The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows
y = 2 (1/5)^x - 5 y = 4^x
Initial value: 2 1
base function: 1/5 = decay function 4 = growth function
Translation: 5 units down no transformation
What is a decay function?
A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.
It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.
Decay function are exponential functions with the base function as
0 < k < 1This is the opposite of growth function which has values greater than 1
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Find the explicit equation.
Answer:
f(n) = 10 + 3n
Step-by-step explanation:
Each of the expressions has 10 + a certain number of 3's
For example for n = 3 we have
f(3) = 10 + 3 threes = 10 + 3 x 3 = 10 + 9 = 19
For n = 4, we have
f(4) = 10 + 4 threes = 10 + 4 x 3 = 10 + 12 = 22
The others follow the same pattern
So the explicit equation is
f(n) = 10 + 3n
Testing on n = 6 we get
f(6) = 10 + 6n = 10 + 6 x 3 = 10 + 18 = 28
Can someone pls help meeeeeee!!!
Answer:
For question 2, Ethan needs 3 cups of milk to make the batter for 3 times as many cakes.
For question 3, Isabella needs 5/4 of a gallon of the food to make 5 gallons of the mixture.
A triangle has sides with lengths of 4 miles, 6 miles, and 8 miles. Is it a right triangle?
yes or no
Answer:
scalene, right triangle
Step-by-step explanation:
Determine whether it is a triangle and the triangle's type:
Answer: scalene, right triangle
Shawna is playing a game that involves rolling a black numbered cube and a red numbered cube. The result of a red numbered cube represents a negative number, and the result of a black numbered cube represents a positive number. Shawna’s current score is 4. Then, Shawna rolls a red 5 and a black 3. Write and solve an equation to represent Shawna’s new score.
Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube
What exactly are algebraic expressions?
Algebraic expressions are expressions made up of variables and constants. Additional algebraic operations include addition, subtraction, and division.
If the result of a red numbered cube represents a negative number, then we can represent the result of the red cube as -5. Similarly, if the result of a black numbered cube represents a positive number, we can represent the result of the black cube as +3.
Shawna's current score is 4, and her new score is obtained by adding the results of the two cubes to her current score. We can represent this situation with the following equation:
New score = Current score + Result of black cube + Result of red cube
Substituting the values we have for the result of the black cube, the result of the red cube, and Shawna's current score, we get:
New score = 4 + 3 + (-5)
Simplifying, we get:
New score = 2
Therefore, Shawna's new score is 2 and the equation to represent Shawna’s new score would be, New score = Current score + Result of black cube + Result of red cube.
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Which of the following is a solution to z2 + 2 < 6?
0, 2, 4, -2, or -4
z = - 4, represents the solution of the inequality → z² + 2 < 6.
What is inequality?An inequality is used to compare numbers or expressions. For example -
2x + 4 > 6 4x + 6 < 8 y > 9 x < 1
All the above expressions mentioned above represent inequalities.
Given is the inequality as -
z² + 2 < 6
The given inequality is -
z² + 2 < 6
Subtract {2} from both side we get -
z² < 4
z < ± 2
Therefore, z = - 4, represents the solution of the inequality → z² + 2 < 6.
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Which shapes from the Clade Race would be considered plesiomorphic?a. Circle b. Heart c. Square d. Arrowe. Cross f. Moon g. Star h. Triangle i. Hexagon
Amongst the options circle shape from the Clade Race would be considered plesiomorphic.
A primitive or ancestral character state is called plesiomorphy or known as a plesiomorphic character), and a shared plesiomorphy is called a symplesiomorphy. For example, let us take an example of hair. It is a unique mammalian character that evolved with the evolution of mammals.
The term apomorphy means a specialized or derived character state which is plesiomorphy. It refers to a primitive or ancestral trait. An same as autapomorphy, it is a derived trait that is unique to one group, while a same as synapomorphy is a derived trait shared by two or more groups.
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An army sergeant works as a trauma surgeon. Which two career clusters is she most likely a part of?
the Energy cluster and the Education and Training cluster
the Health Services cluster and the Energy cluster
the Government and Public Administration cluster and the Health Services cluster
the Education and Training cluster and the Government and Public Administration cluster
Both clusters are relevant to her career.
