The total number of outcomes that are possible are given as follows:
48 outcomes.
How to obtain the number of outcomes?The number of outcomes for each case is obtained using the Fundamental Counting Theorem, with the multiplication of the number of outcomes for each trial.
The number of outcomes in each step is given as follows:
Step 1: 1 + 5 = 6 outcomes.Step 2: 4 + 3 + 1 = 8 outcomes.Hence the total number of outcomes that are possible are obtained as follows:
N = 6 x 8
N = 48.
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I really really need help understanding this geomtry packet.
Based on the definition of congruent triangles, the measures are:
4. m<R = 75°
5. XY = 6
6. m<X = 55°
7. m<S = 50°
What are Congruent Triangles?Congruent triangles are two triangles that have the same size and shape. This means that all corresponding sides and angles of the two triangles are equal in measure.
Since triangles QRS are congruent to each other, therefore, their corresponding parts will be equal. Thus:
4. m<R = 180 - 55 - 50
m<R = 75°
5. XY = QR = 6
6. m<X = m<Q
m<X = 55°
7. m<S = m<Z
m<S = 50°
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Please help me with this question.
The solution to the initial value problem using the method of Laplace transforms is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
How to determine the initial value problemFrom the question, we have the following parameters that can be used in our computation:
y" - 3y' - lOy = 0, y(0) = 1, y'(0) = 12
Let L{y(t)} = Y(s),
Take the Laplace transform of both sides, we have:
s^2Y(s) - sy(0) - y'(0) - 3sY(s) + 3y(0) + 10Y(s) = 0
Using initial conditions y(0) = 1 and y'(0) = 12, we get:
s^2Y(s) - s - 12 - 3sY(s) + 3 + 10Y(s) = 0
Solving for Y(s), we have:
Y(s) = (s + 12)/(s^2 + 3s + 10)
Taking inverse Laplace transform of Y(s), we have:
y(t) = L^-1{Y(s)}
y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
Hence, the solution is y(t) = (1/3)e^3t - (4/3)e^-2t + 4e^2t
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The equation of the least-squares regression line for predicting icicle length, in centimeters, from time, in minutes, is
icicle length=-1.93 +0.173xtime
There are 2.54 centimeters in an inch. If length were measured in inches, what would the slope of the new regression line be?
Enter your answer to three decimal places.
The slope of the new regression line with length measured in inches would be 0.068 inches/minute.
Calculating slope of the new regression lineThe slope of the regression line for predicting icicle length, in centimeters, from time, in minutes, is 0.173 cm/minute.
To convert this to inches, we need to multiply the slope by the conversion factor from centimeters to inches, which is 2.54 cm/inch:
0.173 cm/minute x (1 inch/2.54 cm) = 0.068 inches/minute
So, the slope of the new regression line with length measured in inches would be 0.068 inches/minute.
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In the school garden Winston,Sam and Chris grew carrots.They pulled up 60 carrots and shared them out in the ratio of their familiest. Winston lives in a family of four,Sam in a family of three and Chris in a family of five.
How many carrots did :
Winston recieve:
Sam recieve:
Chris recieve:
Answer:
winston receives 20carrots
Sam receives 15carrots
Chris receives 25carrots
Step-by-step explanation:
number of carrots are 60
Winston has a family of 4
Sam lives in a family of 3
Chris lives in a family of 5
total =5+3+4=12
thus
Winston - 4/12×60=20 carrots
Sam= 3/12×60=15 carrots
Chris=5/12×60=25 carrots
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Subtract.
