_____ is used to test the hypothesis that the values of the regression parameters β1, β2, . . . , βq are all zero.
a. An F test b. A t test c. The least squares method d. Extrapolation

Answer:

12 m

Step-by-step explanation:

Since this is a right triangle, let's use the Pythagorean Theorem.

Recall that the Pythagorean Theorem is:

[tex]a^2+b^2=c^2[/tex]

Where a is the length of one of the legs, b is the length of the other leg, and c is the length of the hypotenuse.

We are given the hypotenuse (15 m) and one of the legs (9 m).

Let's assign some values:

[tex]a=??\\c=15\\b=9[/tex]

Let's solve for b by using the Pythagorean Theorem.

[tex]a^2+b^2=c^2=\\a^2+9^2=15^2=\\a^2+81=225=\\a^2=144=\\a=12[/tex]

So, the length of the missing leg, a, is 12 m.

Answer:

The length of the missing leg is 12 m.

Step-by-step explanation:

SOLUTION :

Here we have given that the base of triangle is 9 m and hypotenuse is 15 m. We have to find the the height of triangle.

Using Pythagoras Theorem to find the height of triangle :

[tex]\quad{\longrightarrow{\sf{{(H)}^{2} = {(b)}^{2} + {(h)}^{2}}}}[/tex]

Substituting all the given values in the formula to find the height of triangle :

[tex]\quad{\longrightarrow{\sf{{(H)}^{2} = {(b)}^{2} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(15)}^{2} = {(9)}^{2} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(15 \times 15)} = {(9 \times 9)} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(225)} = {(81)} + {(h)}^{2}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(h)}^{2} = 225 - 81}}}[/tex]

[tex]\quad{\longrightarrow{\sf{{(h)}^{2} = 144}}}[/tex]

[tex]\quad{\longrightarrow{\sf{h = \sqrt{144}}}}[/tex]

[tex]\quad{\longrightarrow{\sf{\underline{\underline{\pink{h = 12 \: m}}}}}}[/tex]

Hence, the height of triangle is 12 m.

The total number of possible outcomes when flipping a coin 8 times is 2^8 = 256.

a. To get exactly 6 heads, we need to choose 6 out of the 8 flips to be heads, and the remaining 2 flips to be tails. The number of ways to choose 6 out of 8 is given by the binomial coefficient (8 choose 6) = 28. Therefore, there are 28 possible outcomes with exactly 6 heads.

b. To get at least 3 heads, we need to count the number of outcomes with 3, 4, 5, 6, 7, or 8 heads. Using the same logic as part (a), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at least 3 heads.

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Number of outcomes with 7 heads: (8 choose 7) = 8

Number of outcomes with 8 heads: (8 choose 8) = 1

Total number of outcomes with at least 3 heads = 56 + 70 + 56 + 28 + 8 + 1 = 219.

c. To get at most 6 heads, we need to count the number of outcomes with 0, 1, 2, 3, 4, 5, or 6 heads. Using the same logic as part (b), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 6 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Number of outcomes with 3 heads: (8 choose 3) = 56

Number of outcomes with 4 heads: (8 choose 4) = 70

Number of outcomes with 5 heads: (8 choose 5) = 56

Number of outcomes with 6 heads: (8 choose 6) = 28

Total number of outcomes with at most 6 heads = 1 + 8 + 28 + 56 + 70 + 56 + 28 = 247.

d. To get at most 2 heads, we need to count the number of outcomes with 0, 1, or 2 heads. Using the same logic as parts (b) and (c), we can count the number of outcomes with each of these numbers of heads and add them up to get the total number of outcomes with at most 2 heads.

Number of outcomes with 0 heads: (8 choose 0) = 1

Number of outcomes with 1 head: (8 choose 1) = 8

Number of outcomes with 2 heads: (8 choose 2) = 28

Total number of outcomes with at most 2 heads = 1 + 8 + 28 = 37.

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a) Function f(x) = 2^x is an exponential growth function because a = 2 is greater than 0 and b = 2 is greater than 1. The graph of the function starts at (0,1) and increases rapidly as x increases.

b) Function f(x) = (1/2)^x is an exponential decay function because a = 1/2 is greater than 0 and b = 1/2 is between 0 and 1. The graph of the function starts at (0,1) and decreases rapidly as x increases.

Key features of both graphs:

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Answer: To expand the expression, we can use the distributive property of multiplication:

(x+3)(x-3)(3x+2)

= (x^2 - 9)(3x+2) // using (a+b)(a-b) = a^2 - b^2

= 3x(x^2) + 2(x^2) - 9(3x) - 18 // using FOIL

= 3x^3 + 2x^2 - 27x - 18

This is the expanded form of the expression.

