Answer:
Comparing the centers of the data sets:
- The median for Data Set A is greater than the median for Data Set B.
- The mean for Data Set A is greater than the mean for Data Set B.
Comparing the variability of the data sets:
- The range of Data Set A is 22, while the range of Data Set B is 27. Therefore, the range of Data Set B is greater.
- The standard deviation of Data Set A is greater than the standard deviation of Data Set B, indicating higher variability in Data Set A.
y=1x^2 + 2x - 3 in vertex and intercept form
The vertex and the x-intercepts of the quadratic equation are:
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
To express the quadratic equation [tex]y = x^2 + 2x - 3[/tex]in vertex and intercept form, we need to complete the square to find the vertex and rewrite the equation in terms of the x-intercepts.
First, let's complete the square to find the vertex. We can do this by taking half the coefficient of x, squaring it, and adding/subtracting it to both sides of the equation:
[tex]y = x^2 + 2x - 3\\y = (x^2 + 2x + 1) - 1 - 3\\y = (x + 1)^2 - 4[/tex]
Now we have the equation in the form [tex]y = a(x - h)^2 + k[/tex], where the vertex is at the point (-h, k). The vertex is (-1, -4).
Next, let's find the x-intercepts by setting y = 0:
[tex]0 = x^2 + 2x - 3\\0 = (x + 3)(x - 1)[/tex]
The x-intercepts are -3 and 1.
In vertex and intercept form, the equation is:
[tex]y = (x + 1)^2 - 4[/tex]
The vertex is (-1, -4)
The x-intercepts are -3 and 1.
This form allows us to easily identify the vertex and the x-intercepts of the quadratic equation.
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Jane just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Jane works out that's 62 hats for each hospital. Does that sound about right?
Answer:
31
Step-by-step explanation:
you add the hats to get the total number of hats then divide the answer by
No, it is much too high. Then the correct option is B.
What is an equation?An equation is a statement of equality between two expressions consisting of variables and/or numbers.
Given the question above, we need to find if the hats is to high or low.
Calculating the total numbers of hats made, we have
[tex]21 + 29 + 12 = 62 \ \text{hats}[/tex]
If Edna wants to split 62 hats evenly between two hospital, then each hospital will get
[tex]\dfrac{62}{2} = 31 \ \text{hats}[/tex]
Therefore, if Edna works out that each hospital gets 62 hats, No it is too high, as that is the total of all the hat that is available
Hence, the correct option is B.
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Missing informationEdna just joined a group that makes hats for babies in the hospital. Two weeks ago they made 21 hats. Last week they made 29 hats. This week they made 12 hats. All these hats will be split evenly between 2 nearby hospitals. Edna works out that's 62 hats for each hospital. Does that sound about right?
A. Yes
B. No, it is much too high
C. No, it is much too low
GEOMETRY 80POINTS
ty!
Answer:
x ≈ 77.79 ft
Step-by-step explanation:
using the sine ratio in the right triangle
sin40° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{50}{x}[/tex] ( multiply both sides by x )
x × sin40° = 50 ( divide both sides by sin40° )
x = [tex]\frac{50}{sin40}[/tex] ≈ 77.79 ft ( to the nearest hundredth )
Which property best describes the conditional statement below If triangle ABC= triangle DEF then triangle DEF=triangleABC
Answer:
would this not be a converse statement?
Step-by-step explanation:
triangle ABC is the hypothesis and it's conclusion is triangle DEF
The endpoints of AB are A (-7, -14) and B (5,10) . Into which ratio will each point divide AB ?
The point A divides the line segment AB into the ratio 3:1, while the point B divides it into the ratio 1:3.
1. To find the ratio in which each point divides AB, we need to calculate the distances from each endpoint to the dividing point.
2. Let's calculate the distance from point A to the dividing point. The x-coordinate of point A is -7, and the y-coordinate is -14. Similarly, the x-coordinate of point B is 5, and the y-coordinate is 10.
