Joey started at point A and walked 20 m
south, 40 m west and a further 50 m south
to arrive at point B. Lana started at point A
and walked in a straight line to point B.
How much further did Joey walk than Lana?
Give your answer in metres (m) to 1 d.p.
A
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Therefore, the equation of the line that passes through the point (4, -3) and has a slope of 1 is y = x - 7.

The equation of a line that passes through a given point and has a given slope can be found using the point-slope formula: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the given slope.

In this case, the given point is (4, -3) and the given slope is 1. Plugging these values into the point-slope formula, we get:

y - (-3) = 1(x - 4)

Simplifying the equation, we get:

y + 3 = x - 4

y = x - 7

Therefore, the equation of the line that passes through the point (4, -3) and has a slope of 1 is y = x - 7.

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The parent function f(x) = 2^(x) is transformed into the function g(x) = 2^((x+3)) by shifting the graph 3 units to the left.

This means that the maximum value on the interval [-2,2] for the parent function will now occur at the point (-2+3) = 1 for the transformed function.

Therefore, the maximum value for the transformed function on the interval [-2,2] will be 2^(1) = 2.

In summary, the transformation shifts the graph of the parent function 3 units to the left, causing the maximum value on the interval [-2,2] to occur at x = 1 and have a value of 2.

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The we have shown that \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}\).

The given equation is \[\boldsymbol{x} \ast \boldsymbol{y}=\left(x_{1} y_{1}, \ldots, x_{n} y_{n}\right),\] where \(\boldsymbol{x} = (x_1, x_2, ..., x_n)\) and \(\boldsymbol{y} = (y_1, y_2, ..., y_n)\).In the above equation, the output of \(\boldsymbol{x} \ast \boldsymbol{y}\) will contain only 1s if the value of both the coordinates in \(\boldsymbol{x}\) and \(\boldsymbol{y}\) is 1 otherwise it will contain 0.The multiplication of vectors \(\boldsymbol{x}\) and \(\boldsymbol{y}\) is an example of bitwise multiplication. It is used to multiply each bit of two numbers. Here, the vectors \(\boldsymbol{x}\) and \(\boldsymbol{y}\) contain only 1's and 0's.We know that bitwise multiplication of two numbers is also known as logical multiplication. When we multiply two numbers bit by bit, then we get a new number.

The new number will have 1 at the same position where both numbers contain 1, otherwise 0 will be there.We have to show that if \(w\) is a subset of the n-element set \(\{1,2, \ldots, n\}\), then the formula holds: $$\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}.$$Let's break down the above expression into the following steps:First, calculate the product of coordinates of vector \(\boldsymbol{x}\) for every element in the set \(w\). This will give \(\prod_{i \in w} x_{i}\).Secondly, calculate the product of coordinates of vector \(\boldsymbol{y}\) for every element in the set \(w\). This will give \(\prod_{i \in w} y_{i}\).Multiply the result obtained in step 1 and step 2. This will give \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}\).Finally, calculate the product of the coordinates of vector \(\boldsymbol{x} \ast \boldsymbol{y}\) for every element in the set \(w\). This will give \(\prod_{i \in w} x_{i} y_{i}\).Therefore, we have shown that \(\prod_{i \in w} x_{i} * \prod_{i \in w} y_{i}=\prod_{i \in w} x_{i} y_{i}\).

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Answer:

$7.35

Step-by-step explanation:

no step by step lol heres ur answer

The exact value of the distance between L1 and L2 is 131 / √221. Enter this value in the box.

The distance between two parallel lines can be found by taking the distance between a point on one line and the other line. We can use point C and line L1 to find the distance between the two lines.