To simplify further, we can factor out the greatest common factor of the terms:

= 3(x^3 - 9x) + 2(x^2 - 9)

= 3x(x^2 - 9) + 2(x^2 - 9)

= (3x+2)(x^2 - 9)

= (3x+2)(x-3)(x+3)

So, the simplified expression is (3x+2)(x-3)(x+3).

The height of the candle change over time as a linear function

The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.

We can write the equation for the height of the candle as:

h(t) = 12 - 2t

where h is the height of the candle in inches and t is the time in hours.

If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:

h(2) = 12 - 2(2) = 8

So the height of the candle after 2 hours of burning is 8 inches.

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Answer:

Cube

Step-by-step explanation:

A cube is a three-dimensional shape with six square faces that are all congruent to each other. Each face of a cube is perpendicular to the adjacent faces, and all of its edges are the same length.

There are two buildings that you want to have in the amusement park.

a) The expression that represents the area of the gift shop, in terms of x, is

Area = length x width

Area = (20x + 24) (36x - 20)

Area = 720[tex]x^{2}[/tex] + 208x - 480

Therefore, the area of the gift shop is 720[tex]x^{2}[/tex]  + 208x - 480 square feet.

b) The expression that represents the perimeter of the gift shop, in terms of x, is

Perimeter = 2(length + width)

Perimeter = 2(20x + 24 + 36x - 20)

Perimeter = 2(56x + 4)

Perimeter = 112x + 8

Therefore, the perimeter of the gift shop is 112x + 8 feet.

c) If the perimeter is going to be 176 feet, we can set the expression for the perimeter equal to 176 and solve for x

112x + 8 = 176

Subtracting 8 from both sides

112x = 168

Dividing both sides by 112

x = 1.5

Now that we know x, we can substitute it into the expressions for the length and width of the gift shop

Length = 20x + 24 = 20(1.5) + 24 = 54 feet

Width = 36x - 20 = 36(1.5) - 20 = 34 feet

Therefore, the dimensions of the gift shop are 54 feet by 34 feet.

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The possible side lengths of rectangle B are 12 cm and 7 cm, or 9 cm and 5.25 cm, etc.

The side length of rectangle B is calculated as follows;

Side length of rectangle A = 6 cm and 3.5 cm

If the two rectangles are proportional, the possible side lengths of rectangle B is calculated as follows;

Length of B = 2 x 6 cm = 12 cm

Width of B = 2  x 3.5 cm = 7 cm

or

Length of B = 1.5 x 6 cm = 9 cm

Width of B =1.5  x 3.5 cm = 5.25 cm

Thus, the side lengths of rectangle B will be increasing or decreasing at equal proportion.

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Answer:

Step-by-step explanation:

The problem shows a 90° angle split by a ray, we know that both angles are equal to 90° because the whole is equal to the sum of its parts therefore adding 6b+7 and 7b-8 gives us 90° which is simplified as

13b°-1°= 90°

add 1  to both sides

13b°-1° + 1° = 90° +1°

13b° = 91°

divide by 13

13b°/13 = 91°/13

b= 7°

The circle graph that correctly represents the data in the table is that with:  A. four sections, labeled turkey 30 percent, ham 20 percent, chicken 35 percent, and vegetarian 15 percent correctly represents the data in the table.

To find the percentage for each type of sandwich, we can divide the number of customers who ordered that sandwich by the total number of customers (100) and multiply by 100.

Using the data given in the table, we get:

Turkey: 30/100 x 100% = 30%

Ham: 20/100 x 100% = 20%

Chicken: 35/100 x 100% = 35%

Vegetarian: 15/100 x 100% = 15%

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The x - coordinate of B given the y - coordinate, can be found to be 3 units.

Looking at the figure, we notice that the relationship between B and the circle can be modeled as a right triangle. 5 would be the hypotenuse, 4 which is the y - coordinate would the be the height.

The x - coordinate would then be the length which can be found by the Pythagorean theorem.

The x - coordinate is:

= 5² = 4² + x²

Simplifying the equation, we get:

25 = 16 + x²

9 = x²

x = 3

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They will need an additional 18/11 days to finish the job.

There are two sides to it—a left side and a right side—and an equals sign (=) divides them. The members of the equation are the expressions on either side of the equals sign.

