a researcher is comparing the distributions for two studies using Cohen's d. Study 1 results show two samples whose means are close together, while the means in Study 2 are farther apart. Which study has a larger effect size and why

Answers

Answer 1

When the means in Study 2 are farther apart and the standard deviation is either smaller or similar to Study 1, the effect size (Cohen's d) for Study 2 would be larger. This suggests a stronger or more substantial difference between the two groups being compared in Study 2 compared to Study 1.

Cohen's d is a measure of effect size that quantifies the difference between two means in terms of standard deviation units. It takes into account both the difference in means and the variability within the groups being compared.

In this scenario, Study 2 would have a larger effect size compared to Study 1. The reason for this is that Cohen's d is calculated by dividing the difference between the means by the standard deviation.

Since the means in Study 2 are farther apart, the numerator (difference between means) in Cohen's d calculation would be larger for Study 2 compared to Study 1. This larger numerator contributes to a larger effect size.

Additionally, Cohen's d also considers the standard deviation of the samples. If the variability within the groups (standard deviation) in Study 2 is smaller compared to Study 1, it would further increase the effect size.

Therefore, when the means in Study 2 are farther apart and the standard deviation is either smaller or similar to Study 1, the effect size (Cohen's d) for Study 2 would be larger. This suggests a stronger or more substantial difference between the two groups being compared in Study 2 compared to Study 1.

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Related Questions

pls help:(...........———

pls help:(...........

Answers

Answer:

Just for points sorry

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

6+12+14=32

if you have a logical statement in five variables how many rows do you need in the truth table that you would use to evaluate it?

Answers

32 rows are needed in the truth table that we would use to evaluate a logical statement in five variables

As per the given data:

If we have a logical statement in five variables then we have to determine how many rows we need in the truth table that you would use to evaluate it.

It is calculated by both from truth table and by using the formula.

A table with rows and columns is created for a compound statement, and the number of rows depends on the number of statements.

As we know that the formula for number of rows need in the truth table.

Number of rows = \(2^{n}\)

Where n = Number of variables

Here given number of variables are 5.

n = 5

  \(2^{n}\) = \(2^{5}\)

= 32

Therefore 32 rows are needed in the truth table.

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PLSS HELP WITH THIS IMMEDIATELY!!!! only answer if u know. i’ll be giving brainiest if u don’t leave a link.

PLSS HELP WITH THIS IMMEDIATELY!!!! only answer if u know. ill be giving brainiest if u dont leave a

Answers

The answer is Equalatetal acute
equilateral (sides) acute (angle)

An automatic filling machine is used to fill 2-litre bottles of cola. The machine’s output is known to be approximately Normal with a mean of 2.0 litres and a standard deviation of 0.01 litres. Output is monitored using means of samples of 5 observations.
Determine the upper and lower control limits that will include roughly 95.5 percent of the sample means.
If the means for 6 samples are 2.005, 2.001, 1.998, 2.002, 1.995 and 1.999, is the process in control?

Answers

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Please help ? Help !!!

Please help ? Help !!!

Answers

The area of the rectangle is 8- square units

Area of the triangle is 10 square units

The total area is 90 square units

How to determine the value

The formula for the area of a rectangle is expressed mathematically as;

A = lw

Given that the parameters are;

A is the area of the rectangle.l is the length of the rectangle.w is the width of the rectangle.

Now, substitute the values, we have

Area = 8(10)

Multiply the values

Area = 80 square units

The formula for area of a triangle is;

Area = 1/2 base × height

Substitute the values

Area = 1/2 × 10 × 2

Multiply the values

Area = 10 square units

Total area = 10 + 80 = 90 square units

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Parallel and perpendicular lines point slope form,, need help with stuff for midterms :(!!!

Parallel and perpendicular lines point slope form,, need help with stuff for midterms :(!!!

