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graph the function f: f(x)=√x²-4 x+4 and determine its range and discuss its monotony
Range of function is {5, 4, 3, 2, 1, 0,1} and the function is monotonous.
what is function?
A function is a mathematical expression that state the relationship between an independent variable and a dependent variable. The value of independent variable is called domain and the value of dependent variable is called range.
What is the range of the function bellow?
given, a function f(x) = √ (x² - 4x +4)
now for every input value of x we will get an output value for f(x).
we select the domain of function as x = {-3, -2, -1, 0, 1, 2, 3}
when we put the x value in the function, we get f(-3) = √[(-3²) - 4×(-3)+4]
f(-3) = √25 =5
similarly, f( -2) = 4
f(-1) = 3
f(0) = 2
f(1) = 1
f(2) =0
f(3) = 1
the range of function is {5, 4, 3, 2, 1, 0,1}
The range of function indicates that it is neither increasing nor decreasing.
hence the function is a monotonous function.
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How many answers are there in inequality?
There is no single answer to this question as there are many different types of inequalities and each one can have a different number of solutions.
Number of Solutions to InequalitiesInequalities are mathematical statements that compare two values or expressions using an inequality sign. These signs can be:
Greater than (>) Less than (<)Greater than or equal to (>=)Less than or equal to (<=)Depending on the type of inequality and the values involved, the number of solutions can vary.
For example, a linear inequality with two variables will have an infinite number of solutions as the two variables can take on any real number value.
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Find the surface area of the rectangular prism with the following dimensions:
length = 9 m
height = 10 m
width = 12 m
636 m squared
710 m squared
Streak Boost.
630 m squared
1080 m squared
Solving the the provided question we can say that here the surface area will be SA = 2(lb + lh + bh) = 2(108 + 120 + 90) = 636 cm sq.
what is surface area ?An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).
here,
length = 9 m
h = 10
w = 12
SA = 2(lb + lh + bh)
= 2(108 + 120 + 90)
= 636 cm sq.
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Help frrr thankkk you
Answer:
14
Step-by-step explanation:
What are three equivalent ratio to 18:21
The 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.
What are the ratios?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.
A proportion is an equation that sets two ratios at the same value.
For instance, you could write the ratio as follows: 1: 3 if there is 1 male and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
So, we have the ratio:
18:21
3 more equivalent ratios will be:
18/21 = 6/7
18/21 * 2/2 = 36/42
18/21 * 5/5 = 90/105
Therefore, the 3 more equivalent ratios to the given ratios 18:21 are 6/7, 36/42, and 90/105.
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What is the additive inverse of 9 /- 11?
The additive inverse of 9/-11 is 11/-9, and this can be calculated using the formula of multiplying the number by -1.
The additive inverse of any number is the opposite number of that number. The formula for finding the additive inverse is to multiply the number by -1. To find the additive inverse of 9/-11, we can use the formula and multiply -11 by -1. This gives us 11/-9. This means that the additive inverse of 9/-11 is 11/-9.
To explain the calculation in more detail, an additive inverse is the opposite of any number. This means that two numbers that are opposite of each other add up to zero. For example, the additive inverse of 3 is -3, and when 3 and -3 are added together, the result is 0.
The formula for finding the additive inverse is to multiply the number by -1. This means that the additive inverse of any number is the same number multiplied by -1. Applying this formula to 9/-11, we can multiply -11 by -1 to get the additive inverse. This gives us the result of 11/-9, meaning that the additive inverse of 9/-11 is 11/-9.
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What is the total number of years that must pass before only 25. 00 grams of an original 100. 0-gram sample of c-14 remains unchanged?.
The total number of years that must pass before only 25 grams of an original 100-gram sample of C-14 remains unchanged is approximately 5,730 years.
This is because C-14 has a half-life of approximately 5,730 years. Half-life is the amount of time it takes for half of a sample of a radioactive element to decay. Therefore, after 5,730 years, half of the original sample of 100 grams of C-14 will have decayed, leaving 50 grams remaining.
After another 5,730 years, half of the remaining sample (25 grams) will have decayed, leaving only 25 grams remaining. This means that it takes 5,730 years for half of the sample to decay and another 5,730 years for half of the remaining sample to decay, resulting in a total of 5,730 x 2 = 11,460 years for the entire sample to decay to 25 grams.
