The maximum score that can be in the bottom 5% of scores is 2.64
The middle 90% of scores lie between 2.88 and 4.56.
What is the maximum score that can be in the bottom 5% of scores?(a) To find the maximum score that can be in the bottom 5% of scores, we need to find the score that corresponds to the 5th percentile of the normal distribution.
Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28. To convert this back to the original scale, we can use the formula:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score (-1.28), and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
x= 2.64
(b)
To find the range of scores that the middle 90% of scores lie between, we need to find the 5th and 95th percentiles of the normal distribution.
Using the mean and standard deviation provided (3.6 and 0.75, respectively), we can use the standard normal table to find that the 5th percentile corresponds to a standard normal score of -1.28 and the 95th percentile corresponds to a standard normal score of 1.28. To convert these back to the original scale, we can use the formula:
x = mu + z * sigma
Where
x is the original score, mu is the mean (3.6), z is the standard normal score, and sigma is the standard deviation (0.75).Plugging in the values, we get:
x = 3.6 + (-1.28) * 0.75
= 2.88 for the 5th percentile
x = 3.6 + 1.28 * 0.75
= 4.56 for the 95th percentile
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Pls answer................
Answer:
m<C = 43°
Step-by-step explanation:
m<P = m<A = 45°
m<B = (5x + 2)°
m<Q = 6x - 16
m<Q = m<B
6x - 16 = 5x + 2
x = 18
m<B = m<Q = 5 × 18° + 2° = 92°
m<A + m<B + m<C = 180°
45° + 92° + m<C = 180°
m<C = 43°
(04.03 LC)
Which of the following fractions compares BC to BD?
O
213
O
5/2
-3-
-24
2
O
1
O
-1-
B
T
C
2
D
3 4
5
6
The fraction compares BC to BD is 2/3. Therefore, option A is the correct answer.
What is distance formula?The distance formula which is used to find the distance between two points in a two-dimensional plane is also known as the Euclidean distance formula. On 2D plane the distance between two points (x₁, y₁) and (x₂, y₂) is Distance = √[(x₂-x₁)²+(y₂-y₁)²].
Given that, the coordinate points are B(0,1), D(3 ,1) and C(2, 1).
Here, BC is
BC=√[(2-0)²+(1-1)²]
BC=2 units
BD is
BD= √[(3-0)²+(1-1)²]
BD= 3 units
The fraction compares BC to BD is 2/3
Therefore, option A is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Which of the following fractions compares BC to BD? coordinate plane with segment BD at B(0,1) and D(3 ,1); point C is on segment BD and (2, 1).
Answer choices:
A) 2/3
B) 5/2
C) 2/5
D) 3/2
Answer:
2/5
Step-by-step explanation:
d = √[(x2 - x1)² + (y2 - y1)²]
For segment BD:
BD = √[(5 - 0)² + (1 - 1)²]
= √[5² + 0²]
= √25
= 5
For segment BC:
BC = √[(2 - 0)² + (1 - 1)²]
= √[2² + 0²]
= √4
= 2
-9a-2(9a-5) need help
Answer: -81a^2 + 27a + 10
Step-by-step explanation: We can do this question by using FOIL (first, outer, inner, last)
(-9a-2)(9a-5)
First, multiply the first two terms in the parentheses
-9a times 9a is -81a^2
Second, multiply the outer terms
-9a times -5 is 45a
Third, multiply the inner terms
-2 times 9a is -18a
And lastly, multiply the last terms
-2 times -5 is 10
After doing this we end up with -81a^2 + 45a - 18a + 10 = -81a^2 + 27a + 10
Solve.
Find the area of the following shape made of rectangles.
A 176 m²
B 172 m²
C 52 m²
D 180 m²
The area of the shape in the figure is calculated to be 180 m²
How to find the area of the shapeThe area of the shape in the figure can be solved by breaking the shape into three rectangles, calculating the area of each rectangle and adding up
Area of rectangle is calculated by the formula
= length * width
Area of the first rectangle
= 4 * 16
= 64
Area of the second rectangle
= (16 - 4) * (12 - 4 - 5)
= 12 * 3
= 36
Area of the third rectangle
= 16 * 5
= 80
Adding up
= 80 * 36 * 64
= 180 m²
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Some students collected the data below month and average temperatures. They will graph the data. What is the y-intercept? Your answer should be an ordered pair/
The y intercept of the data collected is 42°C
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the average temperature and x represent the month. x = 0 represent the month January.
