julia robert, who is one of the most successful actresses in recent years, has a height that converts to a z score of 2.16 How tall (in inches) is Julia Roberts?

The function f(x) = 9/(4-x^2) does not have any removable or non-removable discontinuities. It is continuous for all real values of x except where x^2 = 4, which leads to undefined values of the function.

To determine the x-values at which the function f(x) = 9/(4-x^2) is not continuous, we need to look for any potential removable and non-removable discontinuities.

First, let's consider removable discontinuities. These occur when there are holes in the graph that can be filled in by redefining the function at that point. In this case, we need to check if there are any values of x for which the denominator (4-x^2) becomes zero.

For the function f(x) = 9/(4-x^2), the denominator becomes zero when x^2 = 4. Solving this equation, we find two potential values for x: x = 2 and x = -2.

To check if these values are removable discontinuities, we need to examine the behavior of the function near these points. However, it seems that there is a mistake in your initial statement. There are no removable discontinuities for the given function f(x) = 9/(4-x^2).

Moving on to non-removable discontinuities, these occur when the function has vertical asymptotes or jump discontinuities that cannot be filled in. In this case, we need to check if there are any values of x that make the denominator zero and cannot be canceled out.

Again, for the function f(x) = 9/(4-x^2), the denominator becomes zero when x^2 = 4. Solving this equation, we find the same two potential values for x: x = 2 and x = -2.

However, upon further inspection, we can see that these values are not non-removable discontinuities either. Plugging them back into the function, we have:

f(2) = 9/(4-2^2) = 9/0,

f(-2) = 9/(4-(-2)^2) = 9/0.

Both f(2) and f(-2) are undefined since division by zero is not allowed. Therefore, x = 2 and x = -2 are not non-removable discontinuities either.

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The effective rate of interest for 1 year with a principal of $15,500 and an interest rate of 12% compounded quarterly is 12.55%.

The effective annual interest rate (APY) is used to calculate the return on an investment after one year, including any compounding that occurs over the year. It is a crucial tool for determining the actual interest rate paid or earned on an investment. In this question, we will use the given information to calculate the APY or effective rate of interest for 1 year.
Given information:
Principal amount (P) = $15,500
Annual Interest rate (r) = 12%
Compounding periods per year (n) = 4 (since interest is compounded quarterly)
Time (t) = 1 year
Formula to calculate APY or effective rate of interest:
APY = (1 + r/n)ⁿ - 1
where r is the annual interest rate, n is the number of compounding periods in a year, and t is the time period for which interest is calculated.
Substituting the values, we get:
APY = (1 + 12%/4)⁴ - 1
APY = (1 + 0.03)⁴ - 1
APY = 1.1255 - 1
APY = 0.1255 or 12.55%
Therefore, the effective rate of interest for 1 year with a principal of $15,500 and an interest rate of 12% compounded quarterly is 12.55%.

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a. Converse: If the interior angles of a shape do not sum to 180°, then the shape is not a triangle. The converse is true. If the interior angles do not add up to 180°, it implies that the shape is not a triangle.

b. Converse: If alternate interior angles of two lines are equal, then the lines are parallel. The converse is true. If alternate interior angles are equal, it implies that the lines are parallel.

c. Converse: If I have a Rhombus, then I also have a Square. The converse is not true. A rhombus is a parallelogram with equal side lengths, but it does not necessarily have right angles like a square.

d. Converse: If I have a shape with four right angles, then I have a rectangle. The converse is not true. A shape with four right angles could be a square, but it could also be a parallelogram or a rhombus.

Answer:

a. Converse: If the interior angles of a shape sum to 180°, then the shape is a triangle.

This is not always true.

b. Converse: If alternate interior angles are equal, then the two lines are parallel.

This is true. This is because alternate interior angles are congruent when two lines are parallel.

c. Converse: If I have a Rhombus, then I also have a Square.

This is not always true.

d. Converse: If I have a shape with four right angles, then I have a rectangle.

This is true. This is because a rectangle is a shape with four right angles.

Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

The distance between point T (-5, 1) and point I (-1, 1) is 4 units.

To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's apply this formula to find the distance between point T (-5, 1) and point I (-1, 1):

x1 = -5, y1 = 1 (coordinates of point T)

x2 = -1, y2 = 1 (coordinates of point I)

Plugging these values into the formula, we have:

Distance = √((-1 - (-5))² + (1 - 1)²)

        = √(4² + 0²)

        = √(16 + 0)

        = √16

        = 4

Therefore, the distance between point T (-5, 1) and point I (-1, 1) is 4 units.

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Answer:

(a) 468 + 59 = 527

Step-by-step explanation:

Attached is the work for solving the addition problem using the compensation method.

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In the given diagram, Triangle A and Triangle B are similar triangles.

From the question, we are to determine which of the given triangles are similar

For two triangles to be considered similar triangles, they must satisfy the similarity criteria.

The triangle similarity criteria include:

In the given diagram, Triangle A and Triangle B satisfy the above criteria.

Hence,

Triangle A and Triangle B are similar.

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To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Yes, a polygon can have a central angle of 25 degrees.

A central angle is an angle formed by two radii (or line segments) extending from the center of a polygon to two consecutive vertices. The sum of the central angles in any polygon is always equal to 360 degrees.

Therefore, if we have a regular polygon with n sides, each central angle would measure 360 degrees divided by n. For example, a regular hexagon (a polygon with 6 sides) would have central angles of 360 degrees divided by 6, which is 60 degrees.

However, in the case of an irregular polygon, the central angles can have different measures. As long as the sum of all the central angles equals 360 degrees, it is possible for one or more central angles to measure 25 degrees.

Answer:

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I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

All the methods are complete and have distributed all the 12 buyers.

The question is about determining the number of buyers that should be assigned to each of the 5 stores. There are 12 buyers to assign. Therefore, each store must get at least one buyer.

In solving the problem, we need to find the standard divisor, which is the total number of buyers divided by the total number of employees of the five stores (12/36). This gives us the standard divisor of 0.3333. We will use Hamilton's, Jefferson's, Webster's and Hill-Huntington's Method to calculate the distribution of buyers per store using the standard divisor.

Hamilton's Method According to Hamilton's Method, each store is assigned buyers from highest to lowest until all the buyers are assigned. Any excess buyers should be assigned to the store with the highest allocation factor.

The allocation factors for the stores are as follows:Store Allocation Factor Buyers Allocation Total AllocationHamilton's0.500.331.331.00Jefferson's0.2860.3330.99Webster's0.1670.3330.83Adams'0.0830.3330.50Madison's0.0560.0030.36

The table shows that Hamilton's method allocates 3 buyers to Hamilton's store, 3 buyers to Jefferson's store, 2 buyers to Webster's store, 1 buyer to Adam's store, and 1 buyer to Madison's store. Hamilton's method distributes all 12 buyers.Jefferson's Method

According to Jefferson's method, each store is assigned buyers using the allocation factor rounded to the nearest integer. The unassigned buyers are distributed using Hamilton's method.The allocation factors for the stores are as follows:Store Allocation Factor Allocation Rounded Buyers Allocation Total AllocationHamilton's0.5001.002.003.00Jefferson's0.2860.003.002.99Webster's0.1670.002.001.99Adams'0.0830.001.001.00Madison's0.0560.001.000.50

The table shows that Jefferson's method allocates 3 buyers to Hamilton's store, 3 buyers to Jefferson's store, 2 buyers to Webster's store, 1 buyer to Adam's store, and 1 buyer to Madison's store. Jefferson's method also distributes all 12 buyers.Webster's MethodAccording to Webster's method, each store is assigned buyers using the allocation factor rounded down to the nearest integer.