First, we need to find the direction vector of line L1. The direction vector can be found by subtracting the coordinates of point A from point B:

u = B - A = (-6,-4,3) - (8,1,3) = (-14,-5,0)

Next, we need to find the vector between point C and point A:

v = C - A = (9,-8,3) - (8,1,3) = (1,-9,0)

Now, we can find the distance between point C and line L1 by taking the cross product of u and v and dividing by the magnitude of u:

w = u x v = (-5*0 - 0*(-9), 0*0 - (-14*0), -14*(-9) - (-5*1)) = (0,0,131)

||w|| = √(0^2 + 0^2 + 131^2) = 131

||u|| = √((-14)^2 + (-5)^2 + 0^2) = √221

distance = ||w|| / ||u|| = 131 / √221

Therefore, the distance between L1 and L2 is 131 / √221.

The exact value of the distance between L1 and L2 is 131 / √221. Enter this value in the box.

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Answer: About 942.48 pounds

Step-by-step explanation:

The volume of a cylinder is πr²h

Plug in values:

(diameter is 2, so the radius is 1)

Volume = π(1)²6

Volume = 6π

Volume ≈ 18.8496 (to 4 decimal places)

Multiply that by 50:

18.8496 x 50 = 942.48

The smallest cylinder will weigh about 942.48 pounds.

Note the answer may change depending on how many decimal places you were told to go out. The standard is 4 places.

Hope this helps!

Answer:

parallelogram

Step-by-step explanation:

Answer:

1)
Number of Seats in next three rows: 37, 41, 45

Number of seats in row 21 = 105

2)

Cost for 4, 5, 6 miles:
Miles            Cost($)
4                    14.50

5                    18.00

6                    21.50

Cost for 12 miles = $42.50

Step-by-step explanation:

1) The arithmetic sequence is
25, 29, 33 ....

Each term is 4 more than the previous term

So the next three terms starting with the 4th term area

33 + 4 = 37
37 + 4 = 41

41 + 4 = 45

In terms of the problem statement these are the number of seats in rows 4, 5, 6 respectively

The general equation for an arithmetic sequence nth term is

a(n) = a(1) + d(n - 1)

Here a(1) is the first term; here a(1) = 25

d = difference between successive terms called the common difference; here common difference = 4

n is of course the number of terms to be considered

using the values we have
a(n) = 25 + 4(n- 1)

= 25 + 4n - 4

= 21 + 4n

So the 21st term is a(21)

a(21) = 21 + 4 (21)

= 21 + 84

= 105

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

2. Another arithmetic sequence

The first term is the charge for the first mile = 4

The second term = 7.5 for 2 miles

The third term = 11.5 for 3 miles

So d = 11 - 7.5 = 7.5 - 4 = 3.5

The cost for 4 miles = 11 + 3.50 = $14.50

The cost for 5 miles = 14.50 + 3.50 = $18

The cost for 6 miles = 18 + 3.50 = $21.50

Using the equation for finding the nth term we get

a(n) = a(1) + d(n - 1)
a(n) = 4 + 3.5(n-1)

a(n) = 4 + 3.5n - 3.5

a(n) = 0.5 + 3.5n

We have the following table

Miles            Cost      ($)

1                     4.00

2                    7.50

3                    11.00

4                    14.50

5                    18.00

6                    21.50

For 12 miles which would correspond to the 12 term

a(12) = 0.5 + 3.5(12)

= 0.5 + 42

= $42.50

The price of T-shirts:

A. f(x) = $15x if x > 100

B. 0 ≤ x ≤ 40

C. $15x if x > 100

D. 41 ≤ x ≤ 100

E. $15x. if x > 100

F. x > 100

G. $1000.

A.

f(x) = $25x if 0 ≤ x ≤ 40

f(x) = $20x if 41 ≤ x ≤ 100

f(x) = $15x if x > 100

B. 0 ≤ x ≤ 40

C. A piecewise function with three cases that depend on the value of x:

If 0 ≤ x ≤ 40, the cost is $25x.

If 41 ≤ x ≤ 100, the cost is $20x.

If x > 100, the cost is $15x.

D. 41 ≤ x ≤ 100

E. A piecewise function with three cases that depend on the value of x:

If 0 ≤ x ≤ 40, the cost is $25x.

If 41 ≤ x ≤ 100, the cost is $20x.

If x > 100, the cost is $15x.

F. x > 100

G. If you purchased 40 shirts, the cost would be $25 per shirt, so the total cost would be:

f(40) = $25(40) = $1000.