Why is it referred to as a cluster?Cluster is derived from the old english word clyster, which means a group. Cluster is now used as both a noun and a verb.
The army sergeant who works as a trauma surgeon is probably in the Health Services and Government and Public Administration clusters.
Health Services occupations include diagnosing, treating, and preventing illnesses and injuries, while Government and Public Administration occupations include planning, managing, and providing government functions and services. The individual is a member of the military, which is a government organisation, and a trauma surgeon, which is a part of the healthcare industry. As a result, both clusters are pertinent to her career.
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Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.
A. (8 * t) + (8 * 8) is equivalent to 8t + 64
B. 4t + 8 + 4t is equivalent to 8t + 8
C. 4(2t + 2) is equivalent to 8t + 8
D. 8t + 64 is equivalent to 8t + 64
E. 8t + 16 is equivalent to 8t + 16
F. (8 + t) + (8 + 8) is equivalent to 16 + t.
So the expressions that are equivalent to 8(t + 8) are B and C, the expression that is equivalent to 8t + 8 is E, and the expression that is neither is F.
In the given problem, we are comparing the given expressions to see if they are equivalent to 8(t + 8), 8t + 8, or neither.
Expression A: (8 * t) + (8 * 8) = 8t + 64
This expression is equivalent to 8t + 64, which is not the same as 8(t + 8) or 8t + 8.
Expression B: 4t + 8 + 4t = 8t + 8
This expression is equivalent to 8t + 8, which means that adding up 4t and 8, and then adding 4t again to the result is the same as multiplying 8 with t and adding 8 to the result.
Expression C: 4(2t + 2) = 8t + 8
This expression is also equivalent to 8t + 8, which means that multiplying 2t + 2 with 4 is the same as multiplying 8 with t and adding 8 to the result.
Expression D: 8t + 64 = 8t + 64
This expression is the same as 8t + 64, which is not equivalent to either 8(t + 8) or 8t + 8.
Expression E: 8t + 16 = 8t + 16
This expression is the same as 8t + 16, which is not equivalent to either 8(t + 8) or 8(t + 8).
Expression F: (8 + t) + (8 + 8) = 16 + t
This expression is not equivalent to either 8(t + 8), 8t + 8, or neither.
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--The question is incomplete, answering to the question below--
"Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.
A. (8 * t) + (8 * 8)
B. 4t + 8 + 4t
C. 4(2t + 2)
D. 8t + 64
E. 8t + 16
F. (8 + t) + (8 + 8)"
There are 4 grams of sugar in 1⁄2 of a liter of a new sports drink. How much sugar is in 3⁄4 of a liter of the sports drink?
Answer:
6 grams of sugar in 3/4 liter.
Explanation:
Recall that two 1/4 portions is equal to 1/2. So if 1/2 liter has 4 grams, 1/4 liter will have 2 grams of sugar.
Every 1/4 liter will have 2 grams of sugar.
Therefore, 3/4 liter will have 3 times as much sugar as 1/4 liter. The amount of sugar in 3/4 liter will be 3 times 2 grams or 6 grams of sugar in 3/4 liter
Is 59 a Prime or Composite Number?
59 is a prime number.
This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.
To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.
If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.
For example, with the number 59:
59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)
Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.
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Bailey is asked to draw a circle. She is given the center and two points on the circle, but she isn't told which point is which. The points are (-6, 3), (-15, 3), and (3,3). Bailey draws an accurate circle from this information. What is the equation of the circle she drew?