14 10/12 −9 4/12
Choose 3 values that would make this inequality true. 8n + 4 ≤ 2
3
6
13
2
5
14
1
The three values are not in the given list of options
How to determine the three valuesFrom the question, we have the following parameters that can be used in our computation:
8n + 4 ≤ 2
Subtract 4 from both sides of the expression
So, we have
8n ≤ -2
Divide both sides by 8
This gives
n ≤ -0.25
This means that the values do not exceed -0.25
None of the valies in the option meet this condition
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PLS HELP!!! Find a function of the form
Step-by-step explanation:
that's your answer im hoping so
Find the limit if the limit exists:
The value of each limit functions are:
72-√512-51/41/513 and 1/2√xLet's try to solve each problem we have:
1. [tex]\lim_{x \to \--3} 2x^2+4x+1[/tex]
= 2(-3)² + 4(-3) +1
= 2(9) + 4(-3) + 1
= 18 - 12 + 1
= 7
2. [tex]\lim_{x \to \-3} \sqrt{x+1}[/tex]
= √(3+1)
=√4 = 2
3. [tex]\lim_{x \to \-3} \frac{\sqrt{x+2} }{x-4}[/tex]
= √(3+2) / (3-4)
= √5 / (-1) = - √5
4. [tex]\lim_{x \to \-2} \frac{x^3-8}{x-2}[/tex] -->hint: use L'hospital rule
= [tex]\frac{(x^3-8)'}{(x-2)'}[/tex]
= 3x² / 1
= 3(2)²
= 12
5. [tex]\lim_{x \to \--1} \frac{2x^2-x-3}{x+1}[/tex]
= [tex]\lim_{x \to \--1} \frac{(2x-3)(x+1)}{(x+1)}[/tex]
= 2(-1) - 3
= -5
6. [tex]\lim_{x\to \-3} \frac{\sqrt{x+1}-2 }{x-3}[/tex]
= [tex]\frac{(\sqrt{x+1}-2)' }{(x-3)'}[/tex]
= 1/2√(x+1)
= 1/2√(3+1)
= 1/4
7.[tex]\lim_{x \to \-0} \frac{sin x}{5x}[/tex]
= [tex]\lim_{x \to \-0} \frac{sin x}{x} .\frac{1}{5}[/tex]
= 1/5 ([tex]\lim_{x \to \-0} \frac{sin x}{x}[/tex])
= 1/5 (1)
= 1/5
8. [tex]\lim_{x \to \pi/2}\frac{cosx}{cotx}[/tex]
= [tex]\lim_{x \to \pi/2}\frac{cosx}{\frac{cosx}{sinx} }[/tex]
= [tex]\lim_{x \to \pi/2}{cosx}.\frac{sinx}{cosx}[/tex]
= [tex]\lim_{x \to \pi/2}\ sinx[/tex]
= sin (π/2)
= 1
9. [tex]\lim_{h \to \-0} \frac{f(x+h)-f(x)}{h}[/tex] = f'(x)
a. f(x) = 3x - 2
f'(x) = 3
b. f(x) = √x
f'(x) = 1/2√x
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Juan rolls a 6-sided number cube 4 times. Each time, the result is
2. Which best describes the events?
•
Dependent: Each outcome was the same.
Simple: One single number cube was rolled.
•
Independent: Each outcome is unaffected by previous outcomes.
Simple: One single number cube was rolled.
O
Dependent. Each outcome was the same.
Compound: Multiple events occurred.
O
Independent: Each outcome was unaffected by previous outcomes.
Compound: Multiple events occurred.
The events described are known as a compound probability experiment.
Compound probability experimentThe situation described involves a single 6-sided number cube being rolled four times.The outcome of each roll was the same, resulting in a 2 each time.This can be described as a compound event, as multiple events occurred.The events are also dependent on each other, as each outcome was the same.However, the outcomes were independent of each other, as each one was unaffected by previous outcomes.This is due to the fact that each roll of the cube has an equal chance of landing on any number.Therefore, the chances of rolling a 2 each time are low, but still possible.In this experiment, a single 6-sided number cube was rolled four times and each time, the result was 2. This experiment is composed of multiple events, and each outcome was unaffected by the previous outcomes, making it an independent probability experiment.In other words, the probability of rolling a 2 on the number cube each time is the same, no matter what the result of the previous rolls were. This experiment is a good example of how probability can be used to analyze the likelihood of certain outcomes in a given situation.To learn more about compound probability experiment refer to:
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ABC and XYZ are similar. Find the missing side length. A B ?,35,40,C X Y 5, 7, 8,
Answer: DF is 24
Step-by-step explanation: DEF is 6x larger than triangle ABC so since AC is 4 DF is 24.
HELP SOS MATH MATH MATH FAST
Answer:
x = 4; 27°
Step-by-step explanation:
JN=NL; JL = KM
therefore you can say 2(4x+6) = 5x+24
Just solve to find x = 4
JN = NL
KN = NM
JK = ML
triangles JKN and MLN are therefore congruent (sss)
Making the angles equal.
Answer:
x = 4; 27°
Step-by-step explanation:
when converting Celsius to Fahrenheit can it come out as a negative ?
Answer:
Yes, it can
Step-by-step explanation:
consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. the yield is assumed to be between
The corresponding sample space is S = {x|150 ≤ x ≤ 150}.
An experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre.
The yield is assumed to be between 150 and 250 bushels.
A sample space is a collection of probable outcomes from a random event. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results.
Depending on the experiment, a sample area could contain a variety of results. Discrete or finite sample spaces are those that have a finite number of outcomes.