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To find the \( x \)-intercepts of a function, we need to set the function equal to 0 and solve for \( x \). This will give us the values of \( x \) where the function crosses the \( x \)-axis. In this case, we have:

\[ f(x)=x^{2}+5 x-14=0 \]

We can solve this quadratic equation using the quadratic formula:

\[ x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a} \]

Plugging in the values of \( a=1 \), \( b=5 \), and \( c=-14 \), we get:

\[ x=\frac{-(5)\pm\sqrt{(5)^{2}-4(1)(-14)}}{2(1)} \]

Simplifying, we get:

\[ x=\frac{-5\pm\sqrt{25+56}}{2} \]

\[ x=\frac{-5\pm\sqrt{81}}{2} \]

\[ x=\frac{-5\pm9}{2} \]

This gives us two solutions for \( x \):

\[ x=\frac{-5+9}{2}=\frac{4}{2}=2 \]

\[ x=\frac{-5-9}{2}=\frac{-14}{2}=-7 \]

So the \( x \)-intercepts of the function are \( (2,0) \) and \( (-7,0) \).

Answer: \[ (2,0),(-7,0) \]

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the total money will be spent is 47.4 ∈.

What is trapezoid?

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or polygon with four sides. It has a set of parallel opposite sides as well as a set of non-parallel sides. The bases and legs of the trapezoid are referred to as parallel and non-parallel sides, respectively. A trapezoid is a four-sided closed 2D figure with a perimeter and an area. The bases of the trapezoid are two of the shape's sides that are parallel to one another. The legs or lateral sides of a trapezoid are its non-parallel sides. The altitude is the shortest distance between any two parallel sides.

Here the parallel sides are given 12m and 20m.

The perpendicular line will be the fence

so the other line is given 17m.

The area of the trapezoid is (a+b/2)*h

h =√17²-8² =15

So the area will be 12+20/2 * 15

A= 16*15 = 240m²

For 100 m² cost 19.75

For 240 it will be 19.75/100 * 240= 47.4

Hence the total money will be spent is 47.4 ∈.

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The fact that the points are located along a straight path does not prove that the relationship is proportional.

A graph is a graphic representation of a collection of data or a mathematical function in mathematics. It consists of several nodes or vertices linked by arcs or edges. Graphs are frequently used to display data in a manner that is simple to comprehend and interpret. They can be used to demonstrate mathematical functions or equations as well as relationships between various variables and patterns or trends in data. Line graphs, bar graphs, scatter plots, pie charts, and other graphs come in a wide variety. Depending on the nature of the data being depicted and the insights that need to be communicated, each type of graph is used for a specific reason.

given

The fact that the points are located along a straight path does not prove that the relationship is proportional. The connection is proportional, though, if y rises by a constant multiple of x every time.

Since y does not have to increase by a fixed constant in order for a relationship to be proportional, the claim that "It must be proportional because each time y increases by 3, x remains the same" is untrue.

Since proportional relationships can have non-zero y-intercepts, the claim that it cannot be proportional because a straight line through the locations would not pass through the origin is false as well.

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The solution to the exponential equation is given as follows:

x = 4.

The equation for this problem is defined as follows:

4^(2x+4) = 16^(3x-6).

Looking at the left-side of the equality, we can apply the power of power property, as 16 = 4², hence:

16^(3x-6) = 4^[2(3x - 6)] = 4^(6x - 12)

(the power of power property means that we keep the base then multiply the powers relative to the same base).

Hence the equation can be written as follows, considering the simplification to the right side of the equality.

4^(2x+4) = 4^(6x - 12)

Applying the one to one property, the solution is obtained as follows:

6x - 12 = 2x + 4

4x = 16

x = 16/4

x = 4.

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To find the total surface area of a cross-section solid, it is necessary to identify all the faces or surfaces of the solid, find the area of each individual face or surface, and then add them all together.

