The average rate of change of the account value from t = 0 to t = 5 is the change in the account value divided by the change in time, or (A(5) - A(0))/(5 - 0).
We can substitute the given function into the equation:
A(t) = 50,000(1.02)^t
So,
A(5) = 50,000(1.02)^5
and
A(0) = 50,000(1.02)^0
Now we can substitute these values in the equation of average rate of change:
(A(5) - A(0))/(5 - 0) = (50000(1.02)^5 - 50000(1.02)^0) / (5-0)
This simplifies to
(50000(1.02)^5 - 50000) / 5
Which is approximately equal to 67,622.05
So the average rate of change of the account value from t = 0 to t = 5 is approximately 67,622.05.
A company sells confetti in boxes in the shape of a triangular pyramid. Each box contains
240 cubic centimeters of confetti. If the height of the box is 15 centimeters, which of the
following could be the dimensions of the base?
A. Base, 8 cm; height, 4 cm
B. Base, 4 cm; height, 4 cm
C. Base, 6 cm; height, 8 cm
D. Base, 12 cm; height, 8 cm
The dimensions of the base would be: base: 12 cm ; height : 8 cm
The correct answer is an option (D)
We know that the formula for the volume of a pyramid is:
V = 1/3 × B × h
where B is the base area of the pyramid
h is the height of the pyramid
The shape of the box is a triangular pyramid.
Each box contains 240 cubic centimeters of confetti.
this means, the volume of the box is V = 240 cubic centimeters
Using above formula of the volume of a pyramid,
V = 1/3 × B × h
here V = 240 cubic centimeters and h = 15 centimeters
240 = 1/3 × B × 15
240 = B × 5
B = 240/5
B = 48 square centimeters
The dimensions of the base must be such that the area of the base would be 48 square centimeters.
Here, a pyramid has triangular base.
Using the formula for the area of triangle,
B = 1/2 × base of triangle × height of triangle
48 = 1/2 × base of triangle × height of triangle
base of triangle × height of triangle = 96
for the dimensions Base, 12 cm; height, 8 cm
12 × 8 = 96
Thus, the dimension of the base: base of triangle = 12 cm and the height of triangle = 8 cm
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in ten dollars more than Sara. How much money did Lisa and Joe put towards the gift?
Answer:
20
Step-by-step explanation:
10$ by lisa
10$ by joe
so, 20$ money did lisa and joe put towards the gift
An electric pole 15 m high is supported by a wire fixing its one end on the ground at some distance from the pole. If the wire joining the top of the pole is inclined to the ground at an angle of 60°, find the length of the wire.
Step-by-step explanation:
Givenlength of the pole : 15 m
angle inclined by the wire to the pole from ground :60 deg
let the length of wire : x
therefore
sin (angle) = opposite/hypothesis
sin 60 = 15/x
√3/2 = 15/x
x= 2*15/√3
x = 30/√3
x = 17.320
the length of the wire is :17 m.
the gardener has 75 shrubs to plant in 4 rows.
If he planted an equal number in each row, there were _____ shrubs left over.
if possible explain why you got this answer please :)
a population of 10 scores has a mean of 50 and a standard deviation of 5. what is the population variance?
The value of the Population Variance is 25.
Given:
The standard deviation of a population is 5
The mean of a population is 50
The size of a population is 10
[tex]Variance = (Standard \ deviation)^{2}[/tex]
[tex]Variance = 5^{2}[/tex]
σ = 25.
So, The value of the Population Variance is 25.
Population variance is a metric for gauging how dispersed a set of data points is. It calculates the typical squared deviation from the mean. Therefore, the variance will be smaller if all of the data points are close to the mean than it will be if the data points are dispersed widely.
We are aware that the population variance describes the distribution of data points within a population by averaging the squared distances between each data point and the mean.
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Describe the symmetries of a rhombus and prove that the set of symmetries forms a group. Give Cayley tables for both the symmetries of a rectangle and the symmetries of a rhombus. Are the symmetries of a rectangle and those of a rhombus the same?
The symmetries of a rectangle and those of a rhombus are not the same, as the rectangle has two additional symmetries.
A rhombus is a quadrilateral with all sides of equivalent length, and it has the accompanying symmetries:
Identity symmetry: The rhombus stays unaltered when reflected about its center.
Rotational symmetry: The rhombus stays unaltered when pivoted 180 degrees about its center.
Reflective symmetry: The rhombus stays unaltered when reflected about its two diagonals.
These symmetries structure a gathering under the operation of the organization of symmetries. A gathering is a bunch of components with a twofold operation (for this situation, the creation of symmetries) that fulfills the cooperative, identity and converse properties.
