The theorem which justifies that two lines are parallel when cut by a transversal k is converse of the alternate interior angles theorem.
Given that two lines m and n are parallel.
We have to find the theorem which justifies that the lines m and n are parallel when cut by a transversal k.
Parallel lines are those lines which do not meet each other at any point on the surface.
If we know that the alternte interior angles are equal,then m and n become parallel to each other.
So the converse of the alternate interior angles theorem correctly justifies that the lines are parallel if cut by a transversal k.
Hence to justify that two lines are parallel if they are cut by a transversal k, we have to use converse of the alternate interior angles theorem.
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Question is incomplete as it should include the following options:
1) converse of the corresponding angles theorem,
2) converse of the alternate interior angles theorem.
3) converse of the same side interior angles theorem,
4) converse of the alternate exterior angles theorem.
Solve 3x − 2 = 3^7
options: 2,5,7,9
The value of x for the given expression is found as 2189/3.
Define the term power of the number?Base number is indeed the factor that is multiplied by itself, and exponent is the how many times its same base number has been multiplied. Power is defined as a base number elevated to the exponent.Exponents and indices are other names for powers. For instance, 8² may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."The stated expression is-
3x − 2 = 3^7
Obtain the value of 3^7 by solving its power.
3x − 2 = 2187
(3x − 2) + 2 = 2187 + 2
3x − 2 + 2 = 2189
3x = 2189
3x / 3 = 2189 / 3
x = 2189/3
Thus, the value of x for the given expression is found as 2189/3.
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The correct question is-
Solve 3x − 2 = 3^7 and find the value of x.
What is the Sin(B)? Need help!
Answer:
Last option: 5/8
Step-by-step explanation:
sin(angle) = opposite / hypotenuse
So, sin(B) = 4/6.4 = 20/32 = 10/16 = 5/8
Hope this helps!
If U = (x:x<10, x EN} is a universal set, A = (x:x is a factor of 6},B
={y: yis aprime number} andC ={z: zis a multiple of 3) are the
subsets of U.
(a) What is the cardinal number set U?
(b) Write(AB)in listing method.
(c) Find(AUB)-Candillustrateitina Venn-diagram by shading.[3]
(d) If C= {4, 7, 8, 9), what will be the relation between AUBUC and
U?
A U B= { If x is a factor of 6 and y is a prime number}, then The collection of elements that belong to either set A or set B, or to both sets A and B, is the union of the two sets A and B.
What is A U B ?[tex]$A=\{x \leq 5 ; x \in N\}$[/tex]
[tex]$: \mathrm{A}=\{1,2,3,4,5\}$\\$\therefore \mathrm{A} \mid=5$[/tex]
The following sets have been entered by you:
A = {(x: If x is a factor, then 6)}
B ={ ( y, where y is a prime number ) }.
A and B are combined to form:
[tex]$A \cup B$[/tex] = { If x is a factor of 6 and y is a prime number}, then
The collection of elements that belong to either set A or set B, or to both sets A and B, is the union of the two sets A and B. We discover togetherness in two steps: STEP 1: Compile a list of each component from each set.
[tex]$$\{(x: \text { xisafactorof } 6), y: \text { yisaprimenumber }\}$$[/tex]
Remove any components that are duplicates in step 2 to obtain:
[tex]$$A \cup B=\{(x: \text { xisafactorof } 6), y: \text { yisaprimenumber }\}$$[/tex]
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Given a pre-image and image, determine if the scale factor is greater than 1, less than 1, or equal to 1.
a. less than 1
b. greater than 1
c. equal to 1
*see attached image for the pre image and image
The scale factor is greater than 1.
Determine if the scale factor is greater than 1, less than 1, or equal to 1?The pre-image and image provided can be used to determine the scale factor between the two shapes.A scale factor is the ratio of the lengths of two corresponding sides of two similar figures.To determine the scale factor, the length of the two corresponding sides must be compared.Looking at the pre-image and image, it can be seen that the pre-image has a longer length than the image.This indicates that the scale factor is less than 1, as the length of the corresponding side in the image is shorter than the pre-image.To confirm this, the lengths of the corresponding sides must be compared.The pre-image has a length of 8 units and the image has a length of 6 units.The ratio of 8/6 is equal to 4/3, which is less than 1.Therefore, the scale factor between the pre-image and image is less than 1.To learn more about the scale factor refer to:
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Is the triangle with sides 4.5 cm 6 cm and 7.5 cm a right triangle?
