified formula:
T' = 2π√(m/(k - mg')),
where g' is the effective gravity.

Since T = 2π√(m/k) and g = k/m, we can rewrite the equation for T' as:
T' = 2π√(m/(k - 3mg)).

Now, we can substitute T back into the equation:
T' = 2π√(m/(k - 3m(k/m))) = 2π√(m/(k - 3k)) = 2π√(m/(2k)).

Comparing this to the original equation for T, we see that:
T' = 2π√(m/k) × √(1/2) = T × √(1/2) ≈ 0.71T.

None of the given options match this value. However, T/2 is the closest option to the calculated value. Therefore, the new period of oscillation of the object when the elevator accelerates upward with acceleration 2g is approximately T/2.

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Using a significance level of 5%, we conclude that there is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often. So, the correct answer is D).

Using a significance level of 5%, the chi-square test statistic is 33.3815 with 2 degrees of freedom and a corresponding p-value of less than 0.0001.

Since the p-value is less than 0.05, we reject the null hypothesis of equal preference for beer, wine, and liquor and conclude that there is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often.

Therefore, the answer is (d) There is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often.

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--The given question is incomplete, the complete question is given

"  Gallup asked a nationally representative sample of adults about their alcohol consumption. Those in the sample who drank alcohol were asked which they drank most often-beer, wine, or liquor. Do the data provide evidence of an equal preference for beer, wine, and liquor as the favored alcoholic drink of American adults who drink alcohol? Here is an incomplete Minitab output for the corresponding chi-square test: Test Contribution Category Observed Proportion Expected to Chi-Sq beer 264 0.333333 216.667 10.3405 wine 237 0.333333 216.667 1.9082 liquor 149 0.333333 216.667 21.1328 N DF Chi-Sq P-Value 650 Using a significance level of 5%, what should you conclude?

a. There are significantly more American adult drinkers who favor beer over wine or liquor.

b. The data are consistent with an equal distribution of beer, wine, and liquor as the alcoholic drink consumed most often by American adults who drink alcohol.

c. We are unable to conclude anything, because the test assumptions are not met.

d. There is significant evidence that American adults who drink alcohol do not favor beer, wine, and liquor equally as the alcoholic drink they consume most often."--

The correct sentence is,

⇒ The IQR of 13 is the most accurate to use, since the data is skewed.

We have to given that;

A histogram is provided to display the data.

⇒ 5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20

Hence, To find range as;

Range = Highest - lowest value

          = 20 - 5

          = 15

And, We have to find IQR as;

In the data set;

First quartile is,

⇒ Q₁ = (6 + 8)/ 2 = 7

Second quartile is,

Q₃ = (20 + 20) / 2 = 20

Hence, The value of IQR is,

⇒ IQR = Q₃ - Q₁

⇒ IQR = 20 - 7

⇒ IQR = 13

Thus, The correct sentence is,

⇒ The IQR of 13 is the most accurate to use, since the data is skewed.

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To compare the two running times, we need to express them in the same units. We can convert Sylvester's time to seconds by multiplying by 60:

Sylvester: 4 minutes x 60 seconds/minute = 240 seconds

Lenworth: 4 minutes 12 seconds = 4 x 60 + 12 = 252 seconds

Now we can find the ratio of Lenworth's time to Sylvester's time:

Lenworth/Sylvester = 252/240 = 21/20

So the ratio of Lenworth's time to Sylvester's time is 21:20.

As per the unitary method, Bethany needs to buy 7 quarts of paint in order to paint 5 storage boxes.

Firstly, we need to find the surface area of one storage box that needs to be painted. The surface area of a box can be found using the formula:

Surface Area = 2(lw + lh + wh)

where l is the length, w is the width, and h is the height of the box.

Substituting the given values, we get:

Surface Area of one box = 2(6 x 3 + 6 x 5.12 + 3.12 x 5.12) square feet

= 131.52 square feet

Next, we need to find the total surface area of 5 boxes:

Total Surface Area of 5 boxes = Surface Area of one box x 5

= 131.52 x 5

= 657.6 square feet

Now, we need to find how many quarts of paint are required to cover this area. From the given information, we know that one quart of paint covers 100 square feet of surface area.