The arrangement of symmetries of a rhombus fulfills these properties, making it a group.
The Cayley table for the symmetries of a rhombus is as per the following:
E R1 R2 R3
R1 E R3 R2
R2 R3 E R1
R3 R2 R1 E
Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one diagonal, and R3 addresses the symmetry about the other diagonal.
Then again, the symmetries of a rectangle are:
Identity symmetry: The rectangle stays unaltered when reflected about its center.
Rotational symmetry: The rectangle stays unaltered when pivoted 180 degrees about its center.
Reflective symmetry: The rectangle stays unaltered when reflected about its two vertical and two horizontal axis.
The Cayley table for the symmetries of a rectangle is as per the following:
E R1 R2 R3 R4
R1 E R3 R2 R4
R2 R3 E R1 R4
R3 R2 R1 E R4
R4 R4 R4 R4 E
Where E addresses the identity symmetry, R1 addresses the 180-degree turn symmetry, R2 addresses the symmetry around one vertical axis, R3 addresses the symmetry around one horizontal axis and R4 addresses the symmetry about the two diagonals.
We can see that the arrangement of symmetries of a rectangle and those of a rhombus are not something similar.
The rectangle has two additional symmetries, the symmetry around one vertical and one horizontal axis, which are not present in the rhombus.
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WILL GIVE BRAINLIEST AND 30 POINTS IF SOMEONE HELPS
urrrrrrrrrrrrrrrf mooookoommm
PLEASE IM BEGGING YOU HELP ME
A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally?
Which equation best models the situation here?
4x + 9 = 76
4(x+9) = 76
4(9x) = 76
If the new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams , then the equation best models the situation here is (b) 4(x+9) = 76 .
the number of sensor in the boxes is = 4 ;
let the weight of each of sensors be = x ;
So , in new design the weight of each sensor is increased by 9 grams ,
the new weight of sensor becomes = x + 9 ;
the new weight of 4 sensors will be = 4(x + 9) ;
the total weight of new package is = 76 grams ;
So , the equation representing the situation is (b) 4(x+9) = 76 .
The given question is incomplete , the complete question is
A company manufactures a special type of sensor, and packs them in boxes of 4 for shipment. Then a new design increases the weight of each sensor by 9 grams. The new package of 4 sensors weighs 76 grams how much did each sensor weigh originally ?
Which equation best models the situation here ?
(a) 4x + 9 = 76
(b) 4(x+9) = 76
(c) 4(9x) = 76
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Johan drives his car to a holiday destination 600
kilometers away. He drives a distance of 90 km every
hour. Which equation shows how far (s) he is from his
destination at the end of 6 hours?
A. (600 – 90) x 6 = s
B. 600 + (90 x 6) = s
C. 600 – (90 X 6) :
= S
D. 600 – (90 + 6) = s
The correct equation that shows how far (s) Johan is from his destination at the end of 6 hours is option C. 600 - (90 X 6) = s
Johan is driving 90 kilometers every hour and he has been driving for 6 hours, so the distance covered by him is 90*6 = 540 kilometers.
The distance he is away from his destination is the total distance to the destination minus the distance he has covered so far.
That is 600 - 540 = 60 kilometers
So, the equation that shows the distance he is from his destination is -
600 - (90 X 6) = s
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The ticket price to a concert is $65 plus an additional (d) dollars service fee per ticket. The total cost for four people to attend the concert is $308. Calculate the cost of the service fee charged for each ticket.
SHOW HOW YOU DID IT PLEASE!!!
Answer: d=12
Step-by-step explanation:
4(65)+ 4d=308
multiply 65 by 4
260+4d=308
move the constant to the right
4d=308-260
calculate
4d=48
divide both sides
d=12
write an equation of the line that passes through the given points and is perpendicular to the given line
The equation of the line parallel to the line is y = -4x + 10
The equation of the line perpendicular to the line is y = 1/4x +3/2
Using the point (1, 6) and (2, 2) on the line to get the slop:
Slope = 2-6/2-1
Slope = -4/1
Slope = -4
The equation is written in point slope form as y-y0 = m(x-x0)
Substitute a point and the given slope for the equation parallel to the line
y - 2 = -4(x-2)
y - 2 = -4x + 8
y+4x = 10
Hence the equation of the line parallel to the line is y = -4x + 10
The needed slope for the perpendicular line is 1/4.