After finding the area of each individual face or surface, the final step is to add them all together to get the total surface area of the cross-section solid. This can be expressed mathematically as:

Total Surface Area = Area of Face 1 + Area of Face 2 + ... + Area of Face n

Where n represents the total number of faces or surfaces of the solid.

Pythagoras theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed mathematically as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

By using Pythagoras theorem to find the length of an unknown side, it is then possible to use the appropriate formula to find the area of the face or surface and then add it to the total surface area of the cross-section solid.

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Answer / Step-by-step explanation:

In a parallelogram, opposite angles are equal in measure. Therefore, we can add the first two angles together and the last two angles together, and set them equal to each other to form an equation:

2x + 3x = 2y + 3y

Simplifying the equation, we get:

5x = 5y

Dividing both sides by 5, we get:

x = y

This means that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.

Let's call each angle "a" and solve for it.

From the given ratio, we know that:

2x = 2a

3x = 3a

We can use the second equation to In a parallelogram, opposite angles are equal in measure. Therefore, we can add the first two angles together and the last two angles together, and set them equal to each other to form an equation:

2x + 3x = 2y + 3y

Simplifying the equation, we get:

5x = 5y

Dividing both sides by 5, we get:

x = y

This means that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.

Let's call each angle "a" and solve for it.

From the given ratio, we know that:

2x = 2a

3x = 3a

We can use the second equation to solve for x:

3x = 3a

x = a

Substituting x = a into the first equation, we get:

2a = 2a

This confirms that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.

Therefore, each angle in the parallelogram has a measure of:

2x = 2a = 2(180 - 3a) = 360 - 6a

3x = 3a = 3(180 - 2a) = 540 - 6a

Simplifying these expressions, we get:

Each of the first and third angles has a measure of 120 degrees, and each of the second and fourth angles has a measure of 180 - 120 = 60 degrees.

for x:

3x = 3a

x = a

Substituting x = a into the first equation, we get:

2a = 2a

This confirms that the first and third angles are equal in measure, and the second and fourth angles are equal in measure.

Therefore, each angle in the parallelogram has a measure of:

2x = 2a = 2(180 - 3a) = 360 - 6a

3x = 3a = 3(180 - 2a) = 540 - 6a

Simplifying these expressions, we get:

Each of the first and third angles has a measure of 120 degrees, and each of the second and fourth angles has a measure of 180 - 120 = 60 degrees.

Answer: 4

Step-by-step explanation:

We can start by simplifying each term step by step:

First, the cube root of 1 is 1, so -3 times the cube root of 1 is simply -3.

Second, the square root of 49 is 7, so 49 divided by the square root of 49 is also 7.

Putting it all together, we have:

-3 × ∛1 + 49 ÷ √49 = -3 + 7 = 4

Therefore, the value of the expression is 4.

Maya bought 5 greeting cards that cost $2.50 each and 7 greeting cards that cost $4 each.

Let's use algebra to solve this problem. Let's call the number of greeting cards that cost $2.50 "x" and the number of greeting cards that cost $4 "y". We know that Maya bought 12 cards in total, so:

x + y = 12

We also know that the total cost of the cards was $40.50, so:

2.50x + 4y = 40.50

Now we have two equations with two variables. We can use the first equation to solve for one of the variables in terms of the other. For example, we can solve for y:

y = 12 - x

Now we can substitute this expression for y in the second equation:

2.50x + 4(12 - x) = 40.50

Simplifying this equation:

2.50x + 48 - 4x = 40.50

-1.50x = -7.50

x = 5

So Maya bought 5 greeting cards that cost $2.50 each. To find out how many cards she bought that cost $4, we can substitute this value of x in the first equation:

x + y = 12

5 + y = 12

y = 7

So Maya bought 7 greeting cards that cost $4 each.

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Answer:

97271.1577

multiply 3374.60 by 2882.45%

Answer:

-85

Step-by-step explanation:

The solution for x is 5/2.

To solve for x, we will first simplify the expression on both sides of the equation and then isolate x on one side.