From the table, at January, the average temperature is 42°C. Hence the y intercept is 42°C.
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What is the equation of the midline of the sinusoidal function
Answer: y = 0
Step-by-step explanation:
A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. For y = sin x, the midline is y = 0 (the x-axis). The midline is parallel to the x-axis and is located halfway between the graph's maximum and minimum values.
Square ABCD has a diagonal AC with the given vertices. Find the coordinates of the remaining vertices.
A(2, 2) and C(6,-2)
The coordinates are ( , ) and ( , )
The coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)).
What is meant by coordinates?A group of values that exhibit precise positioning The first number on a graph represents the distance along, while the second number represents the distance up or down.
To find the coordinates of the remaining vertices of square ABCD, we can use the information given about diagonal AC and the properties of a square. Since a square has equal side lengths and right angles, we know that the distance between opposite vertices on a diagonal must be equal to the side length of the square.
Given the coordinates of vertex A and C, we can use the distance formula to find the length of AC:
Let the equation be Distance [tex]d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
substitute the values in the above equation, we get
AC = [tex]\sqrt{((2 - (-2))^2 + (4 - 1)^2)}[/tex]
simplifying the equation, we get
AC = √(4 + 9) = √(13)
We can utilize the knowledge of the square's side length to determine the locations of the remaining vertices. Vertex B is known to have the same y-coordinate as vertex A, while vertex C is two units to the left in terms of the x-coordinate. Therefore, the coordinates of vertex B exists (-2 + 2√(13), 1).
Similar to vertex A, vertex D is known to have an identical x-coordinate, but its y-coordinate is four units below vertex C. Therefore, the coordinates of vertex D exists (-2, 4√(13))
Therefore, the coordinates of the remaining vertices exists (2√(13),1) and (-2, 4√(13)) respectively.
The complete question is:
Square ABCD has a diagonal AC with vertices A(-2, 1) and C(2, 4). Find the coordinates of the remaining vertices. Express your answers as decimals, if necessary.
The coordinates are and D.
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Solve and check the linear equation.
4(x-2)+11=3(x+3)
What is the solution?
Answer:
Step-by-step explanation:
4(x-2)+11=3(x+3)
Use distributive property to get rid of the parentheses
4x-8+11=3x+9
Simplify the addition and subtraction
4x+3=3x+9
subtract 3 on both sides and 3x on both sides to isolate x
x=6
NO LINKS!!!
Please help me with these Venn Diagram circles
Figures with more than 3 sides but with no pairs of parallel sides:
Kite,Pentagon,HeptagonIntersectionFigures with more than 3 sides and with one or more pairs of parallel sides, almost all even sided polygons:
Square,Parallelogram,Rhombus,Trapezoid,Rectangle,Hexagon,OctagonCircle 2Figures with one or more pairs of parallel sides:
Empty, all included into intersection regionProblem 2Circle 1Figures with less than 4 sides:
Scalene triangleIntersectionFigures with less than 4 sides and with at least two sides of equal length:
Equilateral triangle,Isosceles triangleCircle 2Figures with at least two sides of equal length:
Square,Rectangle,Rhombus,Kite,Isosceles trapezoid,Pentagon,Hexagon,Heptagon,OctagonProblem 3Circle 1Figures with at least one curved side:
CircleIntersectionFigures with at least one curved side and with at least one obtuse angle:
Empty, not considering combination of shapesCircle 2Figures with at least one obtuse angle (polygons with more than 4 sides will have obtuse angles)
Trapezoid,Rhombus,Kite,Parallelogram,Pentagon,Hexagon,Heptagon,OctagonJulio is using Scale modles to help remodel his kitchen. Julio makes a Scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy. The Scale of his drawing is 1 inch: 4 feet.
The length of actual kitchen floor is 18 ft and the width of actual kitchen floor is 13.5 ft.
What is scale?
The ratio that describes the relationship between the actual figure and its model is called the scale. It serves as a representation of the actual figures in smaller units on maps. A scale of 1:5, for instance, means that 1 on the map is equivalent to the size of 5 in the real world.
A scale is a group of levels or numbers that are applied to a specific system of measurement or comparison.
Given:
Julio is using Scale models to help remodel his kitchen.
Julio makes a Scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy.