The unassigned buyers are distributed using Hamilton's method.The allocation factors for the stores are as follows:Store Allocation Factor Allocation Rounded Buyers Allocation Total AllocationHamilton's0.50002.002.332.33Jefferson's0.28601.002.332.33Webster's0.16700.001.001.00Adams'0.08300.000.330.33Madison's0.05600.000.330.33

The table shows that Webster's method allocates 2 buyers to Hamilton's store, 2 buyers to Jefferson's store, 1 buyer to Webster's store, 0 buyers to Adam's store, and 0 buyers to Madison's store. Webster's method distributes a total of 5 buyers.

The remaining 7 buyers are then distributed using Hamilton's method.Hill-Huntington's MethodHill-Huntington's method allocates the remaining fraction by assigning the buyer to the store with the largest decimal portion.The allocation factors for the stores are as follows:Store Allocation Factor Allocation Rounded Buyers Allocation Total AllocationHamilton's0.50002.332.333.00Jefferson's0.28602.332.331.00Webster's0.16700.331.001.00Adams'0.08300.000.330.33Madison's0.05600.000.330.33

The table shows that Hill-Huntington's method allocates 2 buyers to Hamilton's store, 2 buyers to Jefferson's store, 1 buyer to Webster's store, 0 buyers to Adam's store, and 0 buyers to Madison's store. Hill-Huntington's method distributes a total of 5 buyers.

The remaining 7 buyers are then distributed using Hamilton's method.All the methods are complete and have distributed all the 12 buyers.

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Step-by-step explanation:

11.16 days ok hope it helps

Answer: = 8x - 5

Step-by-step explanation:

f(x) = 4x² - 5x

Find:

lim as Δx⇒0  [f(x + Δx) - f(x)] /Δx        

This is the same as finding the derivative.   For f(x + Δx) means substitute x + Δx  into the function everytime you see an x.

Solution:

lim as Δx⇒0  [f(x + Δx) - f(x)] /Δx

lim as Δx⇒0  [4(x + Δx)² - 5(x + Δx) - (4x² - 5x)] /Δx             >Simplify

lim as Δx⇒0  [4(x²+2x(Δx) +(Δx)²) - 5x- 5Δx - 4x²+ 5x] /Δx

lim as Δx⇒0  [4x²+8x(Δx) +4(Δx)² - 5x- 5Δx - 4x²+ 5x] /Δx

lim as Δx⇒0  [8x(Δx) +4(Δx)²- 5Δx] /Δx            >Divide by Δx

lim as Δx⇒0  8x +4(Δx)- 5                >set Δx to 0 because it is approaches

= 8x - 5

You can check this using the power rule and take derivative of f(x) and it checks out.

Certainly! The problem can be solved using the Pythagorean theorem,

which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse, and we need to find the length of the vertical side (height) it reaches up the wall.

The ladder forms the hypotenuse, and its length is given as 12 meters. The distance from the foot of the ladder to the base of the wall represents one side of the triangle, which is 4.5 meters.

By substituting the given values into the Pythagorean theorem equation: (12m)^2 = h^2 + (4.5m)^2, we can solve for the unknown height 'h'.

Squaring 12m gives us 144m^2, and squaring 4.5m yields 20.25m^2. By subtracting 20.25m^2 from both sides of the equation, we isolate 'h^2'.

We then take the square root of both sides to find 'h'. The square root of 123.75m^2 is approximately 11.12m.

Therefore, the ladder reaches a height of approximately 11.12 meters up the wall.

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Answer: -2

Step-by-step explanation:

The slope of the line perpendicular to another slope is the opposite sign and flipped(reciprocal)

The slope of the line = 1/2

So the perpendicular slope = -2

Among the given word problems, the one that exemplifies a linear function is: Kate rented a bicycle for $30 plus $1.50 per hour. Statement 1

In this scenario, the cost of renting the bicycle has a fixed component of $30 and an additional cost of $1.50 per hour. The cost is directly proportional to the number of hours the bicycle is rented.

As the number of hours increases, the cost increases linearly by $1.50 per hour. This relationship can be represented by a linear equation of the form y = mx + b, where y is the cost, x is the number of hours, m is the rate of increase ($1.50 per hour), and b is the fixed cost ($30). The equation for this situation would be y = 1.50x + 30, where x ≥ 0.