From straightforward arithmetic equations like 2 + 2 = 4 to more intricate equations in algebra and calculus, equations can be used to represent a broad variety of mathematical connections.

By determining the values of the variables that make the equation true, equations are frequently employed to solve issues. This is usually accomplished by manipulating the equation with algebraic operations like addition, subtraction, multiplication, and division on both sides of the equation.

In a variety of disciplines, including physics, chemistry, and engineering, equations can also be used to simulate real-world occurrences. For instance, the equation [tex]d=1/2gt^2[/tex] can be used to represent the motion of an object falling, where d is the distance fallen, g is the acceleration caused by gravity, and t is the amount of time that has passed.

Assume that there are D total papers that need to be translated. Then, we can claim that Ann's daily translation rate is D/10 and that she can translate D documents in 10 days. Ben's daily translation pace is D/12 since he can translate D documents in 12 days.

While Ben is still waiting to start working, Ann begins translating the documents at her daily rate. The total amount of work that Ann has finished is (x/10)D after she has worked for x days. Now that Ben has joined them, they can finish the remaining (1 - x/10)D work jointly at a rate of (D/10 + D/12) papers per day. To find x, we can construct the following equation:

(x/10)D + [(1 - x/10)D]/[(D/10 + D/12)] = D

When we simplify the equation, we obtain:

x/10 + (12 - x)/15 = 1

When both sides are multiplied by the least common multiple of 10 and 15, or 30, we obtain:

3x + 2(12 - x) = 30

Solving for x, we get:

x = 6

So, before Ben starts working, Ann finishes (6/10)D = (3/5)D of the work, and the two of them together finish the remaining (2/5)D of the job at a combined rate of (D/10 + D/12) = (11/60)D per day. Therefore, the total number of days required to accomplish the work is:

(2/5)D / (11/60)D = 24/11 days

Ben and Ann will need to work an extra 24/11 - 6 = 18/11 days to finish the work because Ann has already put in 6 days of effort. As a result, they will need an additional 18/11 days to finish the job.

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The lengths of all four sides of parallelogram ABCD:

AB = 15 cm, BC = 33 cm, CD = 15 cm and AD = 33 cm

Consider a parallelogram ABCD

Let's assume that x represents the length of sides AD and BC

y be the length of sides AB and CD

We know that the formula for the perimeter of parallelogram is

P = 2(length + width)

Here,  AD is 3 cm more than twice AB

So we get an expression,

AD = 3 + 2(AB)

AD = 3 + 2y

x  = 3 + 2y

USing above formula of perimeter, the perimeter of parallelogram ABCD would be,

P = 2(x + y)

96 = 2(3 + 2y + y)

48 = 3 + 3y

45 = 3y

y = 15 cm

And x = 3 + 2(15)

x = 33 cm

Therefore, the lengths of sides AD and BC =  33 cm and the lengths of sides AB and CD = 15 cm

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Answer:

Step-by-step explanation:

You want the measures of x and ∠ECB in rectangle ABCD with center point E and AE=3x+6, BD=5x+19, ∠EBA=25°.

The diagonals of a rectangle are congruent and cross at their midponts. This means the triangles they form are all isosceles.

The value of x can be found by relating the length of a half-diagonal to the length of the whole diagonal.

  2·AE = BD

  2(3x +6) = 5x +19 . . . . . . . substitute given lengths

  6x +12 = 5x +19 . . . . . eliminate parentheses

  x = 7 . . . . . . . . . . . subtract 5x+12

The value of x is 7.

Angle EBC is the complement of angle EBA, so its measure is ...

  ∠EBC = 90° -∠EBA

  ∠EBC = 90° -25° = 65°

Angle ECB is the other base angle of isosceles triangle BCE, so has the same measure as ∠EBC.

  ∠ECB = 65°

__

Additional comment

You know the corner angles of a rectangle are 90°, which is what makes angles EBA and EBC complementary.

With x = 7, AE = 27 and BD = 54. The full diagonal is double the length of the half-diagonal, as you expect.

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The y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

When the line touches the y-axis, it forms a y-intercept.

Find the y when x = 0 to find these.

When the line touches the x-axis, the position for the y-intercept will look like (0,y).

So, have the given quadratic function:

y = x² + 2x − 8

Now, plot the given quadratic function on the graph:

(Refer to the graph attached below)

As we can see that the y-intercept is -4.

Therefore, the y-intercept of the given quadratic function y = x² + 2x − 8 is (A) -4.