Step 1: Simplify the expression on the left side of the equation:

2(4x-3) = 8x - 6

Step 2: Simplify the expression on the right side of the equation:

10 + (-4x) + 14 = 24 - 4x

Step 3: Set the simplified expressions equal to each other:

8x - 6 = 24 - 4x

Step 4: Add 4x to both sides of the equation to isolate x on one side:

12x - 6 = 24

Step 5: Add 6 to both sides of the equation:

12x = 30

Step 6: Divide both sides of the equation by 12 to solve for x:

x = 30/12

Step 7: Simplify the fraction:

x = 5/2

Therefore, the solution for x is 5/2.

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So the total pressure experienced by the fish on the surface is 100450 Pa.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The equals sign indicates that the two expressions are equal, and the goal of solving the equation is to find the value of x that makes this statement true. Equations can be solved using various algebraic techniques, such as simplifying and rearranging the expressions, applying operations to both sides of the equation, and factoring or expanding expressions. Solving an equation involves finding the values of the variables that make the equation true.

Here,

When an object is submerged in a fluid, it experiences pressure due to the weight of the fluid above it. This pressure is called hydrostatic pressure, and it increases with depth. The formula to calculate hydrostatic pressure is:

P = ρgh

where P is the hydrostatic pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth of the object below the surface.

In this case, the fish is at a depth of 10m, so h = 10m. The density of water is given as 1025kg/m3, and the acceleration due to gravity is approximately 9.8m/s2. Therefore, the hydrostatic pressure experienced by the fish is:

P = (1025 kg/m3) x (9.8 m/s2) x (10 m)

= 100450 Pa

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Complete question:

"What is the total pressure experienced by a fish on the surface if it is at a depth of 10m? The density of water is 1025kg/m3"

The Quran and Sunnah are two primary sources of Islamic jurisprudence and belief. The Quran is the holy book of Islam, while Sunnah is the teachings of the Prophet Muhammad (peace be upon him).

There are two main differences between the Quran and Sunnah:

1. Content: The Quran contains the divine words of Allah, while the Sunnah is the teachings of the Prophet Muhammad (peace be upon him).

2. Authority: The Quran is the primary source of Islamic law and belief, while Sunnah is the secondary source, which provides clarification and further interpretation of the Quran.

Therefore, the Quran is the final authority on matters of Islamic law and belief, while the Sunnah is the interpretation and application of those laws.

The Qur'an is the holy book of Islam, believed to be the literal word of God as revealed to the Prophet Muhammad through the angel Gabriel. The Sunnah, on the other hand, is a collection of sayings and actions of the Prophet Muhammad, as recorded by his companions.

The Qur'an is considered the primary source of guidance for Muslims, and is seen as infallible and unchangeable. The Sunnah is considered a secondary source of guidance, used to help interpret and apply the teachings of the Qur'an in daily life.

Both the Qur'an and Sunnah are important sources of guidance for Muslims, and are used together to understand and practice the teachings of Islam. While the Qur'an is seen as the primary source of guidance, the Sunnah provides additional context and clarification on how to apply the teachings of the Qur'an in daily life

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The cost to rent one shed is $ 2880 where rental cost is $3 per cubic foot.

The length of the shed is 12 feet , that is l= 12 feet

The width of the shed is 8 feet, that is b=8 feet

The height of the shed ( tallness of the shed) is 10 feet , that is h=10 feet

The volume of the shed can be calculated by the formula

= length*breadth*height (cubic units)

= l*b*h (cubic foot)

= 12*10*8 cubic foot

= 960 cubic foot

The rental cost of  per cubic foot is $3.

