The solution is, 2.5 miles per hour was her walking rate in miles per hour.
We know that,
Speed is measured as distance moved over time.
The formula for speed is speed = distance ÷ time.
To work out what the units are for speed, you need to know the units for distance and time.
In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
Here, given that,
Bao walked 15 miles in 6 hours.
so, we get,
in 6 hours = 15 miles
so, in 1 hour = 15 / 6 miles
=2.5 miles
Hence, The solution is, 2.5 miles per hour was her walking rate in miles per hour.
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Suppose we have data about a three-stock financial market that satisfies the single-index model as below: (the standard deviation of the market-index portfolio is 18%)
Capitalization Beta Excess Return Std Dev
A $3,000 0.15 10% 40%
B $2,000 0.95 2% 30%
C $1,500 1.7 17% 50%
What is the mean excess return of the value-weighted index portfolio?
Express your answer in percent and round it to 2 decimal places. For example, if your answer is 0.25456, then please write down 25.46 (without the percent sign).
The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:
Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500
Next, we can calculate the weight of each stock in the index portfolio as follows:
Weight of Stock A = $3,000 / $6,500 = 0.4615
Weight of Stock B = $2,000 / $6,500 = 0.3077
Weight of Stock C = $1,500 / $6,500 = 0.2308
The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:
Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081
The mean excess return of the index portfolio can be calculated using the single-index model as:
Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio
= 1.081 x 18%
= 19.458%
Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:
Mean Return = Mean Excess Return + Risk-Free Rate
= 19.458% + 2%
= 21.458%
Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.
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for the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. x|y
2|5
6|15
18|45
Yes , y varies directly with x as a proportion of k = 2.5
Given data ,
Let the values of x = { 2 , 6 , 18 }
Let the values of y = { 5 , 15 , 45 }
Now , the proportion equation is y = kx
On simplifying , we get
k = 5/2
k = 2.5
Therefore , the proportionality constant is k = 2.5
Hence , the proportion is y = 2.5 ( x )
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3. Han thinks that since the arc length in circle A is longer, its central angle is larger. Do
you agree with Han? Show or explain your reasoning.
Yes , Han is correct as the a circle with a longer arc length has a larger central angle
Given data ,
Let the arc length of the circle A = 6π units
Let the radius of the circle A = 15 units
Let the arc length of circle B = 2π units
Let the radius of the circle B = 5 units
Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:
Arc length = (Central angle / 360 degrees) x (2πr)
Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.
Hence , the central angle is solved
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What is the 3D shape that would form if the following
Answer:
These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid
A pyramid has a square base with an area of 144 ft. Mark each statement as true or false and correct any false statements.
T/F? - The length of one side of the pyramids base can be found using the equation s^2=144.
T/F? - The Length of one side of the pyramids base is 72 feet.
A = s^2, where A is the area and s is the length of one side of the square gives the area of a square base. The correct option is true
If s^2 = 144, then s = √144 = 12 feet. The correct option is false
What is pyramid ?A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex.
Therefore, s^2 = 144 is a valid equation to find the length of one side of the base. The correct option is true
Therefore, one side of the pyramid's base is 12 feet, not 72 feet.
The correct option is false
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find 5.79 x 3.3.Then, use an estimate to check for reasonableness.
Determining Whether an Integer Satisfies an Inequality
Apr 29, 2:07:45 PM
Which of the following values are solutions to the inequality -10 + 3x ≥-4?
None
O II only
I and II
O II and III
I. 8
II. 2
OI only
O III only
O I and III
O I, II and III
III. 6
Submit Answer
All three values (I, II, and III) are solutions to the inequality, so the correct answer is "I, II and III."
How to solve
To solve the inequality -10 + 3x ≥ -4, we can follow these steps:
Add 10 to both sides of the inequality:
3x ≥ 6
Divide both sides by 3:
x ≥ 2
Now, let's check which of the given values satisfies the inequality:
I. 8:
x ≥ 2, and 8 ≥ 2, so 8 is a solution.
II. 2:
x ≥ 2, and 2 ≥ 2, so 2 is also a solution.
III. 6:
x ≥ 2, and 6 ≥ 2, so 6 is a solution as well.
All three quantities (I, II, and III) fulfill the requirements of the inequality; hence, the right you have to select is "I, II and III."
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
The statements that are always true are:
i. m∠5 + m∠6 = 180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
What is a triangle?A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.
From the given question and information, the statements that are always true regarding the diagram are:
i. m∠5 + m∠6 =180°
ii. m∠2 + m∠3 = m∠6
iii. m∠2 + m∠3 + m∠5 = 180°
The required diagram is attached to this answer as a guide
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Pls help
The shape below contains a triangle and a semi-
circle.