Answers

Tips:

Hey, here are some things that can help:

1. Remember that parallel lines have the same slope, and perpendicular lines have opposite and reciprocal slopes (flip the fraction and change the sign).

2. When it asks you for a line passing through a specific point, using the slope for the new line, plug in for x and y and solve to get b (the y-intercept).

3. Slope-intercept: y=mx+b

Point-slope: y-y1=m(x-x1)

For point-slope form, you simply substitute a given slope and point into the equation. For example, if you are given that m=3 and the point (5,2) your point-slope equation would be: y-5=3(x-2)

If you are asked to change a point-slope equation into slope-intercept, simply solve for y. In this case, our point-slope equation would become y=3x-1.

Hope this helps!

the average starting salary for this year's graduates at a large university (lu) is $20,000 with a standard deviation of $8,000. furthermore, it is known that the starting salaries are normally distributed. a. what is the probability that a randomly selected lu graduate will have a starting salary of at least $30,400? b. individuals with starting salaries of less than $15,600 receive a low income tax break. what percentage of the graduates will receive the tax break? c. what are the minimum and the maximum starting salaries of the middle 95% of the lu graduates? d. if 189 of the recent graduates have salaries of at least $32,240, how many students graduated this year from this university?

Answers

(a) Probability that a randomly selected is 9.68%; (b) 29.12% will receive the tax break; (c) Minimum and the maximum starting salaries are 35,679.71 and 4,320.29. (d) 6.3% of the total number of students.

a) P(X>30,400) = P(Z>(30,400-20,000)/8,000)

                          = 1-P(Z<1.3)

                          = 0.0968

                         = 9.68%

b) P(X<15600) = P(Z<(15600-20000)/8000)

                        = 29.12%

c) Maximum of the starting salaries of the middle 95% is

                     (x - 20,000)/8,000 = 1,96

                                                  x  = 35,679.71

Minimum of the starting salaries of the middle 95% is

                      (x - 20,000)/8,000 = -1,96

                                                   x = 4,320.29

d) P(X>32,240) = 1-P(Z<(32,240-20,000)/8,000)

                         = 0.063

Therefore, the 189 represents 6.3% of the total number of students, means that the total number is 3,000.

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I need help can someone help please !!

I need help can someone help please !!

Answers

The answer is B and I know

Find the equation of the lime shown?

Find the equation of the lime shown?

Answers

Answer:

y = - 2x + 9

------------------------------

Use two points on the line(0, 9) and (4, 1)

The y-intercept is b = 9, find the slopem = (1 - 9)/4 = - 8/4 = - 2

The line isy = mx + by = - 2x + 9

\(\Large \boxed{\sf y = - 2x + 9}\\\\\sf Use\ the\ slope\ formula\ to\ find\ the\ slope\\ using\ two\ points\ from\ the\ graph.\\\\(0,9)\ and\ (4.5,0)\\\\\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}=\frac{0-9}{4.5-0} =-2\\\\The\ line\ intercepts\ at\ the\ y-axis\ at\ (0,9).\\ The\ y-intercept\ is\ b=9.\\\\ y=mx+b\\y=-2x+9\)

there were 800 students in a school. 55% of the students in the school were Caucasian and 22% were African American. The rest were Hispanic. What percent of the students were Hispanic?

Answers

Step 1: Add the given data of races
55 + 22 = 77

Step 2: Subtract the result from the 100
(Since it is in percentages, a whole percentage is 100, and we need to find percent, so subtract the result from 100)
100
- 77
= 23

23% were Hispanic.

5) Build mathematical model of the transportation problem: Entry elements of table are costs. Destination B2 B3 B4 28 A1 27 27 32 A2 15 21 20 A3 16 22 18 b 26 8 Source 3 BI 14 10 21 323324 12 13

Answers

This problem is an example of a balanced transportation problem since the total supply of goods is equal to the total demand.