On the other hand, the other two word problems do not represent linear functions:

Pinocchio's nose grows about 20% of its size each time he lies. His nose was 2 inches long at the beginning.

This situation represents exponential growth since the nose grows by a fixed percentage (20%) of its current size, not by a fixed amount. The growth is not linear but rather compounding, where each increase is a factor of the previous size.

The mean distance of the Earth from the sun is 93 million miles. The distance varies by 1.6 million miles.

The variation in distance does not follow a linear pattern but rather represents a range or interval. The change in distance is not proportional to any other variable; it is simply a measure of the variation or spread in the data.

Statement 1 is correct.

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The calculated value of the function g(x) when x = 5 is -2

From the question, we have the following parameters that can be used in our computation:

The graph of the function g(x)

The value of g(5) is the value of the function at x = 5

When x = 2 is traced on the graph, we have

y = -2 when x = 5

This means that

g(5) = -2

Hence, the value of the function is -2

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The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

To determine if the sequence is arithmetic, geometric, or neither, let's examine the given terms: 972, 324, 108, 36.

To find the missing terms of the sequence, let's look for a pattern in the numbers:

If we divide each term by 3, we get:

972/3 = 324

324/3 = 108

108/3 = 36

It seems that each term is obtained by dividing the previous term by 3.

Now, let's check if the sequence is arithmetic or geometric:

If we calculate the common difference between consecutive terms, we see that there is no constant difference. For example:

324 - 972 = -648

108 - 324 = -216

36 - 108 = -72

Since the differences are not constant, the sequence is not arithmetic.

If we calculate the common ratio between consecutive terms by dividing a term by its previous term, we find that the ratio is constant:

324/972 = 1/3

108/324 = 1/3

36/108 = 1/3

The common ratio is 1/3, which indicates that the sequence is geometric.

The missing terms in the sequence are:

(36/3) = 12

(12/3) = 4

The complete sequence is: 972, 324, 108, 36, 12, 4.

The sequence is geometric, with a common ratio of 1/3, and the missing terms are 12 and 4.

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Among the given word problems, the one that exemplifies a linear function is:

Kate rented a bicycle for $30 plus $1.50 per hour.

A linear function is a mathematical function that represents a straight line. It has a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Among the given word problems, the one that exemplifies a linear function is:

Kate rented a bicycle for $30 plus $1.50 per hour.

In this scenario, the cost of renting the bicycle is determined by a fixed fee of $30 plus an additional charge of $1.50 per hour. The relationship between the total cost and the number of hours can be represented by a linear equation, where the cost increases at a constant rate of $1.50 per hour.

The other two word problems do not represent linear functions. Pinocchio's nose growing by 20% each time he lies involves exponential growth, and the mean distance of the earth from the sun varying by 1.6 million miles represents a variable relationship, not a linear one.

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The hypothesis is If a person is at least 16 years.

The conclusion is Then the person can drive a car

The Converse is If a person can drive a car, then the person is at least 16 years.

A hypothesis is a proposed explanation or prediction that can be tested and investigated to determine its validity. A hypothesis serves as a starting point for an investigation. Hypotheses are often formulated in an "if-then" format.

The conclusion is the outcome or summary reached after conducting a study or investigation. It aims to answer the research question or objective and provide a clear understanding of the implications and significance of the study.

Converse

Converse is the opposite of a statement. It is used in the context of hypotheses and research question

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Answer:

The original number is -22

Step-by-step explanation:

We'll label our mystery number x.

2x + 36 = 4x/11
Multiply both sides by 11
4x = 22x + 396
Isolate x to one side (for this I subtract 4x from both sides, but you can also subtract 22x if you'd like)
0 = 18x + 396
Isolate x pt 2
18x = -396
Divide both sides by 18 to find your answer!
x = -22

Plug in to confirm

-44 + 36 = -88/11S
8 = 8

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

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The triangles in the coordinate plane are congruent to triangle A are: Triangles D and F

Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are the same size. These triangles can be moved, rotated, flipped, and flipped to make them look identical. When repositioned, they match each other.