Round your responses to two decimal places.
perimeter of the shape
167.37 unitsArea of the shape
40.24 square unitsHow to find the perimeter of the shapeThe shape is a composed of two simpler parts which consists of, namely:
The right triangle and the semi circleTherefore, the perimeter of the shape includes perimeter of semicircle and the perimeter triangle
To complete the perimeter of the triangle we add two sides of the triangle. the opposite and the adjacent of the right triangle is given so we solve for the hypotenuse.
The hypotenuse of the triangle = [tex]\sqrt{ 7^2 + 6^2}[/tex] = 9.22 units
perimeter of the shape
= perimeter of triangle side + perimeter of semicircle side
= (9.22 + 6) + (3.142 * 3.5)
= 167.37 units
Area of the shape
= area of triangle + area of semicircle
= 1/2 x 7 x 6 + 1/2 x 3.142 x 3.5^2
= 21 + 19.24
= 40.24 square units
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The exponential function
Answer:
All real numbers
A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)
A.45(x+3)=60x
B.45(x-3)=60x
C.60(x-3)=45x
D.60(x+3)=45x
The correct answer is,
C. 60(x - 3) = 45x.
This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.
Since, Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.
Now, To solve this equation, we must use algebra and solve for x.
First, we multiply both sides of the equation by 4/5. This gives us:
48x + 36 = 45x
-36 = 3x
Finally, we divide left side of the equation by 3, giving us the final solution:
x = -12
Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.
that is, 60 (x - 3) = 45x
This equation shows the correct relationship between the two types of wood that the contractor purchased.
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HELP ASAP ASAP PLS PLS I NEED DONE NOW AND BRAINLIEST
The box plot shows the number of jumping jacks completed in a workout class by the class members.
A box plot uses a number line from 14 to 54, with tick marks every one unit. The box extends from 27 to 45 on the number line. A line in the box is at 37. The lines outside the box end at 16 and 52. The graph is Jumping Jacks Completed, and the line is labeled Number of Jumping Jacks.
Which of the following lists the range and IQR for this data?
The range is 18, and the IQR is 36.
The range is 36, and the IQR is 37.
The range is 36, and the IQR is 18.
The range is 18, and the IQR is 37.
The range is the difference between the maximum and minimum values in the data set. From the box plot, we can see that the maximum value is 52 and the minimum value is 16, so the range is:
Range = Maximum value - Minimum value
Range = 52 - 16
Range = 36
The IQR (interquartile range) is the difference between the first and third quartiles of the data set, which is represented by the length of the box in the box plot. From the box plot, we can see that the length of the box is:
Box length = Upper quartile - Lower quartile
Box length = 45 - 27
Box length = 18
Therefore, the range is 36, and the IQR is 18.
So the correct answer is:
The range is 36, and the IQR is 18.
URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
The correct statements regarding the scatter plot are given as follows:
The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.What is the scatter plot?The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:
(SAT score, GPA).
There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.
For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.
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PLEASE HELP
the pattern for representing a triangular number
The pattern that can be used to represent a triangular number is T(n) = 1 + 2 + 3 + ... + n.
What is a triangular number ?A number that can take the form of an equilateral triangle is called a triangular number. By definition, it represents the sum of positive integers up to n consecutive natural numbers. The pattern for such a calculation is expressed as follows:
T(n) = 1 + 2 + 3 + ... + n.
Triangular numbers exhibit many engaging properties and are applicable across various mathematical and real-world contexts.
In conclusion, the pattern used to represent a triangular number is T (n) = 1 + 2 + 3 + ... + n.
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El profesor de educación física tenía 12 balones y ahora tiene 96 por cuanto se multiplicó la cantidad de los balones
5x^2-8x+12=3x+10
solve quadratic by factoring
On solving the "equation" written as "5x² - 8x + 12 = 3x + 10" by using "factoring-method" , the "solutions" are x = 1/5 and x = 2.
To solve "5x² - 8x + 12 = 3x + 10" by using the "factoring-method", it should first be rearranged in "standard-form", where one side of the equation is = 0,
First, we combine the constant terms on the right side of the quadratic:
⇒ 5x² - 8x + 2 = 3x,
⇒ 5x² - 11x + 2 = 0, Now, we factor the quadratic expression on the left side of the equation as :
⇒ 5x² - 10x -x + 2 = 0,
⇒ 5x(x - 2) -1(x - 2) = 0,
⇒ (5x - 1)×(x - 2) = 0
By applying the zero product property, we know that either "5x - 1 = 0" or "x - 2 = 0";
⇒ 5x - 1 = 0 , We get x = 1/5,
⇒ x - 2 = 0, We get x = 2;
Therefore, the solution are x = 2, and x = 1/5.