Substitute a point and the given slope for the equation parallel to the line
y - 2 = 1/4(x-2)
4(y - 2) = x - 2
4y - 8 =x -2
4y = x + 6
y = 1/4x + 3/2
Hence the line perpendicular to the line is y = 1/4x + 3/2
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The following question may be like this:
write an equation of the line that passes through the given points and is perpendicular to the given line.
16. Rylan claimed that adjacent angles are complementary.
Draw an example that supports Rylan's statement and draw a
counterexample that shows her statement is not always true.
The example of adjacent angles that are complementary and those that are non-complementary are given as attached.
What are adjacent and Non-Adjacent angles?When two adjacent angles have a similar vertex and side, they might be complementary or supplementary angles.
If the total of neighboring angles equals 90 degrees, then they are complementary. If the total of neighboring angles equals 180 degrees, they are complementary to one another.
Non-adjacent Complementary Angles: Two angles that are not next to each other are non-adjacent complementary angles. AOB and XOY are non-adjacent angles since they share neither a vertex nor an arm. They also add up to 90°. As a result, these two angles are non-adjacent complimentary.
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Which functions show a positive rate of change? Select all that apply
Answer:
A and B
Step-by-step explanation:
A: Has a positive slope which will be a positive rate of change
B: Will have a positive if you turn it into 7 + 3x instead of subtracting
Savannah is tiling her kitchen floor. She bought 8 cases of tile for $208. She realizes she bought too much tile and returns 2 unopened cases to the store. What was her final cost for the tile?
The final cost for the tile was $208 − $52 = $156.
An example of an algebraic equation?An algebraic equation is a statement of the equality of two expressions and is calculated by applying the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root to a set of variables. Examples include x3 + 1 and (y4x2 + 2xy - y)/(x - 1) = 12.Consider the equation 3x + 5 = 14, in which the terms 3x + 5 and 14 are separated by the word "equal."A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.208/8 = x/2
8x = 416
x = 416/8
x = 52
The price for the two unopened cases was $52.
Thus, The final cost for the tile was $208 − $52 = $156.
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Find the measures of the numbered angles.
Answer: ∠1= 53°
∠3, ∠6, ∠7 are all 127°
∠4,∠5,∠8 are all 53°
Step-by-step explanation: 127° and ∠1 are supplementary angles meaning they add up to 180° You subtract 127° from 180° to get 53°.
∠3 and 127°are vertical which makes them equal and both 127°.
∠4 is vertical to ∠1 which makes them equal and both 53°.
∠5 is corresponding to ∠1 so they are equal and both 53°.
∠6 is corresponding to 127° so they are equal and both 127°.
∠7 is vertical to ∠6 so they are equal and both 127°.
∠8 is vertical to ∠5 so they are equal and both 53°.
Please answer these questions.. step-by-step
Refer to the image attached.
one must fly at least 16200 and less than 36000 miles each year. if greg takes a 900 -mile round-trip flight to visit his parents, how many times does greg need to visit his parents each year to attain gold status?
Greg would need to visit his parents at least 18 times each year to attain gold status. To calculate this, we need to take the minimum flight miles required for gold status (16200) and subtract 900 miles, the round-trip flight distance to visit his parents.
where the value comes from the calculation of 15300 miles. Then, we divide 15300 miles by 900 miles, the round-trip flight distance to visit his parents, and get the answer of 18. Therefore, Greg needs to visit his parents at least 18 times each year to reach gold status. To be eligible for gold status, one must fly a certain amount of miles within a year.
For the airline company that Greg is using, the minimum flight miles required for gold status is 16200. Since Greg is taking a 900-mile round-trip flight to visit his parents, he needs to make up the difference in order to reach the minimum required flight miles. Thus, he needs to visit his parents at least 18 times each year to ensure that he meets the required flight miles for gold status.
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what is the standard for of y= 4/9x - 3
The Standard form of y= 4/9x - 3 is 4x - 9y = 27.
What is standard form of an equation?
The general form of a linear equation, commonly referred to as the standard form, is written as Ax + By = C.
Given equation : y= 4/9x - 3
Taking LCM on both sides
we get, 9y = 4x - 27
Since the standard form of a linear equation is Ax + By = C.
So, we can write it as 4x - 9y = 27
where A= 4, B = -9 and C= 27.
Hence, the standard form of y= 4/9x - 3 is 4x - 9y = 27.
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Help..
select all the coordinates that represent a point on the line.
0,2
0,6
2,6
3,1
4,1
6,×
Answer:
Okay so 6,0 3,1 4,1 and 0,2
Step-by-step explanation:
So take 3,1 you would go over 3 on the x axes and up 1 on the y axes
Help meeeee please i need help with this
Answer: I believe the answer would be y = 3x.