O (= - 6)3 + (3 - 3)? = 3
O (= - 3)? + (y - 3)? = 3
O (* + 6)3 + (y - 3)? = 81
О (= - 3)3 + (y - 3)? = 81
〇(c+15)+(- 3) = 81
O (= - 6)? + (3 - 3)? = 81
The equation of circle with center ( -6 , 3 ) is ( x + 6 )² + ( y - 3 )² = 9² , where the radius of circle r = 3 units
What is a Circle?A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
The equation of circle is ( x - h )² + ( y - k )² = r²
For a unit circle , the radius r = 1
x² + y² = r² be equation (1)
Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )
Given data ,
Let the radius of the circle be represented as r
Now , the first point is A ( -6 , 3 )
Let the second point be B ( -15 , 3 )
Let the third point be C ( 3 , 3 )
And , from the distance formula ,
Distance D = √ ( x₂ - x₁ )² + ( y₂ - y₁ )²
The distance of AB = √ ( -15 + 6 )² + ( 3 - 3 )² = 9 units
The distance of AC = √ ( 3 + 6 )² + ( 3 - 3 )² = 9 units
The distance of BC = √ ( -15 - 3 )² + ( 3 - 3 )² = 18 units
So , the measure of AB = AC and the radius of the circle r = 3 units
Now , the center of the circle is A ( -6 , 3 )
where the standard form of a circle is
( x - h )² + ( y - k )² = r²,
On simplifying , we get
( x + 6 )² + ( y - 3 )² = 9²
Hence , the equation of circle is ( x + 6 )² + ( y - 3 )² = 9²
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Nicole school is selling tickets to the annual dance competition on the first day of ticket sales the school sold 3 adult tickets and 2 child tickets for a total of 34$ the school took in $114 on the second day by selling 3 adult tickets and 12 child tickets what is the price each of 1 adult ticket and 1 child ticket
Answer: Child ticket: $8, Adult ticket: $6
Step-by-step explanation:
Let's call the price of 1 adult ticket "a" and the price of 1 child ticket "c".
On the first day, the school sold 3 adult tickets for a total of 3a dollars, and 2 child tickets for a total of 2c dollars, for a total of 34 dollars. So, we have the equations:
3a + 2c = 34
On the second day, the school sold 3 adult tickets for a total of 3a dollars and 12 child tickets for a total of 12c dollars, for a total of 114 dollars. So, we have another equation:
3a + 12c = 114
We can now use these two equations to solve for the value of "a" and "c".
We can use substitution to solve for one variable, then substitute it back into either of the equations to solve for the other variable.
Let's solve for "a" by substituting the first equation into the second:
3a + 12c = 114
3a = 114 - 12c
a = (114 - 12c) / 3
Now that we have an equation for "a", we can substitute it back into the first equation to solve for "c":
3a + 2c = 34
3[(114 - 12c) / 3] + 2c = 34
114 - 12c + 2c = 34
-10c = -80
c = $8
So, the price of 1 adult ticket is
a = (114 - 12c) / 3
a = (114 - 12 * 8) / 3
a = (114 - 96) / 3
a = 18 / 3 = $6.
HELPPPPPPPP PLEASEEEE
algebra
Answer:
Your answer would be (x, y) = (0, 0)
Step-by-step explanation:
Please refer to the screenshot underneath.
How many multiples does 19 have?
19 has an infinite number of multiples since we can multiply 19 by any positive integer to get a new multiple.
A multiple of number is product of that number and other integer.
To find the multiples of 19, we need to multiply 19 by every positive integer. So, the multiples of 19 are:
19 × 1 = 19
19 × 2 = 38
19 × 3 = 57
19 × 4 = 76
19 × 5 = 95
19 × 6 = 114
19 × 7 = 133
19 × 8 = 152
19 × 9 = 171
19 × 10 = 190
and so on.
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Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 60 miles per hour. Then, in the second hour, she traveled at a speed of 74 miles per hour. What is the percentage increase of Seraphina's speed? If necessary, round to the nearest tenth of a percent
Seraphina's speed has increased by a factor of around 23% compared to the first hour.
What Is a Change in Percentage?
The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.
How can you determine the percentage to the closest tenth?
Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.
Percent Change Formula = [tex]\frac{ (Final value -Initial value)}{ (Initial value)}[/tex]× 100
Percent Change = [tex]\frac{(74-60)}{60}[/tex]× 100
… = [tex]\frac{14}{60}[/tex] × 100
... ≈ 0.23333 × 100
Percent Change ≈ 23.33%
The pace of Seraphina increased by around 23% in the second hour compared to the first.
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A circular pizza is divided into eight equal slices. The outer edge of the crust from one piece measures 5. 5 inches. What is the diameter of the pizza to the nearest inch?.
The diameter of the pizza to the nearest inch is 11 inches.
Let's call the diameter of the pizza "d". The circumference of the pizza can be calculated using the formula:
C = πd
And since the outer edge of the crust from one piece measures 5.5 inches, that length is equal to 1/8 of the circumference of the pizza:
5.5 = (1/8)C
So we can substitute the formula for the circumference into this equation:
5.5 = (1/8)(πd)
Solving for d, we can multiply both sides by 8/π:
d = (5.5)(8/π)
Calculating the approximate value of π as 3.14, we get:
d ≈ (5.5)(8/3.14) = 11 inches
So the diameter of the pizza is approximately 11 inches, rounded to the nearest inch.