The Scale of his drawing is 1 inch: 4 feet.
we know that
scale ----------> inch / 4 feet = 0.25 in/ft
[scale] = [scale drawing] / [actual]
[actual] = [scale drawing] / [scale]
for length --------> 4 1/2 in ---------> 4.5 in (scale drawing)
[actual] = [4.5] / [0.25] =18 ft
for width ---------> 3 3/8 in ---> (3*8+3)/8 ---> 27/8 in (scale drawing)
[actual] = [27/8] / [0.25] = 13.5 ft
Hence, the length of actual kitchen floor is 18 ft and the width of actual kitchen floor is 13.5 ft.
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Complete question:
Julio makes a scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy . The scale of his drawing is 1 inch:4 feet. (The length is 4 1/2 and the width is 3 3/8)
What is the actual are of Julio's kitchen floor?
17 A customer wants to make screen wash from concentrate and water.
The diagram shows the amount of concentrate she puts into a container.
ml 1000-
800
600
400
200
The customer adds water into the container up to the 1000 ml division.
W67780A
Ratio of concentrate and water in 1:1 would be most reliable for this situation. Thus, A is the correct option.
What is Ratio?A ratio is a way to compare two or more comparable quantities by writing the numbers with a colon in between each one. The figures must be whole numbers without any units.
You must practise the techniques described here repeatedly until they are automatic in order to master them. After reading this text and/or watching the related video tutorial, you should be able to:
• calculate the ratio of two or more similar quantities, regardless of whether they are expressed in the same units;
• divide a quantity into a number of parts in given ratios;
• use ratios to scale up or scale down a list of ingredients.
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Correct answer:
A customer wants to make screen wash from concentrate and water.
The diagram shows the amount of concentrate she puts into a container.
ml
1000
800
600
400
200
The customer adds water into the container up to the 1000 ml division. Which Ratio of concentrate and water would be most reliable.
A. 1:1
B. 4:5
C. 2:5
D. 1:5
What is the equation for the translation of x2 + y2 = 64 three units to the left and two units down?
(x − 3)2 + (y − 2)2 = 64
(x + 3)2 + (y + 2)2 = 64
(x + 3)2 + (y − 2)2 = 64
(x − 3)2 + (y + 2)2 = 64
Answer: The equation for the translation of x2 + y2 = 64 three units to the left and two units down is:
(x − 3)2 + (y − 2)2 = 64
Step-by-step explanation:
This is known as the standard equation of a circle centered at (3, 2) with a radius of 8.
When translating a shape, we need to change the center point of the shape. If we want to translate 3 units to the left and 2 units down, it means that we need to change the center point of the shape from the origin to (3, 2). This can be achieved by subtracting 3 from x and subtracting 2 from y in the equation of the circle. This results in (x - 3)2 + (y - 2)2 = 64, which is the equation for the translated circle.
Answer: (x - 3)^2 + (y - 2)^2 = 64.
Step-by-step explanation:
This is because to translate a point or a function in the x-axis by a certain value we need to add or subtract the value from the x variable. To translate in the y-axis we need to add or subtract the value from the y variable. In this case, we are translating it three units to the left, so we subtract 3 from x, and two units down so we subtract 2 from y.
GEOMETRY HELPPP I NEED HELP
Answer:
91 degrees
angles on a straight line add up to 180
x = 180-89 = 91
therefore angle 5 is 91
HELPP PLSSSSS ! ILL MARK U BRANLIEST
Integer multiplication and division are two fundamental operations on integers. Integer multiplication is the same as repeated addition, which involves adding an integer a particular number of times.
4 3 means to multiply 4 three times, i.e. 4 + 4 + 4 Equals 12. Integer division denotes the equal grouping or division of an integer into a certain number of groups. For example, -6 2 denotes splitting -6 into two equal halves, yielding -3. In this topic, we will study more about integer multiplication and division. Integer multiplication is the process of repetitive addition of positive and negative numbers, or simply integers. When it comes to integer multiplication, the following situations must be considered:
2 positive numbers multiplied
2 negative numbers multiplied
1 positive and 1 negative number multiplied
Integer division entails grouping of objects. It contains both positive and negative numbers. Division of numbers, like multiplication, involves the same instances.
2 positive numbers divided
2 negative numbers divided
1 positive and 1 negative number divided
When you divide numbers by two positive signs, Positive = Positive 16 8 = 2.