The transportation problem is a well-known linear programming problem in which commodities are shipped from sources to destinations at the minimum possible cost. The initial step in formulating a mathematical model for the transportation problem is to identify the sources, destinations, and the quantities transported.
The objective of the transportation problem is to minimize the total cost of transporting the goods. The mathematical model of the transportation problem is:
Let there be m sources (i = 1, 2, …, m) and n destinations (j = 1, 2, …, n). Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
The transportation problem can then be formulated as follows:
Minimize Z = ∑∑cijxij
Subject to the constraints:
∑xij = si, i = 1, 2, …, m
∑xij = dj, j = 1, 2, …, n
xij ≥ 0
where si and dj are the supply and demand of goods at the i-th source and the j-th destination respectively.
Using the given table, we can formulate the transportation problem as follows:
Let A1, A2, and A3 be the sources, and B2, B3, and B4 be the destinations. Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
Minimize Z = 27x11 + 27x12 + 32x13 + 15x21 + 21x22 + 20x23 + 16x31 + 22x32 + 18x33
Subject to the constraints:
x11 + x12 + x13 = 3
x21 + x22 + x23 = 14
x31 + x32 + x33 = 10
x11 + x21 + x31 = 21
x12 + x22 + x32 = 32
x13 + x23 + x33 = 26
xij ≥ 0
In this way, we can construct a mathematical model of the transportation problem using the given table. The model can be solved using the simplex method to obtain the optimal solution.

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336,765=3,14×0.55×(l+0.55) please help​

Answers

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

which scatterplot is it lol

which scatterplot is it lol

Answers

Answer:

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point


If the perimeter of a regular hexagon is 1 foot, each side is
how many inches long?

Answers

Answer:

2 or...?

Step-by-step explanation:

The hexagon is 2 inches long

Multiply it with the given measurement. 1 foot is 12 inches. This means that the perimeter = 12 in. A hexagon has 6 sides. This means that 12 divided by 6 sides = 2 in.


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—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

This is easy I just need the answer thanks!!! :)

This is easy I just need the answer thanks!!! :)

Answers

Answer:

225 inches

Step-by-step explanation:

15 x 15 = 225

Orlando eams a salary of $40,000. If Orlando salary increases by 20% for the next two years, how much money would he be earning​

Answers

Answer:

$57,600

Step-by-step explanation:

first: 20% of 40,000 = 8,000

second: add 40,000 + 8,000 = 48,000

third: 20% of 48,000 = 9,600

fourth: add 9,600 + 48,000 = 57,600

which is your answer

HOPE THIS HELPS :)

leni can decorate the room in 4 hours. her sister lucy do the same jobin 3 hours working together, how long will take them to finish the job

Answers

Fractions are integers that have both a numerator and a denominator. They are represented as; \(\frac{x}{y}\)

Where:

x = Numerator

y = Denominator.

It will take them both \(\frac{7}{12}\) hours or 0.583 hours to finish the job together.

To solve the above question, we would be applying the operations of the addition of fractions.

From the question,

Leni can decorate the room in 4 hours. This means in 1 hour, Leni can paint 1/4 of the room.

Lucy, her sister can decorate the room in 3 hours. This means in 1 hour, lucy can decorate 1/3 of the room.

Let us represent the number of hours it will take them both to decorate the room working together as "T"

Hence,

1/T = 1/4 + 1/3

Lowest Common Denominator for (3, 4 ) = 12

Hence,

1/T = 3 + 4 / 12

1/T = 7/12

Find the reciprocal of both sides

T = 7/12 hours or can be expressed in decimals as 0.583 hours.

Therefore, it will take them both \(\frac{7}{12}\) hours or 0.583 hours to finish the job together.

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A line passes through the points (- 4, 7) and (5, - 8) . What is the slope of the line?
A) -2
B) -1
C) -5/3
D) 3/5

Answers

Answer:

c is the right answer ok....

C is the correct answer. -5/3 Correct. Step by step explain

If these two shapes are similar, what is the measure of the missing length b?