It is important to note that C-14 dating is a method of determining the age of organic materials, such as wood, bones, and teeth, by measuring the amount of C-14 remaining in the sample. This technique is widely used in archaeology, geology, and other fields to date materials that are thousands of years old.
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ASAP 20 points!!
Rectangle A, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-6, -4),A(−6,−4),A, left parenthesis, minus, 6, comma, minus, 4, right parenthesis, comma B(-4,-4)B(−4,−4)B, left parenthesis, minus, 4, comma, minus, 4, right parenthesis, C(-4, -2)C(−4,−2)C, left parenthesis, minus, 4, comma, minus, 2, right parenthesis, and D(-6, -2)D(−6,−2)D, left parenthesis, minus, 6, comma, minus, 2, right parenthesis.
What is the perimeter of rectangle A, B, C, D?
______units
The perimeter of the rectangle ABCD in the coordinate plane is 8 units
What is an equation?An equation is an expression that shows the relationship between variables and numbers.
The distance between two points in the coordinate plane is given by:
[tex]Distance=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
The vertices of the rectangle is A(-6, -4), B(-4, -4), C(-4, -2) and D(-6, -2). Hence:
[tex]AB=\sqrt{(-4-(-4))^2+(-4-(-6))^2}=2\ units \\\\BC=\sqrt{(-2-(-4))^2+(-4-(-4))^2}=2\ units[/tex]
Perimeter of ABCD = 2(AB + BC) = 2(2 + 2) = 8 units
The perimeter is 8 units
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Find the missing values in the ratio table. Then write the equivalent ratios in the order they appear in the table.
Flour (cups)
Oats (cups)
34
13
23
3
1
Missing values: 2 cups, 4 cups, 9 cups,Equivalent ratios: 34:13, 23:3, 1:6, 2:4, 13:9
Find the missing values in the ratio table?The missing value in the ratio table is 4.The equivalent ratios in the order they appear in the table are 34:13, 23:3, and 1:6.This is an example of direct proportion, which is a type of proportional relationship where two quantities vary in the same proportion.Direct proportion states that if one quantity increases, the other will increase by the same factor.It can be expressed as y = kx, where k is the constant of proportionality.For example, if you increase the number of cups of flour by a certain factor, the number of cups of oats must increase by the same factor in order to maintain the same ratio.The missing value in the ratio table is 4. The equivalent ratios in the order they appear in the table are 34:13, 23:3, and 1:6. This theory is called proportionality, which states that two ratios are equal if they both represent the same relationship between two numbers.Proportionality can be written as a fraction, a decimal, a percent, or a ratio. It is often used to solve for missing values in ratio tables. For example, if we know that the ratio of flour to oats is 34:13, and we want to find the amount of oats needed for 34 cups of flour, we can use proportionality to solve for the missing value. In this case, the number of oats needed would be 13 cups.To learn more about Proportionality refer to:
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2. Which equation has the solution x = -1? A 2x1 = 3x - 2
B 8x + 7 = 9x - 8
C -5x -4 = 4x + 3
D 7x+8 = -6x - 5
The equation that has the solution x = -1 is D. 7x+8 = -6x - 5
To find the solution of an equation, we need to find the value of the variable that makes the equation true. In this case, we need to find the value of x that makes the equation 7x+8 = -6x - 5 true.
We can start isolating the x variable by adding or subtracting the same terms on both sides of the equation.
D. 7x+8 = -6x - 5
13x = -13
x = -1
So the solution of the equation is x = -1
We can check if this is the solution by substituting it back in the equation. If the equation is true, both sides will be equal when x is -1.
7x+8 = -6x - 5
7*-1 + 8 = -6*-1 -5
-7+8 = 6 -5
1 = 1 (true)
Therefore, D. 7x+8 = -6x - 5 has x = -1 as the solution.
Point b 4,-16 is dilated by a scale factor of 3/4 to create b’
Answer:
Step-by-step explanation:
Select the correct answer. Which two of the functions shown here have identical graphs and why? A. f and g, because the log of a quotient is the quotient of the logs B. g and j, because the quotient of two logs is the sum of the logs C. f and h, because the log of a quotient is the difference of the logs D. g and h, because the quotient of two logs is the difference of the logs
F and h, because the log of a quotient is the difference of the log. Logs work that way when you subtract one log from another you can rewrite it as a fraction. The correct is option C.
What do logs mean?