Then the sample space should be
S = {x|150 ≤ x ≤ 150}
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The complete question is:
Consider an experiment that records the number of bushels (and fractions of bushels) of corn produced in an acre. The yield is assumed to be between 150 and 250 bushels.
Determine the corresponding sample space.
Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. What is the number of rolls of paper used per wall?
The number of rolls of paper used per wall will be 1.5 rolls per wall.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Andy is hanging wallpaper in his kitchen. He is to cover 2 2/5 of the walls in the room using 6 rolls of paper. We know that the room has 4 walls.
Then the number of rolls of paper used per wall is given as,
⇒ 6 / 4
⇒ 1.5 rolls per wall
The number of rolls of paper used per wall will be 1.5 rolls per wall.
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You measure three segments of the distance between a diffraction slit an the screen on which the pattern forms: x1 = (15.8 +0.2) cm, x2 = (6.7 +0.1) cm, and x3 = (11.3 0.1). What is the uncertainty of the total distance x1 + x2 + x3? 0.2 cm O 0.1 cm 0.3 cm 0.4 cm 0.5 cm
The uncertainty of the total distance is 0.2 cm.
As per the given data, the distance between the diffraction slit and the screen on which the pattern forms,
[tex]x_{1}[/tex] = (15.8 ± 0.2) cm
[tex]x_{2}[/tex] = (6.7 ± 0.1) cm
[tex]x_{3}[/tex] = (11.3 ± 0.1) cm
Let, the uncertainty in the measurements,
[tex]x_{1}[/tex], [tex]x_{2}[/tex] and [tex]x_{3}[/tex] is [tex]e_{1}[/tex], [tex]e_{2}[/tex] and [tex]e_{3}[/tex] respectively.
So,
[tex]e_{1}[/tex] = 0.2 cm
[tex]e_{2}[/tex] = 0.1 cm
[tex]e_{3}[/tex] = 0.1 cm
Again, let the uncertainty in the total distance
[tex]\mathrm{x} =\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3[/tex] is e(error propagation).
The impact of a variable's uncertainty on the uncertainty of a function depending on it is known as propagation of uncertainty. When the variables are experimental measurement values, measurement limits cause uncertainties that are propagated via the function's combination of variables.
Then the error propagation is given as,
e = [tex]\sqrt{\mathrm{e}_1^2+\mathrm{e}_2^2+\mathrm{e}_3^2} \\[/tex]
So, e = [tex]\sqrt{(0.2)^2+(0.1)^2+(0.1)^2} \\[/tex]
Therefore e = [tex]\sqrt{0.06} \\[/tex]
e = 0.245 cm
e ≅ 0.2 cm
Therefore uncertainty of the total distance 0.2 cm
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What is the simplest form of √2437?
O A.
95√3
OB.
9x³√3x
O c. 27x5√2
OD. 27x³√x
Answer:
B
Step-by-step explanation:
sqrt(243x⁷) = sqrt(9×9×3x³x³x) = 9x³×sqrt(3x)
A program began at 6:30 P.M. and ended at 7:00 P.M. There were two 4.5-minute commercial breaks. How long was the program itself?
Answer:
The total length of the commercial breaks is 4.5 minutes x 2 = 9 minutes.
So the length of the program itself is 7:00 P.M. - 6:30 P.M. - 9 minutes = 30 minutes - 9 minutes = 21 minutes.
Answer:
21 minutes
Step-by-step explanation:
30-9-21 minutes of program
A recipe for chocolate chip muffins states that it yields 12 muffins, with 250 calories per muffin. You instead decide to make mini-muffins, and the recipe yields 18 muffins. If you eat 3, how many calories will you consume?
The number of calories that you would consume if you eat 3 mini-muffins is 41.66.
How many calories will each muffin have?To know the number of calories per muffin, let's divide the total of calories (250) by the number of muffins.
Regular muffins: 250 / 12 = 20.83 calories
Mini-muffins: 250 / 18 = 13.88 calories.
This shows that one mini-muffin contains 13.88 calories, while the original recipe contains 20.83 calories per muffin.
How many calories are 3 mini-muffins?13.88 calories x 3 = 41.66 calories
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Figure 10-25 shows a uniform metal plate that had been square before 25% of it was snipped off. Three lettered points are indicated. Rank them according to the rotational inertia of the plate around a perpendicular axis through them, greatest first
The rank of the points having a maximum moment of inertia is c > a > b.
The figure of 25 % snipped off square-shaped uniform metal plate.