3. We'll use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by:
distance = sqrt((x2 - [tex]x1)^2 + (y2 - y1)^2)[/tex]
4. Applying the distance formula, we find the distance from point A to the dividing point:
[tex]distance_A[/tex] = sqrt((5 -[tex](-7))^2 + (10 - (-14))^2)[/tex]
= sqrt((5 + [tex]7)^2 + (10 + 14)^2)[/tex]
= sqrt([tex]12^2[/tex] + [tex]24^2[/tex])
= sqrt(144 + 576)
= sqrt(720)
= 12√5
5. Similarly, let's calculate the distance from point B to the dividing point:
[tex]distance_B[/tex] = sqrt((-7 - [tex]5)^2 + (-14 - 10)^2)[/tex]
= sqrt((-[tex]12)^2 + (-24)^2)[/tex]
= sqrt(144 + 576)
= sqrt(720)
= 12√5
6. The dividing ratio can be determined by comparing the distances from each endpoint to the dividing point. Since distance_A:distance_B = 3:1, we conclude that point A divides the line segment AB into the ratio 3:1, and point B divides it into the ratio 1:3.
Thus, the endpoints A and B divide the line segment AB into the ratios 3:1 and 1:3, respectively.
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Answer:
the ratio for point C is 1 : 2.
the ratio for point D is 3 : 1.
the ratio for point E is 2 : 1.
Step-by-step explanation:
I just got it right on the test
What is 1,0000 ÷ 2,0000
O Velocity stays the same...
Distance increases slower than time.
00
QUESTION 4
Why did you not compute a slope for the accelerated motion graph?
We didn't have enough data.
It graphed as a straight line.
The curve wasn't smooth enough.
A curve has many different slopes.
QUESTION 5
Which of the following is a vector?
For accelerated motion, changes in distance compare with equal changes in velocity as follows:
B. Distance increases faster than time.
A reason why a person will not compute a slope for the accelerated motion graph is that it graphed as a straight line.
Details about accelerated motionAccelerated motion is a form of motion in which the motion is not equal and the object moving does not complete the same distances in the same intervals of time.
The graph formed in the case of an accelerated motion is not a straight line. So, a reason why a person would not compute a slope for the accelerated motion is that it graphed as a straight line.
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what is the square root of the fraction, 3/25?
Answer: 0.3464 (correct upto 4 decimal places )
Step-by-step explanation:
[tex]\sqrt{3/25}[/tex]= [tex]\sqrt{3} /\sqrt{25\\}[/tex] (as the square root of 25 is 5)
=1.73205/5
=0.3464
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. What is the maximum area of a Norman window whose perimeter is 9 feet?
The maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
To find the maximum area of a Norman window with a given perimeter, we can use calculus. Let's denote the radius of the semicircle as r and the height of the rectangular window as h.The perimeter of the Norman window consists of the circumference of the semicircle and the sum of all four sides of the rectangular window. Therefore, we have the equation:
πr + 2h = 9We also know that the area of the Norman window is the sum of the area of the semicircle and the area of the rectangle, given by:
A = (πr^2)/2 + rh
To find the maximum area, we need to express the area function A in terms of a single variable. We can do this by substituting r from the perimeter equation:
r = (9 - 2h)/(π)
Now we can rewrite the area function in terms of h only:
A = (π/2) * ((9 - 2h)/(π))^2 + h * (9 - 2h)/(π)
Simplifying this equation, we get:
A = (1/2)(9h - h^2/π)
To find the maximum area, we differentiate the area function with respect to h, set it equal to zero, and solve for h:
dA/dh = 9/2 - h/π = 0
Solving this equation, we find:h = 9π/2
Substituting this value of h back into the area function, we get:
A = (1/2)(9 * 9π/2 - (9π/2)^2/π) = (81π/2 - 81π/4) = 81π/4
Therefore, the maximum area of a Norman window with a perimeter of 9 feet is 81π/4 square feet.