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The equation for this problem is 3 (x - 10) = 63. Solve for x
Answer:
[tex]\mathrm{x=31}[/tex]Step-by-step explanation:
[tex]\mathrm{3 (x - 10) = 63}[/tex]
Divide both sides by 3:-
[tex]\mathrm{x-10=\cfrac{63}{3} }[/tex]
Divide 63 by 3 = 21:-
[tex]\mathrm{x-10=21}[/tex]
Add 10 to both sides:-
[tex]\mathrm{x=21+10}[/tex]
Add 21 and 10 = 31:-
[tex]\mathrm{x=31}[/tex]
____________________
Hope this helps!
PLEASE IM DESPERATE
The number of rectangular table is equal to 5 rectangular tables.
The number of circular table is equal to 5 circular tables.
How to write a linear system of equations to model this situation?In order to write a linear system of equations to describe this situation, we would a assign variable to the number of circular table and the number of rectangular table respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent the number of circular table.Let the variable y represent the number of rectangular table.Since there are 9 tables and 80 chairs set up with 8 chairs each for the circular table and 10 chairs each for the rectangular table, a linear equation to model this situation is given by:
8x + 10y = 80 .......equation 1.
x + y = 9 .......equation 2.
In this scenario, we would use an online graphing calculator to plot the linear system of equations in order to determine the solution (point of intersection) as shown in the image attached below, which is at the ordered pair (5, 4).
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Petrolyn motor oil is a combination of natural oil and synthetic oil. It contains 4 liters of natural oil for every 5 liters of synthetic oil. In order to make 855 liters
of Petrolyn oil, how many liters of natural oil are needed?
380 liters of natural oil is needed
How to calculate the amount of natural oil that is needed?
The ratio of natural oil to synthetic oil is 4:5
Total number of petrolyn oil is 855
4x + 5x= 855
9x= 855
x= 855/9
x= 95
The number of natural oil is 4x
= 4(95)
= 380
Hence the number of liters of natural oil that is needed is 380
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Volume = 1243.44 in3
Height = 11 in
Solve this equation and you have the answer:
3.14 • 11 • r2 = 1243.44
Radius = in
The radius of the cylinder is approximately 5.88 inches.
What are equivalent equations?
Equivalent equations are algebraic equations that are having identical roots or solutions.
We can solve the given equation to find the radius of the cylinder using the volume and height information
3.14 * 11 * r² = 1243.44
First, divide both sides by 3.14*11 to isolate r²:
[tex]r^2 = 1243.44 / (3.14 * 11)[/tex]
r² ≈ 34.585
Taking the square root of both sides, we get:
r ≈ 5.88
Hence, the radius of the cylinder is approximately 5.88 inches.
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What is the division derivative rule?
Answer:
6
Step-by-step explanation:
9. A helicopter is traveling at a speed of 44 meters per second in the direction of S 61° E. Find the
magnitude of the horizontal and vertical components.
The magnitude of the horizontal and vertical components are 21.33 m/s and 38.48 m/s
How to find the magnitude of the horizontal and vertical components.From the question, we have the following parameters that can be used in our computation:
Velocity = 44 meters per second
Direction = S 61° E
This means that
V = 44 and angle = 61°
The direction angle is 61° from the positive x-axis (E), so we can use the following trigonometric relationships to find H and V:
H = 44 * cos(61°) --- horizontal
V = 44 * sin(61°) --- vertical
Using a calculator, we can find that:
H = 21.33 m/s
V = 38.48 m/s
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PLS HELP
If the difference of a number and nine is doubled, the result is eight more than the number. Find the number. Round your answer to the nearest integer, if necessary.
Instead of charging admission to the fall dance, one high school required that each person bring one can of food for a local food pantry. 100 people came to the dance, and 46 of them brought a can of corn.
What is the probability that a randomly selected can of food will be corn?
Write your answer as a fraction or whole
number. P(corn) =
Answer: 0.46.
Step-by-step explanation:
The probability that a randomly selected can of food will be corn is equal to the fraction of cans that are corn, out of the total number of cans.