Thus the rental cost of 960 cubic foot will be = $ (960*3 )

= $ 2880

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[tex]\cfrac{1}{3}(9x+12)=15\implies \cfrac{9x+12}{3}=15\implies 9x+12=45 \\\\\\ 9x=33\implies x=\cfrac{33}{9}\implies x=\cfrac{3}{3}\cdot \cfrac{11}{3}\implies x=\cfrac{11}{3}\implies x=3\frac{2}{3}[/tex]

Answer:

Chrissy is 7 years old

Step-by-step explanation:

The logarithm expression when evaluated is lg(1000a²/b⁴)

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

3+2lg a-4lg b

Apply the exponent law of logarithm

3 + lga² - lgb⁴

Apply the quotient law of logarithm

So, we have the following representation

3 + lg(a²/b⁴)

Also, we have

lg1000 = 3

Next, we have

lg1000 + lg(a²/b⁴)

So, we have

lg(1000a²/b⁴)

Hence, the solution is lg(1000a²/b⁴)

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The correct Mathematical phrases of the English phrases would be j+4, 16c, 3(z+1), ef+8, and v/17 respectively and the solution of given linear equations (part B) will be -105, -291, 270, -48, and -30 respectively.

In part A, the translation of mathematical phrases gives rise to certain equations of linear nature. It helps in easy understanding of the relations between variables and numerical values. In part B, the values of x, b and c are already given for the sake of simplicity. Substituting these values in given linear equations gives the following results:

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The total amount of interest on the investment if compounded continuously comes out to be $10064.60, rounded off to the nearest dollar and cent.

To find the total amount of money accumulated for an initial investment of $5200 at 6% compounded quarterly after 11 years, we can use the formula A = P(1+r/n)^(nt), where A is the total amount, P is the principal or initial investment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. Plugging in the given values, we get:

A = 5200(1+0.06/4)^(4*11)
A = 5200(1.015)^44
A = 5200*1.9878
A = $10336.96

Therefore, the total amount of money accumulated after 11 years is $10336.96, rounded off to the nearest dollar and cent.

To compute the total amount of interest on the investment if compounded continuously, we can use the formula A= P e^(rt), where e is the base of the natural logarithm. Plugging in the given values, we get:

A = 5200 e^(0.06*11)
A = 5200 e^0.66
A = 5200*1.9355
A = $10064.60

Therefore, the total amount of interest on the investment if compounded continuously is $10064.60, rounded off to the nearest dollar and cent.

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The required pre-image of N'J' is N(8,-4) and J(-6,-10).

The dilation with center (0,6) and scale factor of 1/2 will stretch or shrink any point by a factor of 1/2 relative to the center (0,6).

To find the pre-image of N'J', we need to undo this transformation. We can do this by applying the inverse transformation, which is a dilation with center (0,6) and scale factor of 2.

Let [tex]$N(x_1, y_1)$[/tex] be the pre-image of N' and [tex]$J(x_2, y_2)$[/tex] be the pre-image of J'. Then we have:

[tex]$$\begin{aligned} N &= (0,6) + 2(N' - (0,6)) \ &= (0,6) + 2(4,1-(0,6)) \ &= (0,6) + 2(4,-5) \ &= (8,-4) \end{aligned}$$[/tex]

and

[tex]$\begin{aligned} J &= (0,6) + 2(J' - (0,6)) \ &= (0,6) + 2(-3,-2-(0,6)) \ &= (0,6) + 2(-3,-8) \ &= (-6,-10) \end{aligned}$[/tex]

Therefore, the pre-image of N'J' is N(8,-4) and J(-6,-10).

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Answer:

Therefore, the lower fence is 1.5 and the upper fence is 5.5.

Step-by-step explanation:

To determine the upper and lower fences for a boxplot, we first need to calculate the interquartile range (IQR), which is the difference between the third quartile (Q3) and the first quartile (Q1). Then, we can use the following formulas:

Lower Fence = Q1 - 1.5 * IQR

Upper Fence = Q3 + 1.5 * IQR

In the given boxplot, the box extends from 2 to 5, with the median (Q2) at 3.5. The first quartile (Q1) is 3 and the third quartile (Q3) is 4. Therefore, the IQR is:

IQR = Q3 - Q1 = 4 - 3 = 1

Using the formulas above, we can calculate the lower and upper fences:

Lower Fence = Q1 - 1.5 * IQR = 3 - 1.5 * 1 = 1.5

Upper Fence = Q3 + 1.5 * IQR = 4 + 1.5 * 1 = 5.5

Therefore, the lower fence is 1.5 and the upper fence is 5.5.