Logarithm is a power to which a range of should be raised for you to get a few different wide varieties as an example the bottom ten logarithms of a hundred is two because ten raised to the electricity of is one hundred: log a hundred = 2.
There are three common types of logarithms such as:
Common logarithms: where the base is 10 Binary logarithms: where the base is 2 Natural logarithms: where the base is e ≈ 2.71828Therefore logarithm is the mathematical expression used to answer the question.
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Let U represent the set of people in a certain community who were asked if they subscribe to an information source.Let D ={ x ∈ U | x subscribes to The Daily Informer }andN ={ x ∈ U | x subscribes to News Magazine }(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.a) N ∪ Db) ( N c ∩ D ) ∪ ( N ∩ D c )c) N c ∩ Dd) ( N ∩ D )ce) ( N c ∪ D ) ∩ ( N ∪ D c )
The people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).
What are sets?A set is like a bunch of different stuff put together; it includes elements or members, which can be anything mathematical, like numbers, symbols, shapes, variables, or even other sets.
So, we have:
N = { x ∈ U | x subscribes to News Magazine }
D = { x ∈ U | x subscribes to The Daily Informer }
As, N∩D ≠ ∅.
It looks like a decent amount of people surveyed only have a subscription to News Magazine and not any other magazines.
= Subscribe to News Magazine and not Daily Informer
= N ∩ D c
Out of the people surveyed, 4 of them only subscribe to the Daily Informer.
= Subscribe to Daily informer and not subscribe to News Magazine
= D ∩ N c
Out of the people surveyed, 4 of them only subscribe to the Daily Informer.
= Subscribe to News Magazine and not subscribe to Daily Informer or subscribe to Daily informer and not subscribe to News Magazine
= ( N ∩ D c ) ∪ ( D ∩ N c )
= ( N c ∩ D ) ∪ ( N ∩ D c )
Therefore, the people who only get news from one of the two sources we surveyed are in the group represented by set (B) ( Nc∩D) ∪ (N∩Dc).
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Complete question:
Let U represent the set of people in a certain community who were asked if they subscribe to an information source. Let D ={ x ∈ U | x subscribes to The Daily Informer } and N ={ x ∈ U | x subscribes to News Magazine } (Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.
a. N ∪ D
b. ( N c ∩ D ) ∪ ( N ∩ D c )
c. N c ∩ D
d. ( N ∩ D )c
e. ( N c ∪ D ) ∩ ( N ∪ D c )
Describe the possible lengths of the third side of the triangle given that the lengths of the other two sides are 5 inches and 12 inches.
( )in. < x < ( )in.
To satisfy the lengths of the two sides of the triangle given in the question, the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.
What are triangles?A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon. There are three sides and three angles in every triangle, some of which may be the same.
How are the sides of the triangles related?According to the law of the sides of a triangle, the lengths of any two of the triangle's sides added together are always more than the length of the third side. The triangle inequality theorem is another name for this condition.
If we know the lengths of two sides of a triangle, we can use the "triangle inequality theorem" to determine the possible lengths of the third side. The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given that the lengths of two sides of a triangle are 5 inches and 12 inches, the length of the third side must be:
Greater than 0 inches
Less than the sum of the other two sides (5 inches + 12 inches = 17 inches)
Greater than the difference between the other two sides (abs(5 inches - 12 inches) = 7 inches)
So the possible lengths of the third side are any value greater than 7 inches and less than 17 inches but not equal to 5 or 12 inches.
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put this into standard form y=3x+2
3x-y=2 i hope my answer helped
How do you determine if the triangle is acute obtuse or right?
c² = a² + b² then the triangle is a right-angle triangle.
If c² > a²+ b² then it is an obtuse triangle.
If, C²< a²+ b². Then the triangle is an acute triangle
An acute angle is an angle whose measure is less than 90°. That is, in a pair of intersecting non-perpendicular lines, the smaller of the angles are acute.
A right angle is an angle whose measure is equal to 90°. That is the measure of the angles of perpendicular lines.
An obtuse angle is an angle whose measure is greater than 90°. That is, in a pair of intersecting non-perpendicular lines, the larger of the angles are obtuse.
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What is a table of 10?
Therefore , as a result after answering the question, we may state that the numbers in the tables of ten are 10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.