The postulates of congruency follows:

SAS - Side Angle Side Congruency Postulate

SSS - Side Side Side Congruency Postulate

ASA - Angle Side Angle Congruency Postulate

AAS - Angle Angle Side Congruency Postulate

HL - Hypotenuse Leg Congruency Postulate

Looking at the attached image, the only two triangles that are congruent to Triangle A ae D and F.

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The missing dimensions of the given expressions are as follows:

1. 2x + 24 (81) → 24x2. (82) → 16 3. 2x (83) → 83x4. (84) → 42x

Given expressions are:1. 2x + 24 (81)2. (82) 3. 2x (83)4. (84) Let’s find the missing dimensions of the given expressions one by one:

1. 2x + 24 (81)We know that perimeter = 2 × length + 2 × breadth.

The given expression represents the perimeter of the rectangle. Here, the breadth of the rectangle is 24.

Therefore, length of the rectangle = 2x/2 = x.

So, the missing dimension is x. Dimension of the rectangle = x × 24 Expression of the rectangle as a product = 24x 2. (82)

The given expression represents the area of the rectangle.

Therefore, the two dimensions of the rectangle are (8) and (2). Dimension of the rectangle = 8 × 2 Expression of the rectangle as a product = 16 3. 2x (83)

The given expression represents the area of the rectangle.

Therefore, the two dimensions of the rectangle are (2) and (83/2). Dimension of the rectangle = 2 × 83/2 Expression of the rectangle as a product = 83x4. (84)

We know that perimeter = 2 × length + 2 × breadth The given expression represents the perimeter of the rectangle.

Here, the length of the rectangle is 84/2 = 42.

Therefore, breadth of the rectangle = 2x/2 = x.

So, the missing dimension is x.

Dimension of the rectangle = 42 × x

Expression of the rectangle as a product = 42x

Hence, the missing dimensions of the given expressions are as follows:

1. 2x + 24 (81) → 24x2. (82) → 16 3. 2x (83) → 83x4. (84) → 42x

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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With a pound of flour costing $12 and considering that there are 16 ounces in a pound, the cost per ounce is $0.75. Thus, for $3.30, you can purchase 4.4 ounces of flour.

To find out how many ounces of flour can be purchased for $3.30, we need to determine the cost of one ounce of flour.

Given that a pound of flour costs $12, we know that there are 16 ounces in a pound (since there are 16 ounces in 1 pound). So, the cost of one ounce of flour can be calculated as:

Cost of one ounce of flour = Cost of one pound of flour / Number of ounces in one pound

Cost of one ounce of flour = $12 / 16 ounces

Cost of one ounce of flour = $0.75

Therefore, the cost of one ounce of flour is $0.75.

To determine how many ounces of flour can be purchased for $3.30, we divide the total amount of money by the cost of one ounce of flour:

Number of ounces of flour = Total money / Cost of one ounce of flour

Number of ounces of flour = $3.30 / $0.75

Number of ounces of flour ≈ 4.4 ounce

Therefore, for $3.30, approximately 4.4 ounces of flour can be purchased.

In summary, with the given cost of $12 for a pound of flour, and knowing that there are 16 ounces in a pound, we find that one ounce of flour costs $0.75. Thus, for $3.30, approximately 4.4 ounces of flour can be purchased.

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Answer:

B and F

Step-by-step explanation:

[Note: Work for this problem is shown in the image attached to this answer]

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IN  a case whereby population of a town increased from 3800 in 2006 to 6050 in 2010.  Relative percentage is 59.2 and absolute difference is 2250

Difference in population=6050 - 3800

=  2250

2250 is what percent of 3,800?

2250 = X* 3,800

X =  2250 /  3,800

X = 0.59 or 59%

2250 = X*  6050

X =  2250 /  6050

X =  0.37 or 37%

Relative percentage=

 [tex]\frac{6050 - 3800 }{3800 } * 100\\\\=59.21[/tex]

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