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If a line with slope 4 has one point of intersection with the quadratic function y = x² + 2x − 8, what is the y-intercept of the line?

a. -4

b. 10

c.-10

d. 4

e. -8

Answer:

5x - 15

Step-by-step explanation:

5(x - 3) ← multiply each term in the parenthesis by the 5 outside

= 5x - 15

To find the population of the city, we need to find the total number of people living in the city. We know that there are 1350 people per square mile, so we can find the total number of people by multiplying the number of square miles in the city by the number of people per square mile.

The area of the city is the length times the width, so:

Area = Length x Width

Area = 12 miles x 8 miles

Area = 96 square miles

Now, we can find the population by multiplying the area by the number of people per square mile:

Population = Area x People per square mile

Population = 96 square miles x 1350 people per square mile

Population = 129,600 people

Therefore, the population of the city is 129,600 people.

Hope this helps!

The greatest distance, in feet, a person could be from the parking lot light and be detected is 4 ft. So, correct option is B.

The equation (x + 10)^2 + (y−8)^2=16 describes a circle with center (-10,8) and radius 4. The distance from the center of a circle to any point on its circumference is equal to the radius. Therefore, the greatest distance a person could be from the parking lot light and still be detected is equal to the radius of the circle, which is 4 feet.

This means that any point on the circumference of the circle with a distance of 4 feet or less from the center (-10,8) would be within the range of the motion detector.

Option (a) 2 feet is too small and would fall inside the circle, meaning the person would not be detected. Option (c) 9 feet and option (d) 256 feet are too large and fall outside the circle, meaning the person would also not be detected.

Therefore, the correct answer is option (b) 4 feet.

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Eliminate x by adding the two equations, yielding [tex]y = 6[/tex]. Then, substitute y into either equation to solve for x, obtaining [tex]x = -3[/tex]. The solution is [tex](-3,6)[/tex].

An equation is a mathematical statement that uses symbols, numbers, and variables to show that two expressions are equal, typically with an equal sign between them.

A variable is a quantity or symbol that can take on different values in a mathematical expression, equation, or formula, typically represented by a letter.

To eliminate a variable in a system of equations, we want to find a way to add or subtract the two equations so that one of the variables is eliminated.

In this case, we can eliminate the variable x by adding the two equations

[tex]x- 7y = -45[/tex]

[tex](-x +8y = 51)[/tex]

[tex]y = 6[/tex]

Now that we have found the value of y, we can substitute it into either of the original equations to solve for x. Let's use the first equation

[tex]x-7y = -45\\x- 7(6) = -45\\x = -45+42\\x = -3[/tex]

Therefore the solution to the system of equations is [tex]x= -3[/tex] and[tex]y= 6[/tex]

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the solution to the system of equations is (x, y) = (-3, 6).

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

To eliminate the variable x, we can add the two equations together. This will result in the x variable being eliminated, leaving us with an equation in terms of y:

(x - 7y) + (-x + 8y) = -45 + 51

Simplifying and solving for y, we get:

y = 6

Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation:

x - 7(6) = -45

Simplifying and solving for x, we get:

x = -3

Therefore, the solution to the system of equations is (x, y) = (-3, 6).

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Answer:

First image.

Step-by-step explanation:

Second image.

The correct statement regarding the best measure of center from the box and whisker plot is given as follows:

The median is the best measure of center and equals 11.

A box and whisker plots shows these five features from a data-set, listed as follows:

The features for the data-set in this problem are given as follows:

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A function has access to parameters that are passed to it and any variables created within the function (local and function scope).

The variable names that a function has access to depend on the scope of the variables. Scope refers to the visibility of a variable within a program.

There are four different scopes that a variable can have in relation to a function:
Global scope -

A variable that is declared outside of a function has global scope.

This means that it can be accessed by any function within the program.
Local scope -

A variable that is declared within a function has local scope.

This means that it can only be accessed within the function in which it was declared.
Parameter scope -

A variable that is passed as a parameter to a function has parameter scope.

This means that it can only be accessed within the function in which it was passed.
Function scope -

A variable that is created within a function has function scope.

This means that it can only be accessed within the function in which it was created.

It does not have access to variables declared outside of the function (global scope) unless they are explicitly passed as parameters.

It is important to note that naming conflicts can occur if variable names are not chosen carefully, especially when dealing with global and local scope.

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Craig should make approximately 36 shirts to maximize his earnings for the week.

The maximum value of x for a quadratic equation, ax² + bx + c is given by the formula:

x (max) = -b/2a

Since the weekly income can be modeled by the function p(x)= −2x² + 145x.