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Sin(theta)=2/3 and theta is in quadrant II, find cos theta
Answer: Choice C. [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]
===================================================
Work Shown:
Part 1
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]
Part 2
[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]
1. The difference of two supplementary angles is 70° which is the larger angle?
A/ 135° B/145 C/55 D/125°
1. The difference of two supplementary angles is 70° which is the larger angle?
A/ 135°
B/145
C/55
D/125° ✓Let the numbers be x and x-70 we know that,sum of two supplimentary angles = 180°x+x-70=180°2x-70=180°2x=180°+70°2x=250°x=125°and x-70°= 125°-70° = 55° hence,the larger angle is 125°Instructions: Complete the following proof by dragging and dropping the correct reason into the space provided.
Given: ∠NYR and ∠RYA form a linear pair, ∠AXY and ∠AXZ form a linear pair, ∠RYA≅∠AXY
If you are using a screen-reader, please consult your instructor for assistance.
Prove: ∠NYR≅∠AXY
Step Reason
∠NYR and ∠RYA form a linear pair
∠AXY and ∠AXZ form a linear pair Given
∠NYR and ∠RYA are supplementary
m∠NYR+m∠RYA=180
∠AXY and ∠AXZ are supplementary If two angles form a linear pair, then they are supplementary angles
Definition of Supplementary Angles
m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality
∠RYA≅∠AXY
m∠NYR+m∠RYA=m∠AXY+m∠RYA Substitution Property of Equality
m∠NYR=m∠AXY
≅
Answer:
Step Reason
∠NYR and ∠RYA form a linear pair
∠AXY and ∠AXZ form a linear pair Given
∠RYA≅∠AXY Given
∠NYR and ∠RYA are supplementary Definition of Linear Pair
If two angles form a linear pair, then they are supplementary angles Definition of Linear Pair
∠NYR and ∠AXY are supplementary Transitive Property of Equality
m∠NYR+m∠RYA=180
m∠AXY+m∠AXZ=180 Definition of Supplementary Angles
m∠NYR+m∠RYA=m∠AXY+m∠AXZ Substitution Property of Equality
m∠NYR+m∠RYA=m∠NYR+m∠AXZ Substitution Property of Equality
m∠RYA=m∠AXZ Subtraction Property of Equality
∠NYR and ∠AXY are supplementary Definition of Supplementary Angles
m∠NYR+m∠AXY=180
m∠NYR+m∠RYA=m∠NYR+m∠AXY Substitution Property of Equality
m∠RYA=m∠AXY Subtraction Property of Equality
∠NYR≅∠AXY Definition of Congruent Angles.
Jacob spent 5 hours skiing and snowboarding. He skied for 2 hours 10 minutes.
How long did he spend snowboarding?
Answer:
he spent 2hours 50minutes snowboarding
the time he spent skiing and snowboarding minus the time he skied
5hours minus 2hours 10minutes
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: D
Step-by-step explanation:
Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.
D) 4x2=8
12x2=24
15x2=30 All sides were multiplied by 2 so D is similar
Answer:
D)
Step-by-step explanation:
Figure D is similar in all mesurements .
...
What transformation is shown below? (Look carefully at the vertices.)
translation
reflection
rotation
can't be determined
The transformation that moves the shape is (a) translation
What transformation moves the shapeFrom the question, we have the following parameters that can be used in our computation:
The figure
Where, we have:
Rectangle ABCD and rectangle ABCD have the same orientationRectangle ABCD and rectangle ABCD have the same sizeThis means that the only transformation is translation
So, the transformation is (a) translation
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need help to understand
Answer:
C
Step-by-step explanation:
x ≥ 25
Because this inequality has an equal sign, it will be a close circle. x ≥ -25 meaning the x go to the right of -25.
So, the answer is C
State whether the function graphed is continuous on [-1,4]. If not, where does it fail to be continuous and why?
Answer: C
Step-by-step explanation:
The function exists at all points on the interval with no discontinuities (such as jump discontinuities).
Ms. Garcia, an art teacher, is buying supplies for her next unit on ceramics. Her 25 sixth graders are making mugs, and she estimates each one will use about 3/4
of a pound of clay. She also wants to have 20 pounds of clay for her seventh graders' sculptures. If Ms. Garcia has 5 2/5 pounds of clay leftover from last year, how much more clay does she need?