If these two shapes are similar, what is the measure of the missing length b?

Answers

Answer:

B = 7mm

Step-by-step explanation:

This is probably an enlargement problem.

To solve this:

the blue triangle has all of it's measurements you need. Let's start with that.

6/36 =

We know that one side, the bottom side of the green triangle is 42mm.

6/36 = b/42

We could simplify 6/36 into 1/6

1/6 = b/42

AHA! the denominators are easy! 6 times 7 is equal to 42, so 1 times 7 should equal b!

1/6 = 7/42

Check:

6/36 = b/42

36b = 6*42

36b = 252

   b = 252/36

   b = 7

So yes! B is 7 mm. Pls mark me brainliest, as I never have a single brainliest.

Henry was thinking of a number. Henry halves the number and gets an answer of 32.5. Form an equation with
x
from the information.

Answers

Answer:

x/2=32.5

Step-by-step explanation:

his number is x and it is cut in half which is divided by 2, then it equal 32.5

If it takes an airplane 3 hours to fly 3600 miles, how long will it take to fly
5400 miles. Use a decimal for your answer rounded to the nearest tenth.

Answers

The number of hours it will take the airplane to fly the given distance would be = 4.5 hours

How to calculate the number of hours that can be used for the distance?

To calculate the number of hours that can be used for the distance, the following needs to be done. That is;

The number of hours it take to complete 3600 miles = 3 hours

Therefore the number of hours it will take to complete 5400miles = X hours.

That is;

3600 miles = 3 hours

5400 miles = X hours

make X the subject of formula;

X = 5400×3/3600

= 16,200/3600

= 4.5 hours.

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what is the rationale and basis for statistical process control? multiple choice question. results of previous corrective actions on the existing process acceptable variation within probability limits last month's quality metrics on process stability and how current month changed six sigma calculations and alpha error score

Answers

As per the concept of probability, the rationale behind statistical process control is to understand and control the sources of variation in a manufacturing process to change the six sigma calculations and alpha error score (option d).

Statistical Process Control (SPC) is a methodology used in manufacturing industries to monitor and control a process by measuring and analyzing the process variables over time.

The results of previous corrective actions on the existing process are important in determining the effectiveness of those actions and whether further adjustments are needed.

Acceptable variation within probability limits is a key aspect of SPC. By understanding the probability distribution of the process variables, we can determine the acceptable range of variation and use control charts to monitor the process and identify any deviations from this range.

Six sigma calculations and alpha error score are also important aspects of SPC. Six sigma is a statistical measure that indicates the level of quality in a process, and the alpha error score is the probability of rejecting a true null hypothesis.

Hnce the option (d) is correct.

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On Monday, a bakery sold 67 dozen cookies. How many total cookies did the bakery sell?​

Answers

Answer:

804

Step-by-step explanation:

dozen means 12

67 times 12 is 804

804

In this problem, we need to use multiplication to find the answer

Since we know that the bakery sold 67 dozen cookies on Monday and a dozen means 12, we need to multiply 67 and 12. We get:

67 × 12 = 804

Hope this helps :)

Solve for x in the triangle. You must show your starting equation and all work. Then calculate the value of each angle in the triangle.

Solve for x in the triangle. You must show your starting equation and all work. Then calculate the value

Answers

Answer: x = 59

Step-by-step explanation:

Solve for x in the triangle. You must show your starting equation and all work. Then calculate the value
A triangle all adds up to 180°.
Therefore you must add them all up and equal them to 180.


Shown below:

2x+1+3x+x+5=180

Then of course you have to solve it.

Shown below:

6x+6=180

Move the 6 over to the side of 180 which leaves 6x by itself.

Shown below:

6x=180-6

Then solve the equation:

6x=174

Solve x:

x= 174/6

Hence, leaving x as 29°

After finding x, you must substitute it in the x values. Hope this was helpful.