Using the unitary method, we can set up a proportion:

1 quart of paint covers 100 square feet

x quarts of paint cover 657.6 square feet

Solving for x, we get:

x = (657.6/100) quarts of paint

= 6.576 quarts of paint

Since we can only buy whole quarts of paint, we need to round up the answer to the nearest whole number.

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The example of nonprobabilistic sampling among the given choices is judgment sampling.

In judgment sampling, the researcher uses their judgment or expertise to select a sample that they believe is representative of the population. This type of sampling does not involve random selection and is therefore nonprobabilistic. The sample may be selected based on certain criteria or characteristics that the researcher believes are important.

In contrast, simple random sampling, stratified simple random sampling, and cluster sampling are all examples of probabilistic sampling methods, which involve random selection of a sample from the population using a probability-based approach.

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Answer:

The answer for b is

b)199237.5$

Step-by-step explanation:

=189.75×1050

=199237.5$

Answer:

6 violin players can play the 9th symphony in 36 minutes

Step-by-step explanation:

Assuming that the six violin players can play the 9th symphony at the same rate as the two violin players who can play and sing it in 12 minutes, we can use the following proportion:

2 violin players can play and sing in 12 minutes

6 violin players can play at the same rate in x minutes

The proportion can be written as:

2/12 = 6/x

To solve for x, we can cross-multiply and simplify:

2x = 6 * 12

2x = 72

x = 36

Therefore, 6 violin players can play the 9th symphony in 36 minutes, assuming they can play at the same rate as the two violin players who can play and sing it in 12 minutes.

The concept of proportional reasoning suggests that 6 violin players would need 4 minutes to perform the 9th symphony.

To solve this problem, we need to use the concept of proportional reasoning. If two violin players can sing the 9th symphony in 12 minutes, we can write this as a ratio: 2 players/12 minutes. To find out how much time six violin players need, we can set up a proportion:

2 players/12 minutes = 6 players/x minutes

To solve for x, we can cross-multiply and simplify:

2x = 6 * 12
2x = 72
x = 36

Therefore, six violin players can sing the 9th symphony in 36 minutes.
Hi! If two violin players can perform the 9th symphony in 12 minutes, then 6 violin players would be able to complete it in less time. Assuming they work at the same pace, you can use the formula:

(time for 1 group) / (number of groups) = time for multiple groups

In this case, 1 group consists of 2 violin players, and there are 6 violin players in total, which makes 3 groups. So the calculation would be:

12 minutes / 3 groups = 4 minutes

Therefore, 6 violin players would need 4 minutes to perform the 9th symphony.

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The slope of the line represented by the table of values is: D: 3

The formula for the equation of a line in slope intercept form is given by the expression:

y = mx + c

where:

m is slope

c is y-intercept

The formula for the equation of a line between two coordinates is expressed as:

m = (y₂ - y₁)/(x₂ - x₁)

Using the first two coordinate points, we have the slope as:

m = (-1 - (-4))/(0 - (-1))

m = 3/1

m = 3

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If we compare Jenna's original test score of 65% to her retake score of 80%, the test statistics do indeed demonstrate an improvement.

As her score grew by 15 percentage points, there was an improvement, which suggests that her performance improved or increased between the first exam and the second.

This represents an improvement in Jenna's test results, in our opinion. Her retake score was 80%, which is a greater percentage than her first score of 65%.

This demonstrates an improvement in her performance since it shows that she performed better on the second test than she did on the first.

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Answer: [tex]\sqrt{0.15}[/tex] and [tex]\frac{11}{28}[/tex]

Step-by-step explanation:

       First, we will turn the percent into a decimal. A percent divided by 100 becomes a decimal.

42% / 0.42

       Next, we will divide [tex]\frac{3}{8}[/tex] and turn it into 0.375 because it makes them easier to compare.