Step-by-step explanation: I like to start by counting the x-values, then the y-values. Since the y-values are increasing by a constant of 3 and the x-values are increasing by 1, that would technically make the equation y = 3x + 0, but you don't need the 0 in this case. So it's just y = 3x. I hope this helps! :)
which of the following describes the domain of the piecewise function
Answer:
(c) (-∞, -2) ∪ (-2, 1) ∪ (1, ∞)
Step-by-step explanation:
You want the domain of the given piecewise-defined function.
x < 2For x < 2, the function is ...
[tex]g(x)=\dfrac{x^2+2x}{x^2+x-2}-\dfrac{x(x+2)}{(x-1)(x+2)}=\dfrac{x}{x-1}\quad x\ne\{-2,1\}[/tex]
Both of these exclusions are in the region x < 2, so both must be excluded from the domain.
x ≥ 2The log function is defined for all values x > -2, so there are no exclusions in this region.
The domain is (-∞, -2) ∪ (-2, 1) ∪ (1, ∞).
6. The graph of an exponential function is
shown. Write an equation for the function.
manu (3,13.5)
(2,4.5)
(1, 1.5)
olismolensando
On soloing the provided question, we can say that an equation from the graphs for the function. 3x + 13.5y = 4.5 and x+1.5y = 2
What is graphs?Mathematicians use graphs to logically represent or chart facts or values. Typically, a graph point will show the relationship between two or more objects. A graph is a non-linear data structure made up of nodes, or vertices, and edges. The nodes, also known as vertices, should be joined with glue. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 4, and 2.5. (3.5). (4.5). Graphical depictions of exponential growth in statistical charts (bar charts, pie charts, line charts, etc.). triangle-shaped logarithmic graph.
an equation for the function.
3x + 13.5y = 4.5
and x+1.5y = 2
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PLEASE HELP ASAP
The tide at an Eastern seaport is at its maximum at 3 a. M. High tide is 24 ft deep. Low tide occurs at 9 a. M. With a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight
The water depths can be modeled by a sinusoidal function. So the value of period is 18 hours, amplitude is 14.5, maximum is 24, equation of the midline is 10, and minimum is -4.
The tide at an Eastern seaport is at its maximum at 3 a.m.
High tide is 24 ft deep.
Low tide occurs at 9 a.m. with a depth of 4 ft.
We have to determine the period.
Period = time between two consecutive high tides
Period = 2 × Time between high and low tide
Time between 3 a.m. and 9 a.m. is 6 hours.
Period = 2 × 6
Period = 18 hours
We have to determine the Amplitude.
Amplitude = (High - Low)/2
Amplitude = (24 - (-5))/2
Amplitude = (24 + 5)/2
Amplitude = 29/2
Amplitude = 14.5
We have to determine the Maximum.
The maximum tide is 24.
We have to determine the Equation of the midline.
Equation of the midline = (max + min)/2
Equation of the midline = {24 + (-4)}/2
Equation of the midline = (24 - 4)/2
Equation of the midline = 20/2
Equation of the midline = 10
We have to determine the minimum.
The minimum tide is -4.
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The complete question is:
The tide at an Eastern seaport is at its maximum at 3 a.m. High tide is 24 ft deep. Low tide occurs at 9 a.m. with a depth of 4 ft. The water depths can be modeled by a sinusoidal function. Allow x=0 to represent midnight
Find the following and make sure to show work for the midline and amplitude:
period=
Amplitude=
Maximum=
Equation of the midline:
minimum:
nine more than the product of 9 and a number
Answer:
9 + 9n
Step-by-step explanation:
let 'n' = 'a number'
'more than' implies addition
'product' implies multiplication
9 + 9n
Answer: 9+(1)4=9+r
Step-by-step explanation:
Sophia bought snacks for her team's practice. She bought a bag of popcorn for $1. 98 and a 10-pack of juice bottles. The total cost before tax was $12. 48. Write and solve an equation which can be used to determine j, how much each bottle of juice costs?
Each bottle of juice costs $ 1.05 that Sophia bought snacks for her team's practice.
j - The cost of each bottle of juice .
The cost of popcorn - $1.98
The cost of juice 10 * j = 10 j
The total cost = $12.48
So , 1.98 + 10 j = 12.48
10 j = 10.5
j = 1.05
The whole expense a company incurs to produce a specific level of production. On the other hand, the total cost represents the cost of all fixed and variable expenses combined. It displays as TC (total cost). The sum of the two yields the Total Cost (TC). The total cost formula is used to total up the variable and constant expenses associated with providing commodities. Total cost is calculated as follows: (Average Fixed Cost x Average Variable Cost) x Units Produced.