Since 46 out of 100 people brought a can of corn, we can assume that there were 46 cans of corn donated. We do not know how many total cans were donated, but we can find out by using the fact that each person was required to bring one can of food. Therefore, the total number of cans donated is equal to the total number of people who attended the dance, which is 100.
So, the probability of selecting a can of corn is:
P(corn) = Number of cans of corn / Total number of cans
P(corn) = 46 / 100
Simplifying the fraction, we get:
P(corn) = 23 / 50
Therefore, the probability that a randomly selected can of food will be corn is 23/50 or approximately 0.46.
a equation of a line that passes through point. (-3, 1) and point (4, 8).
Gavin is moving into a new apartment that has a kitchen with a area of 50 ft.² if the area of the kitchen is 10 feet more than 1/3 the area of the bedroom where is the area of the bedroom complete the steps below to find the area of golf his bedroom but the variable B represent the area of the bedroom by any Quetion in terms of be to represent Galvin situation
The area of Gavin's bedroom is 120 square feet.
What is a square feet?
Square feet can be defined as the area of a square with sides of 1 foot.
Let B be the area of Gavin's bedroom in square feet.
According to the problem, the area of Gavin's kitchen is 10 square feet more than one-third of the area of his bedroom. So we can write:
Area of kitchen = (1/3)B + 10
We also know that the area of the kitchen is 50 square feet. So we can set up an equation:
(1/3)B + 10 = 50
Subtracting 10 from both sides, we get:
(1/3)B = 40
Multiplying both sides by 3, we get:
B = 120
Therefore, the area of Gavin's bedroom is 120 square feet.
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A common height at which commercial aeroplanes fly is 30 000 feet above sea level. This corresponds to how many miles?
Answer:
Below
Step-by-step explanation:
There are 5280 ft in a mile...how many 5280's are there in 30 000 ?
30 000 ft / 5280 ft/mile = 5.68 miles
The height of 30,000 feet above sea level corresponds to 5.68 miles.
To convert feet to miles,
we can use the conversion factor 1 mile = 5280 feet.
Therefore, to find how many miles 30,000 feet corresponds to, we can divide 30,000 by 5280:
=30,000 feet / 5280 feet/mile
≈ 5.68 miles
So, 30,000 feet above sea level corresponds to 5.68 miles.
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If a hexagon represents 1 whole, what fraction does each of the following shapes represent?
A triangle represents 1/4 of the trapezoid, a diamond represents 1/2 of the trapezoid, and a hexagon represents 1/1 of the trapezoid.
Determine the fraction of shapesEach shape represents a different part of the overall trapezoid.
The triangle represents 1/4 of the full trapezoid. This is because the trapezoid has four triangles, all of the same size. So each triangle is 1/4 of the whole trapezoid. The diamond represents 1/2 of the full trapezoid. This is because the trapezoid has two diamonds, each of the same size. So each rhombus is 1/2 of the whole trapezoid.
The hexagon represents 1/1 of the whole trapezoid. This is because the trapezoid has only one hexagon, which is the same size as the entire trapezoid. So the hexagon is 1/1, the whole trapezoid.
In summary, a triangle represents 1/4 of a trapezoid, a diamond represents 1/2 of a trapezoid, and a hexagon represents 1/1 of a hexagon. Using these fractions, we can determine the value of each shape relative to the overall trapezoid.
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The bank grants Marcus Dobson a loan for $22,000 with an APR
of 10 percent. He agrees to a down payment of 20 percent and will repay the loan over 24
months. What amount will Dobson have to repay?
A. $24,340.80
B. $17,600 C. $19,472.64 D. $1,872.64
The solution is, Dobson have to repay B. $17,600.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
The bank grants Marcus Dobson a loan for $22,000 with an APR
of 10 percent.
He agrees to a down payment of 20 percent and will repay the loan over 24 months.
so, he paid = 22000*20%
= $4400
so, remained loan = $ 17600
using the formula of interest , we get,
he has to repay with interest = $ 17600* 10%* 2 + $ 17600
=$ 3520 + $ 17600
=$ 21120
Hence, The solution is, Dobson have to repay B. $17,600.
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The measure of central location most often reported for annual income and property value data is the__
A. Mode
B. Median
C. aggregate mean
D. weighted mean