       Lastly, we will compare all the given answer options and see which are greater than 0.375 and less than 0.42.

✗ [tex]\frac{4}{9}[/tex] = 0.444444

✓ [tex]\sqrt{0.15}[/tex] = 0.387

✗ 0.3

✗ 3.9

✓    = 0.39

Answer:

(x, -y)

(-x, y)

Step-by-step explanation:

If m(x) = -h(x), then each point (x, y) on the graph of h(x) becomes the point (x, -y) on the graph of m(x).

This is because the negative sign in front of h(x) in the equation for m(x) reflects the graph of h(x) across the x-axis. So, the y-coordinate of each point on the graph of h(x) becomes its opposite on the graph of m(x), while the x-coordinate remains the same.

If n(x) = h(-x), then each point (x, y) on the graph of h(x) becomes the point (-x, y) on the graph of n(x).

This is because the expression h(-x) means that we are replacing the variable x in the function h with -x. This reflects the graph of h(x) across the y-axis, since each value of x is replaced by its opposite. So, the x-coordinate of each point on the graph of h(x) becomes its opposite on the graph of n(x), while the y-coordinate remains the same.

Answer:  (a) (x,-y)   (b)(-x, y)

Step-by-step explanation:

Because it's saying that you need to take the negative of the function h(x)  which is y so  make y negative

(a) (x,-y)

The question now say that only the x is going to be come negative so

(b)(-x, y)

As a result, twenty-five percent of the responses were not cataloged in the table.

To begin with, discover the amount of replies that failed to be noted:

Complete Responses - Documented Responses = Unrecorded Responses

200 - 150 = 50

Next, estimate the proportion of responses not represented in the table:

(Unrecorded Responses / Total Responses) * 100%

(50 / 200) * 100% = 0.25 * 100% = 25%

As a result, twenty-five percent of the responses were not cataloged in the table.

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Cecilia collected a total of 200 service responses for her study. She noticed that only 150 responses were recorded in the table. What percent of the responses were not recorded in the table?

The back-to-back stem-and-leaf plot or parallel boxplots can be use to compare. GPAs for successful students are generally higher. A significant relationship exists between GPA and credit hours for successful students. An applicant with a 3.5 GPA is likely to be successful, as the predicted value is closer to successful students' values.

To compare the GPAs for the two groups, an appropriate graphical display could be a back-to-back stem-and-leaf plot or parallel boxplots. Based on the graph, we can observe that successful students generally have higher GPAs than unsuccessful students.

To determine if there is a significant relationship between GPA and mean number of credit hours per semester for successful students, we can use a t-test for the slope or linear regression t-test.

Given the provided computer output, with a t-value of -5.90 and a p-value of 0.000, we can reject the null hypothesis and conclude that there is a significant relationship between GPA and mean number of credit hours per semester for successful students.

Using the regression equation to predict the number of credit hours for an applicant with a GPA of 3.5,

For the successful group predicted hours = 23.514 – 2.7555(3.5) = 13.86975

For the unsuccessful group predicted hours = 24.200 – 3.485(3.5) = 12.0025

we get a predicted value of 13.86975 for successful students and 12.0025 for unsuccessful students.

Since the actual value of 14 is closer to the predicted value for successful students, we can infer that this applicant is likely to be successful in the Ph.D. program.

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--The given question is incomplete, the complete question is given

" The statistics department at a large university is trying to determine if it is possible to predict whether an applicant will successfully complete the Ph.D. program or will leave before completing the program. The department is considering whether GPA (grade point average) in undergraduate statistics and mathematics courses (a measure of performance) and mean number of credit hours per semester (a measure of workload) would be helpful measures. To gather data, a random sample of 20 entering students from the past 5 years is taken. The data are given in photo.

a. Use an appropriate graphical display to compare the GPAs for the two groups.(provide names only) Write a few sentences commenting on your display.

b. For the students who successfully completed the Ph.D. program, is there a significant relationship between GPA and mean number of credit hours per semester?