Answer: 2 1/2 pounds of more clay
Step-by-step explanation:
To calculate how much more clay Ms. Garcia needs, we need to add up the clay requirements for each grade level and then subtract the amount she already has.
For the sixth graders:
Number of students: 25
Clay required per student: 3/4 pound
Total clay required for sixth graders: 25 * (3/4) = 75/4 = 18 3/4 pounds
For the seventh graders:
Clay required for sculptures: 20 pounds
Total clay required for both grade levels: 18 3/4 + 20 = 38 3/4 pounds
Clay leftover from last year: 5 2/5 pounds
To find out how much more clay Ms. Garcia needs, we subtract the clay she already has from the total required:
38 3/4 - 5 2/5 = 38 3/4 - 27/5 = 38 3/4 - 27/5 = (155 - 108 + 3)/20 = 50/20 = 5/2 = 2 1/2 pounds
Therefore, Ms. Garcia needs an additional 2 1/2 pounds of clay.
8. Given the figure at right, which of the following is a
true statement?
a. sin(0) = ²/
b. tan(N) =
C. cos(0) =
d. cos(N) =
12
6√5
6
6√5
6√5
6√5
Answer:
Step-by-step explanation:
a. sin(0) = 0
The sine of 0 degrees is 0.
b. tan(N) = 6√5
We don't have enough information to determine the value of tan(N) without knowing the specific value of N.
c. cos(0) = 1
The cosine of 0 degrees is 1.
d. cos(N) = 6√5/6
Again, we can't determine the specific value of cos(N) without knowing the value of N.
Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
77110
03-x--2
- 3-4-x
Oy+4x-1
Mark this and retum
C
Save and Exit
€
6
Next
Submit
The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
How to determine the equation, when graphed with the given equation, will form a system that has an infinite number of solutionsTo form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.
The given equation is: y + 4x - 1 = 0
To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.
Let's multiply the given equation by 2:
2(y + 4x - 1) = 2(0)
2y + 8x - 2 = 0
The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.
Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
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please answer ASAP I will brainlist
Answer:
(a) To find the average cost in 2011, substitute 11 for x in the function.
g(11) = -1,736.7 + 1,661.6 ln 11 = $2,247.64
The average cost in 2011 was $2,247.64.
(b) Using the graphing calculator, graph the function in the viewing window
[6, 15] by [1,000, 3,000].
The correct graph is B.
(c) A. The average cost increases at a slower rate as time goes on.
solve this system of equations by using the elimination method x-5y=16 4x-2y=-8
Answer:
(- 4, - 4 )
Step-by-step explanation:
x - 5y = 16 → (1)
4x - 2y = - 8 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x
- 4x + 20y = - 64 → (3)
add (2) and (3) term by term to eliminate x
(4x - 4x) + (- 2y + 20y) = - 8 - 64
0 + 18y = - 72
18y = - 72 ( divide both sides by 18 )
y = - 4
substitute y = - 4 into either of the 2 equations and solve for x
substituting into (1)
x - 5(- 4) = 16
x + 20 = 16 ( subtract 20 from both sides )
x = - 4
solution is (- 4, - 4 )
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8————-4
16————8
24———-12
32———-?
Answer here
Answer:
The number is 16
Step-by-step explanation:
This follows a multiplication rule,
4 times 1 = 4
4 times 2 = 8
4 times 3 = 12
4 times 4 = 16
So, the number is 16
Rewrite as a simplified fraction.
--
0.612 = 101/165
0.612 can be rewritten as the simplified fraction 153/250.
Question: Rewrite as a simplified fraction. 0.612
To rewrite 0.612 as a simplified fraction, we need to convert the decimal into a fraction.
Step 1: Count the number of decimal places.
In this case, 0.612 has three decimal places.
Step 2: Write the decimal as a fraction with the decimal part as the numerator and the denominator as the place value of the rightmost digit.
Since there are three decimal places, the denominator will be 1000 (10 raised to the power of 3).
0.612 = 612/1000
Step 3: Simplify the fraction.
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. In this case, both the numerator and denominator are divisible by 4.
612/1000 = (612 ÷ 4) / (1000 ÷ 4) = 153/250
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How would you describe the difference between the graphs of f (x) = 3x²
and g(x) = -2² ?