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The given question is incomplete, the complete question is
Solve the quadratic-equation "5x² - 8x + 12 = 3x + 10" by factoring.
8. A graph represents the proportional relationship between the number of pages printed, y, and the time in minutes, x. If there is a point on the graph at (4, 720), how many pages can be printed in half a minute?
The number of pages that can be printed in half a minute is 90 pages
How many pages can be printed in half a minute?From the question, we have the following parameters that can be used in our computation:
The graph represents a proportional relationship
Where
x = minutes
y = pages
When the time is half a minute, we have
x = 0.5
So, we have the following ordered pair
(0.5, y)
From the question. we have
(4, 720)
So, we have
(0.5, y) = (4, 720)
Express as an equation
So, we have
y/0.5 = 720/4
This gives
y = 0.5 * 720/4
Evaluate
y = 90
Hence, the number of pages is 90
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PLEASE HELP
Parts a, b, c, d, and e
The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x), g(x) and h(x)
Solving the composite functions, we have
f(g(2)) = f(3) i.e. g(2) = 3
This gives
f(g(2)) = 5.5
Next, we have
h(f⁻¹(5))
Here, we have
f⁻¹(5) = 4
So, we have
h(f⁻¹(5)) = h(4)
Evaluate
h(f⁻¹(5)) = 1
Next, we have
f(h(x)) = 7
From the graph, we have
f(0) = 7
This means that
h(x) = 0
From the table, we have
h(5) = 0
This means that
x = 5 for f(h(x)) = 7
Evaluating R(x) at x = 4. we have
R(x) = 2f(x) - 3g(x) + h(x)
This means that
R(4) = 2f(4) - 3g(4) + h(4)
So, we have
R(4) = 2 * 9 - 3 * 5 + 1
R(4) = 4
Evaluating k(x) at x = 5. we have
k(x) = h⁻¹(g(f⁻¹(x)))
This means that
k(x) = h⁻¹(g(f⁻¹(5)))
From the graph, f⁻¹(5) = 4
So, we have
k(x) = h⁻¹(g(4))
Next, we have
g(4) = 5
So, we have
k(x) = h⁻¹(5)
From the table, we have
h⁻¹(5) = 2
This means that
k(x) = 2
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Select the correct answer. Solve the equation by using the quadratic formula. x^2+2x=6
The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.
Rearranging the Given equation and Putting all values on other side of Zero.
x^2+2x=6
x^2+2x-6=0 ____________(1)
It can be seen that we can not have the multiples that counts of 6 so that they have a subtraction value 2. therefore, Using the Quadratic Formula for the above equation,
x=(-b±√(b²-4ac))/(2a) ___________(2)
where
a=1
b=2
c=-6
putting the values of a,b,c in the equation (2)
x=(-2±√(4²-4*1*(-6)))/(2*1)
x=(-2±2√7)/2
x=(-1±√7)/2
Solving the Values of x in simplified form, we get x=1.645 and -3.654.
Therefore, The Value of x in the equation x^2+2x=6 is 1.645 or -3.654.
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HELP ASAP I NEED DONE RESLLY FAST AND BRSINKIEST
An image of a right rectangular prism is shown.
A rectangular prism with dimensions of 4.5 centimeters by 6 centimeters by 4 centimeters.
What is the surface area of the prism?
138 cm2
169 cm2
31 cm2
69 cm2
Answer:
2((4.5)(6) + (4.5)(4) + (6)(4))
= 2(27 + 18 + 24) = 2(69) = 138 square cm
Find the area of the shaded region
Area= 69π or 216.77 square units.
Step-by-step explanation:1. Find the area of the white circle.Remember that the formula for the area of a circle is the following:
[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.
Hence, the area of the white circle is:
[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]
2. Find the area of the red circle.Here you can use the same formula, just need to change the value of the radius:
[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]
3. Find the difference between the 2 areas.[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]
4. Express the final result.The area of the shaded region is 69π or 216.77 square units, approximately.
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A group of researchers wanted to know whether having a flexible start time for when workers began work impacted the number of minutes they spent commuting. To examine this, they had one group of workers leave home at 7am one morning and the next week let them choose the time they wanted to leave home to get to work. The minutes are given below. Conduct the steps of hypothesis testing on these data.