When two negative signs are used to divide integers, Negative Negative = Positive -16 -8 = 2.
Negative Positive = Negative -16 8 = -2 when you divide numbers with one negative sign and one positive sign.
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The fourth grade is going on a field trip and taking two buses. One bus has 3 rows of seats with 9 deatd in each row the other bus has four times as many seat as the first bus. How many seats are there in both buses?
The number of seats in the two buses are: first bus includes 27 seats and second bus includes 108 seats.
What is proportion?An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometres per hour is equal to the time it needs to travel 500 kilometres in five hours. Example: 100 km/hr = 500 km/5 hour.
Given that:
Three rows of nine seats each make up one bus, hence the first bus's seating arrangement is as follows:
3 x 9 = 27.
Since the other bus has four times as many seats as the first bus, the second bus's seat count is as follows:
4 x 27 = 108.
Hence, the number in the two buses are first bus includes 27 seats and second bus includes 108 seats.
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Edward marks exam scripts for a grade 11 extra class he charges R150 for a maths paper 1 script and R200 maths paper 2 scripts as shown below
What type of relationship is shown on the graph
The type of relationship shown on the graph that depicts Edward's exam scripts is a Linear relationship.
What is a linear relationship ?A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Both a graphical representation of a linear relationship, in which the variable and constant are connected by a straight line, and a mathematical representation, in which the dependent variable is determined by multiplying the independent variable by the slope coefficient and a constant.
Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
Edward's cost per math paper 1 or math paper 2 script marked will change depending on the type of paper and the number of papers. This simply means that Edward's charges are increasing per paper marked which is shown a linear relationship in the attached graph.
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James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours. How many hours will James have to work each week?
Please help me with the formula
The number of hours that James have to work each week will be 25 hours.
How to calculate the number of hours?The word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge.
In this case, James has a job moving lawns during the summer. Suppose the formula for calculating the number of hours he will have to work each week is five times the difference of thirty-eight and three times the difference of fifteen and four hours.
The number of hours that James have to work each week will be:
= 5(38) - 3(15 - 4)
= 5(38) - 3(11)
= 5(38 - 33)
= 5 × 5
= 25 hours
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. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
volume of the cylinder.
1/5+3/10 as a proper fraction
Step-by-step explanation:
Add
1/5+3/10=5/10
Find common denominator
1/5+3/10=1*2/5*3+3*1/10*1=2/10+3/10
10 is the least common multiple of denominators 5 and 10. Use it to convert to equivalent fractions with this common denominator.
Add
2/10+3/10=2+3/10=5/10
Simplify
5/10=1/2
5 is the greatest common divisor of 5 and 10. Reduce by dividing both the numerator and denominator by 5.
Hope it saved your day and don't forget to rate-me down below!Thank you,EdwinA can of soda can be modeled as a right cylinder. Ajay measures its height as 8.9 cm
and its radius as 1.9 cm. Find the volume of the can in cubic centimeters. Round your
answer to the nearest tenth if necessary.
Answer:
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.
So, using the given measurements, we can substitute in the values and solve for the volume:
V = π(1.9 cm)^2(8.9 cm) = 301.958 cm^3
Rounded to the nearest tenth, the volume of the can is 301.9 cm^3.
Step-by-step explanation:
Eliana loves music, especially 80's punk rock. Eliana looked at the number of songs in her itunes account and she has 6 less than 4 times her best friend. Eliana's classmate David has 3 more than double her best friend. When talking to her Social Studies teacher, Eliana found out social study teacher has 7 more than two times the number of songs in his library than Eliana. Define a variable, then write and solve an equation. If the total number of songs is 382, how many songs does Eliana, her best friend, David and her social study teacher have?
Answer
Step by step explantion:
bsf= 26
Eliana:98
SS teacher=203
David=55
Step-by-step explanation:
m= music
bsf: m
eliana:4m-6
David:2m+3
SS teacher: 2(4m-6)+7
m+4m-6+2m+3+8m-12+7
382=15m-7
7+ +7
389=15m
/15m /15m
m=26
multiply 26 to each one of them
Need help with the first and third problem
In the given graph, expression of function f(x) in following interval of values of x is,
1. In interval -6 ≤ x ≤ -3; F(x) = (3x-1)/2
2. In interval 2 ≤ x ≤ 6; F(x) = -2x+7
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
In the given graph,
In interval -6 ≤ x ≤ -3
we can make equation of line by using two point form of straight line,
y-y₁ = y₂-y₁/x₂-x₁(x-x₁)
points are (-6, 0.5) and (-3, 5)
After putting both the points in the equation
⇒ 2y = 3x-1
Similarly, in the interval 2 ≤ x ≤ 6
for the points (3,2) and (6, -5)
⇒ 2x + y =7
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A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year. If the interest received in one year totaled $2000, how much was loaned at 7%
How much of the $14000 did the bank loan out at 7%
The required loan out of 14000 which is on 7% interest is given as $3800.