We can rank the points according to the moment of inertia using the relation between the moment of inertia and the radius of gyration of the elements.
The formulae are as follows:
I = mh²
Where h = Radius of gyration, m is mass, and I is the moment of inertia.
Here,
I = mh²
So, the final moment of inertia will be maximum for the axis, which consists of elements having more h (which are more distant from the axis).
From this, it can be concluded that the moment of inertia about an axis through point c is maximum, followed by (a) and then (b).
Rank is c > a > b
Therefore, the points can be ranked according to the moment of inertia about the axis passing through it using its relationship with the radius of gyration.
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Problem:
The number is a solution to the equation
5x²+4= 3x + 9.
What is the value of (10x − 3)²?
Step-by-step explanation:
collect like terms
5x-3x=9-42x= 5Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2), 0 < x < 1,0 < y < 1 Find Cov(x,y) (round off to third decimal place). Find E(Y) (round off to third decimal place).Find E(XY) (write up to third decimal place).
Let the random variables x and y have joint pdf as follows: f(x,y) = 1/5(11x^2 + 4y^2) so Cov(x,y) (round off to third decimal place) is 0.241.
The covariance formula in statistics is used to evaluate the relationship between two variables. In essence, it serves as a gauge for the variation between two variables. Covariance is calculated by multiplying the units of the two variables, and it is expressed in units. Any positive or negative value might be the variance.
E[(X−EX)(Y−EY)]
=E[XY−X(EY)−(EX)Y+(EX)(EY)]
=E[XY]−(EX)(EY)−(EX)(EY)+(EX)(EY)
=E[XY]−(EX)(EY).
E(Y) = ∫ 1/x dx = ∫ 11/5 = ln 11/5 = 0.788
E(XY) = E[X 1/X]= 1
It is feasible to get the correlation coefficient formula from the covariance using the aforementioned formula, and vice versa. Units of covariance are calculated by multiplying the units of the two provided variables.
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A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
The frequency of the A allele is 82.7%.
The frequency of the B allele is 17.3%.
We know that :
10,000 individuals
6,840 individuals have blood type AA
2,860 individuals have blood type AB
300 individuals have blood type BB
AA genotype frequency: 68.4%
AB genotype frequency: 28.6%
BB genotype frequency: 3%
The A allele occurs 6,840 * 2 + 2,860 * 1 = 16,540 times, which is a frequency of 82.7%, meaning the B allele occurs 3,460 times, which is a frequency of 17.3%. In the next generation, 3%, or 750, individuals would have blood type BB.
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The complete question is:
A hypothetical population of 10,000 humans has 6840 individuals with the blood type AA, 2860 individuals with blood type AB, and 300 individuals with the blood type BB.
What is the frequency of each genotype in this population?
What does the frequency of the A allele?
What is the frequency of the B allele?
r square+4r+4 in the square forms
If x and 40 degree are pair of cointerior the x =?
The square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.
What is co-interior angle?Co-interior angles, also known as consecutive interior angles, are those between two lines that are split by a third line (transversal), and are located on the same side of the transversal.
Given that, r^2 + 4r + 4.
Expand the terms as follows:
r^2 + 4r + 4.
r^2 + 2r + 2r + 4 = 0
r(r + 2) + 2(r + 2) = 0
(r + 2) (r + 2)= 0
The sum of co-interior angles is 180 degrees:
x + 40 = 180
x = 140 degrees.
Hence, the square form of r^2 + 4r + 4. is (r + 2) (r + 2)= 0 and the value of co-interior angle x is 140 degrees.
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Modeling with Composite Functions
A store is offering a 10% discount on all items. In addition, employees get a 25% discount.
a. Write a composite function to model taking the 10% discount.
b. Write a composite function to model taking the 25% discount first.
c. If you were an employee, which would you prefer or does it matter?
a. A function to model taking the 10% discount will be 0.9x.
b. A function to model taking the 25% discount first will be 0.75x.
c. If I was an employee, I'll prefer the 25% discount.
How to illustrate the functionFrom the information given, the store is offering a 10% discount on all items and in addition, employees get a 25% discount.
Let the price of the goods be given as x.