It is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm because the sum of two sides are greater than third sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm.
To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always grater than the third side.
To check this we firstly add the 4.5 and 6
4.5 + 6 > 7.5
10.5 > 7.5
Now we add 6 and 7.5
6 + 7.5 > 4.5
13.5 > 4.5
Now we add 4.5 and 7.5
7.5 + 4.5 > 6
12 > 6
It is possible to construct a triangle whose sides are 4.5 cm 6 cm and 7.5 cm because the sum of two sides are greater than third sides.
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Solve each system by graphing
As a result, the graph illustrating how one face's side width and diameter are linearly associated is the resolution to the given linear equation problem.
A linear equation is exactly what?One degree is the highest number of levels that can be employed in a linear model. Nonlinearity is the property of any equation having a theoretical extent of at least two. On a map, there is a horizontal line with a straightforward equation. The graph shows the curve that a nonlinear equation produces.
Here,
the side lengths and perimeter of one face are linearly connected.
formula for lines
A regular model is described by the equation y = mx + b.
If b is in fact the y intercept and m is the changing rate, then y and x are variable.
One face's length and perimeter have a linear relationship, as seen by the graph.
As a result, the graph illustrating how one face's edge length or perimeter are linearly associated is the answer to the given linear equation problem.
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Solving Equations
Solve for the variable in each of the following equations. Write your final solution as an equation.
please tell me the answer for each of them
Therefore ,the solution to the given problem of linear equation comes out to be m =1,b =24, z = 21 and r =-7.
Define a linear equation.A function is said to be linear if it can be written algebraically as y=mx+b. The y-intercept is m, and the slope is B. Because y and x are both elements in the previous sentence, it is widely termed to as a 2 different equation system. Linear equations featuring two variables are known as bivariate equations. Two examples of the many applications of linear equations are x + z = 2 , 3z - y + z = 3. If a mathematical equation has the form y=mx+b, where m stands for the slope and b for the y-intercept, it is said to be linear. The equation is represented as Y=mx+b, where m denotes the elevation and b the y-intercept.
Here,
Given :
=> 6m =6
=> m =1
2)
=>b/-8 =-3
=> b =24
3)
=>3/7 * z =9
=> z = 9 * 7 /3
=> z = 21
4)
=> -5/7 *r = 5
=> r =-7
Therefore ,the solution to the given problem of linear equation comes out to be m =1,b =24, z = 21 and r =-7.
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Use a trigonometric ratio to solve for c. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
How do you do trigonometric ratios step by step?Determining Side Lengths Using Trigonometric Ratios.The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.Identify the reference angle, the adjacent leg, the opposite leg, and the hypotenuse.Identify the information you are given and the information you are looking for.Identify the trigonometric ratio that relates the two side lengths from Use cos because it deals with the adjacent angle and the hypotenuse, which is all that we have here.The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).The three basic functions in trigonometry are sine, cosine and tangent. Based on these three functions the other three functions that are cotangent, secant and cosecant are derived.Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.cos (61 degrees) = c/19
plug in cos(61) degrees into your calculator to get .484
484 = c/19
Multiply both sides by 19 to isolate c by itself.
9.20 = c
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Gaya buy 2 orange and 1 cauliflower he pay £2. 00
Eteben buy 4 orange and 1 cauliflower he pay £2. 90
Work out the price of one orange
The price of one orange is £0.45 and one cauliflower is £1.1.
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. For example, the phrase “6 added to some number” can be written as the expression x + 6, where the variable x represents the unknown number.
Let's consider the price of one orange be x and price of one cauliflower is y.
so, from given conditions,
2x + y = 2
y = 2 - 2x - ( 1 )
4x + y = 2.90 - ( 2 )
substitute equation (1) in equation (2),
4x + 2 - 2x = 2.90
4x - 2x = 2.90 - 2
2x = 0.90
x = 0.90 / 2
x = 0.45
now, put the value of x in equation ( 1 ),
y = 2 - 2 × 0.45
y = 2 - 0.9
y = 1.1
Therefore, the price of one orange is £0.45 and one cauliflower is £1.1.