What are simultaneous linear equations?Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let part of the loaned amount at 7 % interest be x and another part with 17% interest be y,
A bank loaned out $14000, part of it at the rate of 7% per year and the rest at 17% per year, and the interest received in one year totaled $2000,
According to the question,
x + y = 14000
x = 14000 - y - - - - - (1)
and,
0.07x + 0.17y = 2000 - - - - (2)
Put x from equation 1 in equation 2
Gives,
y = 10200
Now,
x = 14000 - 10200
x = 3800
Thus, the required loan out of 14000 which is on 7% interest is given as $3800.
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5. There are two tall buildings across the street from each other. The floors of the two
buildings are different heights. You are standing on the 10th floor of building A. Across the
street a friend is standing on the 12th floor of building B. Your feet are at exactly the same
height above the ground. If you go to the 15th floor, what floor will be directly across from
your feet in the other building?
According to the information, when I am on the 15th floor of building A, my friend is on the 18th floor of building B.
How to find which floor of building B is my friend?To find the floor number where my friend is in building B while I am on the 15th floor of building A, we must perform the following mathematical operation:
Rule of three
10A - 12B15A - ?B15 * 12 / 10 = 18Based on the above, we can infer that to find the number of the floor where my friend is, we must follow a rule of three. This gives us 18 as a result, that is, he is on that floor number in building B, while I am on 15 in building A.
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The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it.
The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it which is true.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
Similar polygons are those whose perimeter ratios are identical to their respective scale factors. The common fraction of the sizes of two matching sides of two identical polygons is known as a scale factor.
The given statement is true.
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(3x3y)(-14x2y2z) can someone solve this
Answer:
-252 y^3 z
Step-by-step explanation:
easy qs no need steps
What is the standard form of the equation of a quadratic function with roots of 3 and −1 that passes through (1, −10)?
y = 2.5x2 − 5x + 7.5 y = 2.5x2 − 5x − 7.5 y = −2.5x2 − 5x + 7.5 y = −2.5x2 − 5x − 7.5
The quadratic equation with the given zeros is:
y = 2.5*x^2 - 5x - 7.5
How to find the quadratic equation?
For a quadratic equation with the zeros h and k, and a leading coefficient a is:
y = a*(x - h)*(x - k)
Here we know that the zeros are 3 and -1, replacing these values we will get:
y = a*(x - 3)*(x + 1)
Finally, we also know that the quadratic goes through (1, -10)
Replacing these values we will get:
-10 = a*(1 - 3)*(1 + 1)
-10 = a*(-2)*2
-10 = -4a
10/4 = a
5/2 = a = 2.5
Then the quadratic equation is:
y = 2.5(x - 3)*(x + 1)
Expanding that we will get:
y = 2.5*(x^2 - 3x + x - 3)
y = 2.5*x^2 - 5x - 7.5
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please helpppp me!!!
Answer:
K = Fr^2/q1q2
first one option A is the correct
The conjugate of x-14 is?
Step-by-step explanation:
the conjugate is where we change the sign in the middle of the two terms
so we change the - to a +
x + 14 is our answer
Looking for the answer of a to the power of 3 - B to the power of 3
The expression a³ - b³ is not a feasible mathematical operation.
What are index forms?The index form of a number is described as that number that is written in the form of an exponential expression, or single number having another number or variable as its power.
It is a mathematical method of writing numbers that are too large or too small in a more convenient form.
Other names for index forms are standard forms and scientific notation.
Some of the rules for the addition, subtraction or multiplication of index forms are;
In multiplying index forms, the bases must be the same for you to add the powers. In dividing index forms, the bases must be the same for subtraction of the exponential valuesIn the presence of brackets, multiply the powersFrom the information given, we have that;
a³ - b³
From the rules given, this is not mathematically feasible as the bases are not similar.
Hence, the expression is non-feasible
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