In this case a = -2 and b = 145. Thus,
x (max) = -145/2(-2)

           =  145/4

           =  36.25

Thus, Craig should make approximately 36 shirts to maximize his earnings for the week

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Answer: If every hour the candle decreases in height by 2 inches, turn it into a chart! If you learned this already, figure out which variable is the constant and the decrease in height for each hour. Or you could just multiply the amount of hours by 2, there for 2x2=4 so that a 4 inch decrease. 12-4=8 and the candle will be 8 inches tall. Hope this helps :D

Step-by-step explanation:

Corresponding to the data, we can deduce that the stairs can be broken into a series of blockish prisms.

The stairs can be broken into a series of blockish prisms. The confines of each blockish prism would be the same range and height as the stairs, but the length of each blockish prism would be the depth of one step.

To determine the quantum of concrete demanded to form the stairs, you would need to calculate the total volume of all the blockish prisms that make up the stairs. This can be done by multiplying the length, range, and height of each blockish prism and also adding the volumes of all the blockish prisms together.

The formula for calculating the volume of a blockish prism is V = l x w x h, where V is the volume, l is the length, w is the range, and h is the height. So, for illustration, if each stair is 3 bases wide,1.5 bases high, and 1 bottom deep, and there are 10 stairs, also the total volume of concrete demanded would be

V = (3 x 1.5 x 1) x 10 = 45 cubic feet of concrete.

Note that this calculation assumes that there is no space between the stairs or the rectangular prisms making up the stairs. If there is any space between the stairs or the rectangular prisms, this would need to be accounted for in the calculation.

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To proof that ΔLMQ ≅ ΔNPQ; we use the given statement "∠L is congruent to ∠N"

To complete the proof that ΔLMQ is congruent to ΔNPQ, we have to follow the following steps.

Congruent triangles are two triangles that have exactly the same size and shape. In other words, all corresponding sides and angles of the two triangles are equal.

There are several ways to show that two triangles are congruent, including:

We will apply ASA method to proof that ΔLMQ ≅ ΔNPQ;

∠L is congruent to ∠N

Length LM is congruent to length NP

Looking at the options, only one was stated. (∠L is congruent to ∠N).

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The statement is true: If x and y are linearly independent, and if z is in Span {x, y}, then {x, y, z} is linearly dependent.

The statement is true.
Let's first understand the terms used:
Linearly independent:

A set of vectors is linearly independent if none of them can be expressed as a linear combination of the other vectors. In other words, no vector in the set can be written as a sum of scalar multiples of the other vectors.
Span:

The span of a set of vectors is the set of all linear combinations of those vectors.

In this case, Span[tex]{x, y}[/tex] is the set of all vectors that can be formed by adding scalar multiples of x and y.
Now, let's consider the given statement:
If x and y are linearly independent, it means that neither x nor y can be expressed as a linear combination of the other. However, it is given that z is in the Span[tex]{x, y}.[/tex]

This means that z can be expressed as a linear combination of x and y:
[tex]z = ax + by[/tex], where a and b are scalar constants.
Let's analyze the set[tex]{x, y, z}[/tex]. We know that z can be expressed as a linear combination of x and y, as shown above. This implies that the set [tex]{x, y, z}[/tex]is linearly dependent, because one vector (z) can be expressed as a linear combination of the others [tex](x and y)[/tex].

Thus, the statement is true: If x and y are linearly independent, and if z is in Span[tex]{x, y}[/tex], then[tex]{x, y, z}[/tex] is linearly dependent.

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The fuel efficiency of the vehicle with the greatest weight which is around 2375kg on this scatter-plot showing vehicle weights & fuel efficiency is 16 mpg.

The relationships between two variables in a data set are represented by graphs or scatter plots.  It displays data points on a Cartesian system or a two-dimensional plane. The dependent variable is represented or plotted on the Y-axis, while the independent variable or attribute is plotted or represented on the X-axis. The scatter plot's objective is to show what happens to one variable when another variable is modified. A theory that the two variables are connected is tested using the scatter plot.

The scatter plot shows the vehicle weights & fuel efficiency.

Data represented on X-axis(independent variable) : weights of vehicle

Data represented on Y-axis(dependent variable) : fuel efficiency.

Lowest weight of vehicle=1125 kg(approx)

Greatest weight of the vehicle=2375 kg(approx)

Lowest fuel efficiencies of surveyed vehicles=16 mpg.

Greatest fuel efficiency of surveyed vehicles=30 mpg.

∴The fuel efficiency of the heaviest vehicle=16 mpg.

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