Give a statistical justification to support your response.

c. If a new applicant has a GPA of 3.5 and a mean number of credit hours per semester of 14.0, do you think this applicant will successfully complete the Ph.D. program? Give a statistical justification to support your response. "--

The expression that can be classified as equivalent to the first expression is -10 ( second option).

To find the equivalent expression of the one given, we will need to simplify the original expression. Simplifying involves solving any mathematical operation that is possible to make the expression shorter. The process is shown below:

[tex](\sqrt{6} - 4) (\sqrt{6} +4)[/tex]

(2.4 - 4) (2.4 +4)

(-1.6) (6.4)

-10.24

This number can be rounded as -10. Based on this, the expression that would be equivalent would be -10 (second option).

Note: This question is incomplete; below I attach the missing section.

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At a rate of 1231 kilometers attendant to an hour, it will take an estimated 30 hours for a pilot to circumnavigate the whole earth and acquire the applicable standard.

In estimating the amount of time a pilot would require to fly around the globe while averaging 1231 kilometers per hour, we can easily employ the formula: Time = Distance ÷ Speed.

Multiplied passage this equation in tandem with the minimal distance necessary to qualify for an around-the-world speed record produces 36,763 kilometers: thus, these measurements yield 29.87 hours. To clarify, at a rate of 1231 kilometers attendant to an hour, it will take an estimated 30 hours for a pilot to circumnavigate the whole earth and acquire the applicable standard.

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If "employed-adults" were asked how likely they thought that they will lose their jobs, then percent of adults that are "fairly-likely" to lose jobs is 6.23%.

To find the percent of adults that are fairly-likely to lose their jobs, we  first add the total number of adults who responded to survey;

⇒ Total number of adults = 626 + 902 + 3745 + 9212 = 14,485

Next, we determine number of adults who responded "Fairly Likely";

⇒ Number of adults who responded "Fairly Likely" = 902,

To find the percentage, we use formula;

⇒ Percentage = (Number of adults responded "Fairly Likely"/Total number of adults) × 100,

Substituting the values,

We get,

⇒ Percentage = (902/14485) × 100 = 6.23%,

Therefore, 6.23% of employed adults in the survey are fairly likely to lose their jobs within next-year.

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The given question is incomplete, the complete question is

In a survey, employed adults were asked how likely they thought it was that they would lose their jobs within the next year. the results are :

 Response     Frequency

 Very Likely         626

 Fairly Likely        902

Not too Likely      3745

  Not Likely          9212

Find the percent of adults that are fairly likely to lose their jobs.  

An equivalent fraction of students that does not be a part of students who attended choir practice is given by 1/4 or 0.25 as a decimal.

Total number of students are equal to 20.

If 15 out of 20 students attended choir practice.

Then the fraction of students who attended can be written as 15/20.

An equivalent decimal fraction that does not represent the part of students who attended choir practice is

= Subtract the fraction of students who attended from 1 which represents the whole group of students.

= 1 - 15/20

= 20/20 - 15/20

= 5/20

= ( 1/ 4) as simplified fraction form.

= 0.25 as a decimal

Therefore, equivalent decimal fraction of students does not represent part of students who attended choir practice is 1/4 or 0.25 as a decimal.

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The above question is incomplete, the complete question is:

Yesterday 15 out of 20 students attended choir practice. Write an equivalent decimal fraction of students which does not represent the part of students who attended choir practice?

The two forms of writing that have a similar purpose of entertaining an audience are as follow,

A short story

An epic poem

Short stories and epic poems are both forms of literature.

That are designed to entertain readers through the use of compelling characters, interesting plots, and vivid descriptions.

A news article, a book report, and do-it-yourself instructions have different purposes.

A news article is designed to inform readers about current events.

The current event may relates to day day life or to the nature.

A book report is designed to summarize and analyze a book.

IN book report mostly famous books are included to spread the awareness about the book.

And do-it-yourself instructions are designed to provide step-by-step guidance on how to complete a task.

Do -t - yourself is consider as a individual task.

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