What is a table?A set of numbers who represents the result of a calculation with several inputs is the concept of a mathematical table. data that is organized into rows and columns and contains numbers and descriptions. It is simple to recollect the table and ten pattern. The numbers are in the following order: 10, 20, 30, 40, 50, 60, 70, 80, 90, etc. Value tables are used to visualize connections between data elements. The values table can be used in your science lesson. To store data and look for patterns in that data, scientists and researchers utilize tables of values. Forecasting then makes use of this pattern.
Here,
table of ten are as follows:
10, 20, 30, 40, 50, 60, 70, 80, 90, and 100.
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Okay, I'm very confused about this one.
100,60,20 are the values in the triangle.
What is known as a triangle?
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to 180 degrees in total.
The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. The triangle's three angles add up to a total of 180 degrees.
5x+ 3x + x = 180°
9x = 180
x = 180/9
x = 20
5x = 5 * 20 = 100
3x = 3 * 20 = 60
x = 20
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A cientit ue a ubmarine to tudy ocean life. She begin at ea level, which i an elevation of 0 feet. She travel down 4. 2 feet. She then travel directly up 3. 4 feet. Next, he decend a econd time, 10 feet
According to the given angle of elevation, she now ascend to get back to sea level at 111.6 feet.
The term in angle of elevation in math is defined as an angle that is formed between the horizontal line and the line of sight.
Here we have given that a scientist uses a submarine to study ocean life.
Here we also know that She begins at sea level, which is an elevation of o feet.
As we all know that she descends 28.7 feet and then She ascends 9.9 feet.
Finally she descends a second time, 92.8 feet.
Now, she is at the level of,
In first stage, she is at the level of
=> 28.7 - 9.9
=> 18.8
Then she descends at the level of
=> 18.8 + 92.8
=> 111.6
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If θ is an angle in standard position and its terminal side passes through the point (-20,21), find the exact value of \sin\thetasinθ in simplest radical form.
The exact value of the sine of the angle is 21/29
How to determine the exact value of sineFrom the question, we have the following parameters that can be used in our computation:
(x, y) = (-20, 21)
We start by calculating the value of r using
r = √(x² + y²)
So, we have
r = √(-20² + 21²)
Evaluate
r = 29
Also, we have the following equation on a Cartesian plane
sin(θ) = y/r
So, we have
sin(θ) = 21/29
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kyle has been playing basketball for 3 1/2 years longer than his sister. write an equation that shows how many years y kyle has been playing if his sister has been playing x years
A hockey team of 14 players needs to choose 3 players to help devise a game plan. How many different combinations of players can be chosen?
The number of ways the players can be selected is given by combination and the value of C = 364 ways
What are Combinations?The number of ways of selecting r objects from n unlike objects is given by combination :
ⁿCₓ = n! / ( ( n - x )! x! )
where
n = total number of objects
x = number of choosing objects from the set
Given data ,
Let the number of ways of selecting players be C
Let the total number of players n = 14 players
The number of players to be chosen x = 3 players
So , the combination is
ⁿCₓ = n! / ( ( n - x )! x! )
Substituting the values in the equation , we get
¹⁴C₃ = ( 14 )! / ( 14 - 3 )! 3!
On simplifying the equation , we get
¹⁴C₃ = ( 14 )! / ( 11 )! 3!
¹⁴C₃ = ( 14 x 13 x 12 ) / ( 3 x 2 x 1 )
¹⁴C₃ = 14 x 13 x 2
¹⁴C₃ = 364 ways
Hence , the combination of ways is 364 ways
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a. What is the volume of this piece of lumber in cm³?
b. What is the volume of this piece of lumber in m³?
Answer:
Step-by-step explanation:
a.v = 10 * 5 * 7 = 350cm^3
b.because 1m^3=1000dm^3=1000000cm^3
so 1cm^3=0.000001m3
350cm^3=0.00035m^3
The solve by substitution calculator allows to find the solution to a system of two or three equations in both a point form and an equation form .of the answer.true or false
Given statement is True.
A system of equations can be represented in different forms, such as point form (showing the x and y values that make the equations true) or equation form (showing the equations in standard form, with variables on one side and constants on the other). A solve by substitution calculator can be used to find the solution to a system of two or three equations in both point form and equation form of the answer.
The process of solving a system of equations by substitution involves isolating a variable in one equation and then substituting it into the other equation(s) to find the values of the other variable(s). The calculator can display the solution in point form by showing the values of x and y (or x, y, and z for a system of three equations) that make the equations true. It can also display the solution in equation form by showing the equations with the variable(s) replaced by the values found in the solution.