Together, fixed and variable costs make up the overall cost.
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Two boxes need to be wrapped in paper (with no overlap). Both boxes are in the shape of right rectangular prisms.
Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide. Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.
The wrapping paper costs $6.79 per 80 square feet.
What is the cost of wrapping both boxes?
Enter your answer in the box.
The cost of wrapping both boxes is $0.92.
What is prism?In three-dimensional space, a prism is a polyhedron where two ends are similar.
Given:
Two boxes need to be wrapped in paper (with no overlap).
Both boxes are in the shape of right rectangular prisms.
Box A measures 1.2 feet high, 0.8 feet long, and 1 foot wide.
The surface area of the rectangular prism A,
= 2(1.2 × 0.8 + 1 × 0.8 + 1 × 1.2)
= 5.92 square feet.
Box B measures 1.6 feet high, 0.5 feet long and 0.8 feet wide.
The surface area of the rectangular prism A,
= 2(1.6 × 0.5 + 0.5 × 0.8 + 0.8 × 1.6)
= 4.96 square feet.
The wrapping paper costs $6.79 per 80 square feet.
That means,
unit rate = 6.79 / 80 = $0.08 per square feet.
The cost of wrapping both boxes,
= 5.92 x 0.08 + 4.96 x 0.08
= $0.92
Therefore, the cost is $0.92.
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a farmer owns three full sections, four half-sections, and two quarter-sections. how many acres is this?
The correct option is Option 1 - 3520.
A farmer owns 3520 acres in which three full sections, four half-sections, and two quarter-sections are there.
Three of a farmer's sections were full. Let's say a full section is 640, which is
=3 x 640,
= 1,920.
He had four half portions as well. Divide 640 by two to get 320 (640/2), which is
= 4 X 320
= 1,280.
He had three quarter portions as well. Divide 640 by 4 to create a quarter piece (640/4 = 160)
= 2 X 160
= 320.
Now we have to add all these,
Three full sections = 1920
Four half-sections = 1280
Two quarter-sections = 320
= 1,920 + 1,280 + 320
= 3,520.
Therefore the acres a farmer had is 3520.
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The following question may be like this:
A farmer owns three full sections, four half-sections, and two quarter-sections. How many acres is this?
3520324044404020Choose the correct graph of LMN below.
After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-4, -5) and (2, -4). Therefore, option C is the correct answer.
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
Given that, triangle LMN with vertices L(2, -2), M(5, -4) and N(4, 2).
After clockwise rotation 90° we get
Here, L(2, -2) →L'(-2, -2)
M(5, -4) →M'(-4, -5)
N(4, 2) →N'(2, -4)
Therefore, option C is the correct answer.
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2434base6 divided by 42 base 6
The answer for the given senary expressions is 35₆.
What are senary numbers?
A senary numeral system (also known as base-6, heximal, or seximal) has six as its base. It has been adopted independently by a small number of cultures. Like decimal, it is a semiprime, though it is unique as the product of the only two consecutive numbers that are both prime (2 and 3). As six is a superior highly composite number, many of the arguments made in favor of the duodecimal system also apply to senary.
Now,
To find 2434₆/42₆
2434\(_6\) to base 10
2 \(\times\) 6\(^3\) + 4 \(\times\) 6\(^2\) + 3 \(\times\) 6\(^1\) + 4 \(\times\) 6\(^0\)
2 \(\times\) 216 + 4 \(\times\) 36 + 3 \(\times\) 6 + 4 \(\times\) 1
432 + 144 + 18 + 4 = 598
And: 42\(_6\) to base 10
4 \(\times\) 6\(^1\) + 2 \(\times\) 6\(^0\)
4 \(\times\) 6 + 2 \(\times\) 1
24 + 2 = 26
Then divide 598 by 26
= 23
Then convert 23\(_{10}\) to base 6
i.e. 35₆
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Please help! Write a transformation rule that maps the figure to its image. Some might require more than one transformation.
Top triangle: figure
Bottom triangle: image
The transformation rule that is used to map the figure to the image is;
Shift the figure by 2 units to the right and then reflect the figure about the line y = -1.5
What is the transformation used?Looking at the figure which is the top triangle, we can see that it is not in line with the image at the bottom and as such, we need to make it to be in vertical alignment by shifting the figure first of all by 2 units to the right.
When the figure is shifted by 2 units to the right, then it will be in alignment with the image at the bottom and as such we can reflect the figure about the line y = -1.5 to achieve the final mapping that is required.
The transformation rule used will be shifting and reflection
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