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two times the defference of a number and three
What is the answer please im confused
Answer:
40
Step-by-step explanation:
total: 56+80+40+24 = 200
(80x100)/200
Answer:
What you first want to do is see what all of the numver of students add up to:
80 + 40 = 120
120 + 24 = 144
144 + 56 = 200
So there are a total of 200 votes. 40 of the 200 vote mystery, so you need to find how many times 40 will go into 200. To find this you can just divide.
200/40 = 5
5% prefer mystery books!
Step-by-step explanation:
Hope it helps! =D
I think I did the math wrong, but just by looking Im pretty sure its 5%
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements about the function and its graph are:
The graph of the function is a parabola.
The graph of the function opens up.
The graph contains the point (0, 12)
What is the quadratic function?
A quadratic function is a type of polynomial function of degree 2. It is defined as a function of form f(x) = ax² + bx + c, where a, b, and c are constants and a is not equal to 0. The graph of a quadratic function is a parabola, which is a U-shaped curve that opens up or down, depending on the value of the coefficient a.
The value of f(–10) = x² - 5x + 12 = (-10)² - 5(-10) + 12 = 100 - (-50) + 12 = 62, not 82.
The graph of the function is a parabola.
The graph of the function opens up.
The graph of the quadratic function is a parabola that opens up or down, which depends on the coefficient of x². If the coefficient of x² is positive, the parabola opens up, if it is negative, the parabola opens down. In this case, the coefficient of x² is positive, so the parabola opens up.
The graph contains the point (0, 12)
The graph does not contain the point (20, -8) since the x-coordinate is outside the domain of the function.
Hence, The true statements about the function and its graph are:
The graph of the function is a parabola.
The graph of the function opens up.
The graph contains the point (0, 12)
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6 times a number plus 15 is equal to 6 times a number minus 41
The given statement as an expression is 6x + 15 = 6x - 41
How to represent the statement as an expressionFrom the question, we have the following parameters that can be used in our computation:
A mathematical statement
The mathematical statement is given as
6 times a number plus 15 is equal to 6 times a number minus 41
Represent the number with x
So, we have the following representation
6 times x plus 15 is equal to 6 times x minus 41
is equal to implies =
So, we have:
6 times x plus 15 = 6 times x minus 41
Plus implies +, minus implies - and times *
This gives
6x + 15 = 6x - 41
The question does not require that we solve the expression
So, we leave it at 6x + 15 = 6x - 41
Hence, the required expression is 6x + 15 = 6x - 41
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What is factor in Grade 8?
So on solving the provided question we can say that factors 8 = 1,2,4,8 factor 20 = 1,2,4,5,10,20
what is prime factor?Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.
here,
factors 8 = 1,2,4,8
factor 20 = 1,2,4,5,10,20
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Is there a trick for 8 times tables?
One common trick for memorizing the 8 times table is to pair it with the 4 times table.
For example, 8 x 4 = 32, so 8 x 5 = 40 because 5 is one more than 4. Similarly, 8 x 6 = 48 because 6 is two more than 4, and so on. Another trick is to think of it as 8 x 10 = 80 and then subtract 8. For example, 8 x 7 = 80 - 8 = 72.
The eight times table trick states that when you multiply eight by a number between one and five, the result always begins with a digit one lower than the number from one to five. The answer begins with a digit that is two less than the number from 6 to 10 when multiplying 8 by a number between 6 and 10.
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What is a pattern rule example?
An example of a pattern rule is "add 3" which means that to find the next term in a sequence, you add 3 to the previous term.
What is patter rule?A pattern rule is a mathematical relationship used to find the value of each term in a sequence. To describe certain sequences, a pattern rule can be established. This is an algebraic equation that enables you to quickly find the value of a term in a sequence using its rank.
To write a rule for a sequence, you need to identify the pattern. This involves looking at the differences between the numbers and seeing if there is a pattern of increasing or decreasing numbers. Once you have identified the pattern, you can then write a rule that expresses that pattern.
Examples of pattern sequences include the Fibonacci sequence (1,1,2,3,5,8,13,21,34, etc.), the even numbers (2,4,6,8,10, etc.), and the multiples of 3 (3,6,9,12,15, etc.).