OA. g(x) is a reflection of f(x) over the line y = x.
B. g(x) is a reflection of f(x) over the line y = -1.
C. g(x) is a reflection of f(x) over the x-axis.
D. g(x) is a reflection of f(x) over the y-axis.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C).
The given functions are f(x) = 3x² and g(x) = -2².
To understand the difference between their graphs, let's examine the characteristics of each function individually:
Function f(x) = 3x²:
The coefficient of x² is positive (3), indicating an upward-opening parabola.
The graph of f(x) will be symmetric with respect to the y-axis, as any change in x will result in the same y-value due to the squaring of x.
The vertex of the parabola will be at the origin (0, 0) since there are no additional terms affecting the position of the graph.
Function g(x) = -2²:
The coefficient of x² is negative (-2), indicating a downward-opening parabola.
The negative sign will reflect the graph of f(x) across the x-axis, resulting in a vertical flip.
The vertex of the parabola will also be at the origin (0, 0) due to the absence of additional terms.
Comparing the characteristics of the two functions, we can conclude that the graph of g(x) = -2² is a reflection of the graph of f(x) = 3x² over the x-axis (option C). This means that g(x) is obtained by taking the graph of f(x) and flipping it vertically. The reflection occurs over the x-axis, causing the parabola to open downward instead of upward.
Therefore, the correct answer is option C: g(x) is a reflection of f(x) over the x-axis.
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Let N be the greatest number that will divide 1305,4665 and 6905 leaving the same remainder in each case. What is the sum of the digits in N.
Answer:
4
Step-by-step explanation:
You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.
Largest divisorWe can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.
For 1305 and 4665, if r is the remainder, we require ...
4(1305 -r) = 4665 -r
5220 -4665 = 4r -r
555/3 = r = 185
If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...
6905/1120 = 6 r 185
Sum of digitsThe sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.
The sum of the digits in N is 4.
13. A cylinder is shown. Find the exact volume of a cone with the
same dimensions.
on filled to the very top, it holds 480 cub
The exact volume of a cone with the same dimensions is 9428.57 cubic inches
Find the exact volume of a cone with the same dimensions.From the question, we have the following parameters that can be used in our computation:
The cylinder
The volume of the cone with the same dimensions is calculated as
Volume = 1/3 * Volume of cylinder
So, we have
Volume = 1/3 * 22/7 * (30/2) * (30/2) * 40
Evaluate
Volume = 9428.57
Hence, the exact volume of a cone with the same dimensions is 9428.57 cubic inches
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The data set shows the ages of everyone in a dance class.
4, 17, 17, 17, 17, 17, 18, 18, 18
Select the statement that correctly describes the data.
3 of 5 QUESTIONS
The typical value is 9 because that is the total number of people.
The typical value is 18 because it is the maximum.
The typical value is 4 because it is the minimum.
The typical value is 17. Most values are close to 17, except 4, which is an
extreme value.
Answer: The statement that correctly describes the data is:
The typical value is 17. Most values are close to 17, except 4, which is an extreme value.
This is because the value 17 appears most frequently in the data set, making it the mode or the typical value. The value 4 is an extreme value as it is the minimum value in the data set. The maximum value of 18 is not the typical value because it is not as representative of the overall distribution of ages in the data set as the mode, which is 17.
Step-by-step explanation:
In circle I, IJ = 9 and m/JIK = 140°. Find the length of JK. Express your answer as a fraction times pie.
The calculated length of the arc JK is 7π
Finding the length of the arc JKFrom the question, we have the following parameters that can be used in our computation:
Central angle = 140 degrees
Radius, IJ = 9 inches
Using the above as a guide, we have the following:
JK = Central angle/360 * 2 * π * Radius
Substitute the known values in the above equation, so, we have the following representation
JK = 140/360 * 2 * π * 9
Evaluate
JK = 7π
Hence, the length of the arc is 7π
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priya and han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). priyas equation is y - 2 = 1/3 (x-1) and hans equation is 3y-x=5. do you agree with either of them? explain or show your reasoning
I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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