Data table: The number of minutes spent commuting for six subjects when they left a 7am vs leaving at a flexible time
Subject Leaving at 7am Leaving at a flexible time
1 24 20
2 18 17
3 30 30
4 24 25
5 20 12
6 15 5
The necessary information to carry out the hypothesis are given below.
How to carry out the hypothesisFor carrying out a hypothesis examination on the information, we need to do the following steps:
Step 1: Express the null and alternative hypotheses
Step 2: Pick the pertinent measure of value and significance level
Step 3: Compute the test statistic
Step 4: Estimate the p-value
Step 5: Draw a conclusion and interpret the results
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ANSWER ASAPPP I NEED IT!
Answer:a
Step-by-step explanation:
Answer:
Step-by-step explanation:
It is a A
if x = 6 units and h = 5 units whats the area of the triangle
Answer: 15 square units
Step-by-step explanation:
Area of a triangle is 1/2bh
x = b = 6
H=5
1/2(6)(5)
1/2(30)
Area = 15 square units
help me pleaseeeeeeee
brainliest for 1st answer
Answer:
A
Step-by-step explanation:
sqrt 5 ( 4pi - 2pi) = 2 pi sqrt 5 for the numerator
then 2 pi sqrt (5) / 3 sqrt (5) the sqrt (5) 's cancel out and you have
2pi / 3
Find the area of square ABCD shown below. Round to the nearest tenth if necessary.
O
D
y
O
A
B
square units
The area of the square given in the diagram is: 25 square units.
What is the area of the square?Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
Using Pythagoras theorem, we can find the length of a side of the square:
AB = √(3² + 4²)
AB = √(9 + 16)
AB = √25
AB = 5
Area of a square is given by the formula:
A = side * side
Thus:
A = 5 * 5
A = 25
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The cone below has a volume of 264 m³ and a radius of 6 m. Calculate the size of the angle between the slant height and the base to 1 dp.
The angle between the slant height and the base of the cone is 30.2°.
How to solve for angle of a coneRecall the formula of the volume of a cone:
V = (1/3)πr²h
where
V = volume,
r = radius,
h = height.
To get the h, we use the volume formula and substitute:
264 = (1/3)π(6²)h
Make h the subject of the formula and simplify:
h = (3/π)(264/36) = 8.8
Therefore, h = 8.8 m.
Now, we find the slant height using the Pythagorean theorem:
s² = r² + h²
Plugging in the values, we get:
s² = 6² + 8.8² = 102.64
s = √(6² + 8.8²)
s = 10.13
To find the angle between the slant height and the base, we use trigonometry:
tan θ = r / s
r = radius of the base
s = slant height
Plugging in the values, we get:
tan θ = 6 / 10.13
tan θ = 0.5925
Find the arctan of θ
θ = tan⁻¹(0.5925)
θ = 30.2°
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Your class hopes to collect at least 325 cans of food for the annual food drive. there were 135 cans donated the first week and 89 more the second week.
A. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
B. How many cans are needed to meet or surpass the goal
a.) [tex]135 + 89 + \text{C} \geq 325[/tex]
[tex]224 + \text{C} \geq 325[/tex]
b.) [tex]224 + \text{C} \geq 325[/tex]
[tex]\text{C} \geq 325 - 224[/tex]
[tex]\text{C} \geq 101[/tex]
CAN SOMEONE HELP WITH THIS PROBLEM?
The value of the infinite series expression [tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] is -30.
Given information:
[tex]\sum^{124}_{i = 1}a_i = -10[/tex] and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].
The required series form can be rearranged as,
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i[/tex]
Substitute the provided values of [tex]\sum^{124}_{i = 1}a_i = -10[/tex] and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].
We get,
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = 29(-10) - 13(-20)
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -290+ 260
[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -30.
As a result, the required value is -30.
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can someone help me on number 1 through 4.
The values are expressed as;
1. radius = 13cm
2. Diameter = 27.2cm
3. Diameter = 24m
4. Radius = 24. 5m
How to determine the valuesIt is important to note the formula for calculating the circumference and area of a circle.
The formula for calculating area of a circle is expressed as;
A = πr²
Such that the parameters are given as;
A is the area of the circler is the radius of the circleAlso, the formula for circumference is expressed as;
C = 2πr
To determine the formula for diameter is expressed as;
Diameter = 2Radius
1. Substitute the values
r = d/2
r = 26/2
r = 13cm
2. If r= 13.6m
d= 2(13.6)
d = 27.2m
3. If r = 12m
d = 2(12)
d = 24m
4. If d = 49m
Then, r = 49/2 = 24. 5m
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