Write a slope-intercept equation for a line passing though the point (2,20) that is parallel to y=1/2x+13. Then write a second equation for a line passing through the given point that is perpendicular the given line.

Answers

The linear function passing though the point (2,20) that is parallel to y=1/2x+13 is given as follows:

y = 0.5x + 19.

The perpendicular line is given as follows:

y = -2x + 24.

How to define a linear function?

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The slope m represents the rate of change.The intercept b represents the value of y when x = 0.

When two lines are parallel, they have the same slope, hence:

y = 0.5x + b.

When x = 2, y = 20, hence the intercept b is given as follows:

20 = 0.5(2) + b

b = 19.

Hence:

y = 0.5x + 19.

When two lines are perpendicular, the multiplication of their slopes is of -1, hence:

0.5m = -1

m = -2.

Thus:

y = -2x + b.

When x = 2, y = 20, hence the intercept b is obtained as follows:

20 = -2(2) + b

b = 24.

Hence:

y = -2x + 24.

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Sketch a graph y= f(x) of a function defined everywhere on (-[infinity], [infinity]) with the following properties:
lim x +[infinity] f(x) = 2 limx +[infinity] f(x) = 4
f(0) = 0

Answers

There are infinitely many functions that satisfy the given conditions.

To sketch a graph y = f(x) of a function defined everywhere on (-∞, ∞) with the given properties, we need to consider the following steps: First, consider the given limit lim x→+∞ f(x) = 2andlim x→-∞ f(x) = 4Since we are given that the function is defined everywhere on (-∞, ∞), there are no vertical asymptotes.

Therefore, the function has a horizontal asymptote at y = 2 as x approaches infinity and a horizontal asymptote at y = 4 as x approaches negative infinity.

Secondly, we are given that f(0) = 0, which means that the graph passes through the origin (0, 0). Now, we need to consider the shape of the graph between the origin and positive infinity, and the shape of the graph between the origin and negative infinity.

Based on the given limits, we know that the graph must approach the horizontal line y = 2 as x approaches infinity and approach the horizontal line y = 4 as x approaches negative infinity.

A possible sketch of the graph y = f(x) is shown below: Graph of y = f(x) with given properties The graph can take any shape between the origin and infinity, and between the origin and negative infinity, as long as it approaches the horizontal lines y = 2 and y = 4, respectively, as x approaches infinity and negative infinity.

Therefore, there are infinitely many functions that satisfy the given conditions.

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The coordinates of the four vertices of quadrilateral ABCD are listed below
4
• A(-3,3)
.
.B(2,6)
. C(5, 1)
. D(-5,-5)
Which statement proves whether or not this quadrilateral is a rectangle?
OA
The slope of CD is-
rectangle
OB The slope of AB is
-5-1
-5-5
OD. The slope of AB is
6-3
2-(-3)
3
5
6-3
2-(-3)
3
and the slope of DA IS
OC. The slope of BC is and the slope of CD is
rectangle
3-(-5)
-3-(-5)
and the slope of BC is These two segments are perpendicular, so the shape is a rectangle.
These two segments are not perpendicular, so the shape is not a
These two segments are not perpendicular, so the shape is not a
and the slope of CD is-7
These two segments are perpendicular, so the shape is a rectangle.

The coordinates of the four vertices of quadrilateral ABCD are listed below4 A(-3,3)..B(2,6). C(5, 1).

Answers

For the quadrilateral ABCD the statement which proves that this quadrilateral is not a rectangle is (a) The slope of CD is "(-5-1)/(-5-5) = 3/5", and the "slope of DA is [3-(-5)]/[-3-(-5)] = 8/2", these "two-segments" are not perpendicular , so the shape is not a rectangle;

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

To prove whether the quadrilateral is a rectangle or not, we need to show that its adjacent sides are perpendicular and its diagonals are congruent.

In this question, we are given the coordinates of the four vertices of the quadrilateral.