In conclusion, solve by substitution calculator can find the solution to a system of two or three equations in both point form and equation form of the answer, it can be a helpful tool for solving systems of equations.
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What is the solution of the pair of linear equations 37x 41y 70 41x 37y 86?
The solution of the pair of linear equations 37x+41y=70, 41x+37y=86
x=5 andy=-3
An equation that has the highest degree of 1(one) is known as a linear equation.
The standard form of linear equations in two variables is expressed as
Ax + By = C;
where A, B, and C are any real numbers,
x and y are the variables.
consider
37x+41y=70 ----------(1)
41x+37y=86 -----------(2)
By, Adding both the equations
78x+78y=156
taking 78 common
78(x+y)=156
x+y=2 --- (3)
sub. both the eq. so the sign will be changed
37x+41y=70
41x+37y=86
(-) (-) (-) {changing da signs}
-4x+4y= -16
taking -4 common
-4(x-y)=-16
x-y=8 --- (4)
now from (3) and(4)
x+y=2
x-y=8
Again adding (3) and (4)
2x=10
x=5
substitute x value in (3)
5+y=2
y=-3
so, values of x=5 nd y= -3
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Solve the system of equations using substitution. y = −2x + 14x + 2y = −1 a. (0, −3) b. (−3, 0) c. no solution d. infinitely many solutions
The system of equations y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].
What is algebraic equation ?
An algebraic equation is a mathematical expression that contains one or more variables, and an equal sign. The goal is to find the value or values of the variables that make the equation true. Algebraic equations can take many forms, such as linear equations, quadratic equations, polynomial equations, and more.
y = −2x + 14
x + 2y = −1
We can use the first equation to solve for y in terms of x:
y = −2x + 14
Now we can substitute this expression for y into the second equation,
x + 2(-2x + 14) = -1
x + (-4x + 28) = -1
-3x = -29
x = 9/3
Now we can substitute this value for x back into the first equation to find y,
y = -2(9/3) + 14 = -6/3 + 14 = -2 + 14 = 12
Hence , The system of equations y = −2x + 14x + 2y = −1 using substitution is [tex](\frac{9}{3} ,12)[/tex].
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What is 10535 divided by 86
Answer:
Step-by-step explanation:
Answer:
122.5
Step-by-step explanation:
First, multiply 86 by 122.
Then subtract 10492 from 10535.
Add a decimal point then add 0.
Multiply 86 by 5 and you get your answer.
what is -8r=64 step by step
P 18 The circle C has equation (x-3)² + (y + 3)² = 52. The baselines, and are tangents to the circle and have gradient a Find the points of intersection, P and Q, of the tangents and the circle. b Find the equations of lines and 12, giving your answers in the form ax + by + c = 0.
Answer:
a) To find the points of intersection, P and Q, of the tangents and the circle, we can use the fact that a tangent line is perpendicular to the radius at the point of tangency. Therefore, the slope of the tangent line is the negative reciprocal of the slope of the radius.
We know that the equation of the circle is (x-3)² + (y + 3)² = 52. To find the slope of the radius, we can differentiate the equation of the circle with respect to x and y.
dx/dt = 2(x-3) and dy/dt = 2(y+3)
We know that the slope of the tangents is a. So, the slope of the radius is -1/a
Now we can use the point slope form of a line to find the equation of the tangent line.
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
We can substitute the point of tangency, which is on the circle, into the point slope form.
y + 3 = -1/a(x - 3)
We can now substitute the point (3, -3) and the slope -1/a into the point slope form to find the equation of the line
y + 3 = -1/a(x - 3)
y = -1/a
Step-by-step explanation:
Not sure if this helps, hope it does!
A class was interested in the amount of time it takes them to travel to and from school. They gathered data from a random sample of 200 students in the school and wanted to create an appropriate graphical representation for the data. Which graphical representation would be best for their data?
Circle graph
Bar graph
Line plot
Box plot
Answer: The best graphical representation for their data would be a box plot. A box plot, also known as a box and whisker plot, is a useful tool for displaying the distribution of a dataset, including the minimum, first quartile, median, third quartile, and maximum values. This type of plot is particularly useful for comparing the spread of different sets of data, which would be useful for the class to compare the time it takes different students to travel to and from school.
Step-by-step explanation:
Answer:a box plot i did the exam
Step-by-step explanation: i did the exam.