A function to model taking the 10% discount will be:
= x - (10% × x)
= x - 0.1x
= 0.9x
A function to model taking the 25% discount first will be:
x - (25% × x)
= x - 0.25x
= 0.75x
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help what's we Have : (x, y,z) = (1, 2, 3) ; (3,2,1); (1,3,2) ; (2,1,3) ; (2,3,1), and (3,1,2)
For k= 43 we have (x,y,z) = (2,2,3) or (2,3,2) or (3,2,2)
For k = 44 we have ( 8,-7,-5) or (8,-5,-7) or (-5,-7,8) or ( -5,8,-7) or (-7,-5,8) or (-7,8,-5)
For k =54 => (x,y,z) = (13,-11,-7) ,
for k = 55 => (x,y,z) = (1,3,3) or (3,1,3) or (3,1,1)
and (x,y,z) = (10,-9,-6) or (10,-6,-9) or ( -6,10,-9) or (-6,-9,10) or (-9,10,-6) or (-9,-6,10)
For k = 62 => (x,y,z) = (3,3,2) or (2,3,3) or (3,2,3)
For k =64 => (x,y,z) = (0,0,4) or (0,4,0)
Answer:
For k = 43, the possible values of (x,y,z) are (2,2,3), (2,3,2), and (3,2,2). For k = 44, the possible values of (x,y,z) are (8,-7,-5), (8,-5,-7), (-5,-7,8), (-5,8,-7), (-7,-5,8), and (-7,8,-5). For k = 54, the possible values of (x,y,z) are (13,-11,-7). For k = 55, the possible values of (x,y,z) are (1,3,3), (3,1,3), (3,3,1), and (1,3,1). For k = 62, the possible values of (x,y,z) are (3,3,2), (2,3,3), and (3,2,3). For k = 64, the possible values of (x,y,z) are (0,0,4) and (0,4,0).
Evaluate the expression for v = -1.
-63+37|v| =
The expression is -63 + 37|-1|. The absolute value of -1 is 1, so the expression becomes -63 + 37(1) = -26.
What is the value ?The value of depends on the context in which they are used. In general, words can have a variety of different values, such as conveying information, expressing an opinion, or providing entertainment. Each individual word can have different meanings and associations depending on the situation. writing is important in any context in which words are used, as it ensures that the ideas expressed are original and properly attributed.
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Find the largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x2
The largest possible area for a rectangle with a base on the x-axis and both upper vertices on the curve y=5−x² , is equals to the 20√15/ 9 .
In optimizing the objective function f(x), solve for the critical points by putting the first derivative f′(x), equals to zero. Then the objective function is evaluated at the critical points to determine the it's minimum or maximum. We have, a rectangle with base as x-aixs and both upper vertices on the curve y = 5 − x², which is a parabola equation. Thus width of the rectangle is based from the equation of the parabola y= 5 - x² --(1)
Area of rectangle is expressed as A = xy , where x -->length of it and y-->width or vertices of curve. The length of the rectangle with base x- axis is equal to 2x. Therefore, the area is A = w× l
= 2x( 5 - x² )
A = 10x - 2x³ --(2)
If area is maximum, then dA/dx = 0
Differentiating the equation (2) with respect to x
dA/dx = 10 - 6x²
so, 10 - 6x² = 0
=> 6x² = 10
=> x² = 10/6
=> x² = 5/3
=> x = ±√5/3
but x represents the length so, it's value always be positive. Thus, x = √5/3. The area is equal to A = 10x - 2x³
= 10(√5/3) - 2(√5/3)³
=> A = 10√5/3 - 10/3(√5/3)
=> A = √5/3( 10 - 10/3) = 20√5/3√3
=> A = 20√15/ 9 ( using rationalzation )
Hence, the required area is 20√15/ 9 .
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Please help me with this question.
Answer:
Try continuity formula you get your answer
Please help with this:(
Answer:
Step-by-step explanation:
a.0.002
What is the interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58
The interquartile range of the following data set 4, 6, 10, 13, 18, 28, 34, 46, 50, 58 is 36.
What is interquartile range?
The difference between the third and the first quartile is defined by the interquartile range. The partitioned values known as quartiles divide the entire series into four equally sized segments. There are so three quartiles. The first quartile, also known as the lower quartile, is marked by Q1, the second quartile by Q2, and the third quartile, sometimes known as the upper quartile, is denoted by Q3. The lower quartile less the upper quartile equals the interquartile range.
The data set given is - 4, 6, 10, 13, 18, 28, 34, 46, 50, 58
Divide the data set into two parts -
D1 = 4, 6, 10, 13, 18
D2 = 28, 34, 46, 50, 58
The two middle value for data set is 18 and 28.
The median of D1 and D2 is -
Median = (18 + 28) / 2
Median = 46 / 2
Median = 23
The middle value for D1 is Q1 = 10 and for D2 is Q3 = 46.
The interquartile range is given as -
Q3 - Q1
46 - 10
36
Therefore, the interquartile range is 36.
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