To describe the pattern of a sequence, you need to look at the differences between the numbers and the pattern of increases or decreases. For example, in the Fibonacci sequence, the pattern is that each number is the sum of the two numbers before it so 1+1=2, 1+2=3, 2+3=5, etc.
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2 If the side lengths of an 8-inch square are doubled, which of the following statements about its area is true?
A the new area will be 16 times the old area
B) the new area will be 4 times the old area
c) the new area will be 2 times the old area
D) the new area will be 9 times the old area
Answer:
B 4 times
Step-by-step explanation:
since the area is
side length × side length,
any doubling of the side length is included twice in this multiplication.
2×2 = 4
and so, answer B is correct. the new area will be 4 times the old one.
Solve |10x + 50| = 0.
Answer:
x = -5
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ |10x + 50| = 0
Then the value of x will be,
→ |10x + 50| = 0
→ 10x + 50 = 0
→ 10x = 0 - 50
→ 10x = -50
→ x = -50/10
→ [ x = -5 ]
Hence, the value of x is -5.
The Darnell Company had a catered dinner. The cost of the dinner was $730. It tipped the caterers 18%. What was the total cost of the dinner, including the tip
Total cost of dinner including tip = $861.40
What is percentage?In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Given
Cost of the dinner = $730
Amount tipped to the caterers = 18% of 730
= 18/100 × 730
= $131.40
Total cost of dinner = 730 + 131.40
Total cost of dinner = $861.40
Hence, $861.40 is the total cost of the dinner including tip.
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Do sequences start at 0 or 1?
Sequences can start at either 0 or 1, depending on the specific sequence and the conventions used.
In mathematics, there are two main ways to number the elements of a sequence: zero-indexing and one-indexing. In zero-indexing, the first element of a sequence is assigned the index 0, the second element is assigned the index 1, and so on. This is the standard convention used in computer science and programming.
On the other hand, in one-indexing, the first element of a sequence is assigned the index 1, the second element is assigned the index 2, and so on. This is the standard convention used in mathematics and many other fields.
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HELP HELP 15 POINTSSSSSS
Answer:
I believe B, E, and F is the answer
Expand and combine like terms.
(9c^2+c^6)(9c^2-c^6
Answer: -c^12+9c^4
Step-by-step explanation:
Answer: 81 c^4 - c^12
Step-by-step explanation:
(9c^2+c^6)(9c^2-c^6)
Step-by-step explanation: (9c^2+c^6)(9c^2-c^6)
This is the difference of squares
(a+b) (a-b) = a^2 - b^2
(9c^2) ^2 - ( c^6)^2
81 c^4 - c^12
What is a 2 3 aspect ratio?
A 2 3 aspect ratio is an image size format that refers to the proportion of width to height.
What is ratio?Ratio is a comparison between two or more quantities expressed as a fraction, or a set of relative quantities. It is used to compare the size of one number to another, or to compare changes over time. Ratios can be expressed in words, as fractions, or as decimals. Ratios are an important concept in mathematics, used to analyze data and solve problems.
It is commonly used in photography and video and is expressed as two numbers separated by a colon. The first number represents the width and the second number represents the height. For example, a 2 3 aspect ratio would be expressed as 2:3, meaning that the width is twice as wide as the height. This aspect ratio is also known as the "Golden Ratio" and is often used for print and digital media.
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The temp this week is increasing by 8 deg each day. How much has the temp risen after three weeks?
Answer:
168 deg
Step-by-step explanation:
Assuming the increase in temperature in constant during the 3 weeks, we do the following calculations-
8 deg * 7 = 56 deg / week (Since there are 7 days in a week)
56 * 3 = 168 deg in 3 weeks.
3
At a stream cleanup, the ratio of
adult volunteers to child volunteers
is 7:4. If 20 children volunteer, how
many adults are there?
Answer:
35
Step-by-step explanation:
a=adult c=children
7a:4c
?a:20c
20 is 5 times more than 4 which I found by doing 20/4
So now we multiply 7 by 5 to get 35
35a:20c
There are 35 adults
Write the quadratic equation in general form.
40x² = 30
The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].
Now, According to the question:
What is Quadratic Equation?