To determine if it's a rectangle, we use the slope formula to find the slopes of the sides of the quadrilateral. If slopes of adjacent sides are "negative-reciprocals" of each other, then they are perpendicular. If the slopes of the diagonals are equal, then they are congruent.

Using the given coordinates, we find that the slope of CD is = (-5-1)/(-5-5) = 3/5, and

The slope of DA is = [3-(-5)]/[-3-(-5)] = 8/2. These two slopes are not negative reciprocals of each other, so CD and DA are not perpendicular.

So, the quadrilateral is not a rectangle.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

The coordinates of the "four-vertices" of the quadrilateral ABCD are :

A(-3,3), B(2,6), C(5, 1), D(-5,-5);

Which statement proves whether or not this quadrilateral is a rectangle?

(a) The slope of CD is (-5-1)/(-5-5) = 3/5, and the slope of DA is 3-(-5)/-3-(-5)=8/2, these two segments are not perpendicular , so the shape is not a rectangle;

(b) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of BC is (6-1)/(2-5) = -5/3, these two segments are perpendicular , so the shape is a rectangle;

(c) The slope of BC is (6-1)/(2-5) = -5/3, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are not perpendicular, so the shape is not a rectangle;

(d) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are perpendicular , so the shape is a rectangle;


what are the answer ?? please
24. Plants will turn ideas into practical action a. True b. False 25- Shapers will see the "small picture" and make sure that the solution results in a change of direction a. True b. False

Answers

24. The answer is False. Plants will not turn ideas into practical action.
25. The answer is True, Shapers will see the "small picture" and make sure that the solution results in a change of direction.


24. Plants are the creative innovators in an organization. They are characterized by their creativity, originality, and unorthodox problem-solving abilities. They generate new ideas and approaches to problem-solving. However, they may not have the necessary drive to see those ideas through to fruition. So, it is not true that plants will turn ideas into practical action. Thus, the statement is false.

25. Shapers are dynamic individuals who thrive on challenge, possessing the drive and courage to overcome obstacles and make things happen. They provide the necessary impetus to ensure that ideas are turned into action and that decisions are taken quickly and efficiently. They are the ones who see the "small picture" and make sure that the solution results in a change of direction. So, it is true that shapers will see the "small picture" and make sure that the solution results in a change of direction. Thus, the statement is true.


The correct answer for statement 24 is False and for statement 25 is True.

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Divide. Look for patterns in your answers.

c. (x⁴ - 1) / (x-1) .

Answers

The result of the division is x³ + x² + x + 1, and there is no remainder.

To divide (x⁴ - 1) by (x - 1), we can use long division:

           x³ + x² + x + 1

     _____________________

x - 1 | x⁴ + 0x³ + 0x² + 0x - 1

         -(x⁴ - x³)

         ____________

                 x³ + 0x²

             -(x³ - x²)

             ____________

                     x² + 0x

                 -(x² - x)

                 ____________

                         x - 1

                     -(x - 1)

                     __________

                              0

The result of the division is x³ + x² + x + 1, and there is no remainder.

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find the area between a large loop and the enclosed small loop of the curve r = 2 4 cos(3).

Answers

The area between the large loop and the enclosed small loop of the curve r=24cos(3) is approximately 8.75 square units.

To find the area between the large loop and the enclosed small loop, we need to first determine the values of θ where the loops occur. The polar equation r=24cos(3) has two loops, with the smaller loop enclosed within the larger one. The smaller loop occurs when cos(3)=0, which happens when theta is a multiple of π/6. The larger loop occurs when r=0, which happens when cos(3)=-1/2 or when theta is a multiple of π/3. To calculate the area between the loops, we can integrate the area of the sector between two adjacent θ values and subtract the area of the smaller loop from the larger loop. This gives us an approximation of 8.75 square units for the area between the loops. The actual value can be obtained by using calculus to calculate the definite integral of the difference in the areas of the two loops.

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