The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:
ax² + bx + c = 0
where x is the unknown variable and a, b and c are the constant terms.
The given equation is :
40x² = 30
40x² - 30 =0
Common factor:
10(4x²- 3) = 0
Divide both sides by the same factor
10(4x²- 3) = 0
4x²- 3 = 0
Use the quadratic formula:
x = -b±[tex]\sqrt{b^2-4ac}[/tex]/ 2a
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula:
4x²- 3 = 0
a = 4
b = 0
c = -3
x = -0±[tex]\sqrt{0^2-4(4)(-3)}[/tex]/ 2(4)
By simplify:
x = ±[tex]\frac{4\sqrt{3} }{8}[/tex]
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x = [tex]\frac{4\sqrt{3} }{8}[/tex]
x = -[tex]\frac{4\sqrt{3} }{8}[/tex]
Rearrange and isolate the variable to find each solution
x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex]
Hence, The solution of the equation is x = [tex]\frac{\sqrt{3} }{2}[/tex] and - [tex]\frac{\sqrt{3} }{2}[/tex].
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1/2+(-2/5) times ( -5/7) + 1/14
The value of the multiplication of the given fractions [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.
What are fractions?In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.
What is multiplication of factors?A fraction multiplied by another fraction, an integer, or a set of variables is referred to as a fraction. The steps for multiplying fractions are as follows:
Add the numerator to the numerator to multiply. Add the denominator to the denominator and multiply. If necessary, simplify the fractions.
The multiplication of the given numbers is:
[tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} ) \\\\(\frac{5-4}{10} ) * (\frac{-10 + 1}{14} )\\\\\frac{1}{10} * \frac{- 9}{14} \\\\\frac{-9}{140}[/tex]
Hence, value of the multiplication of the given fractions [tex](\frac{1}{2} - \frac{2}{5}) * (- \frac{5}{7} + \frac{1}{14} )[/tex] is -9/ 140.
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I’ll give brainliest :)
Write the rule for the linear function
Answer:
y = f(x) = a + bx
Step-by-step explanation:
Step-by-step explanation: A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the gradient of the line, and b represents the y-axis intercept (which is sometimes called the vertical intercept).
3. Give two examples of four-sided figures that have two acute angles
and two obtuse angles. Draw pictures in your explanation.
Answer:
follow me if this helped
Step-by-step explanation:
A kite is a four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.
[asy]
size(5cm);
draw((0,0)--(1,1.5)--(3,1)--(2,-0.5)--cycle);
draw((1,1.5)--(2,-0.5));
label("$A$",(0,0),SW);
label("$B$",(1,1.5),NE);
label("$C$",(3,1),SE);
label("$D$",(2,-0.5),NW);
[/asy]
A bow tie shape is another four-sided figure that has two acute angles and two obtuse angles. The angles are formed by the intersection of the diagonals, which are not parallel.
[asy]
size(5cm);
draw((0,0)--(1,1.5)--(2,0)--(1,-1.5)--cycle);
draw((1,1.5)--(1,-1.5));
label("$A$",(0,0),SW);
label("$B$",(1,1.5),NE);
label("$C$",(2,0),SE);
label("$D$",(1,-1.5),NW);
[/asy]
53 63 55 56 62 54 59 60 53 61 88 IQR
The interquartile range (IQR) of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.
IQR stands for Interquartile Range, which is a measure of the variability of a dataset. It is defined as the difference between the third quartile (Q3) and the first quartile (Q1). To calculate the IQR, you first need to order the data set and find the median (middle value) of the dataset, and the Q1 and Q3.
Here is the dataset you provided, in order:
53 53 53 54 55 56 59 60 61 62 63 88
The median of the dataset is: (56+59)/2 = 57.5
Q1 is the median of the lower half of the dataset: (53+53+54)/3 = 53
Q3 is the median of the upper half of the dataset: (60+61+62+63)/4 = 61.25
Now you can calculate the IQR:
IQR = Q3 - Q1 = 61.25 - 53 = 8.25
So the interquartile range of this dataset is 8.25, it means that half of the observations fall between 53 and 61.25, while half of the observations fall outside of that range.
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The correct question should be:
"Find the interquartile range (IQR) of the following dataset
53 53 53 54 55 56 59 60 61 62 63 88"