The function f and g are given by [tex]f(x)=x^2[/tex] and [tex]g(x)=-^1_2 x+5[/tex].
Let R be the region bounded by the x-axis and the graphs f and g as shown at the bottom. Also, I only need you to answer part b, I've already finished part a.
a) Describe how you would find the area of R.
[tex]R=18 \frac{2}{3}[/tex]
b) The region R is the base of a solid. For each y, where
0 < y < 4, the cross-section of the solid taken perpendicular to the y-axis is a rectangle whose base lies in R and whose height is 3y. Explain how you would write an expression that gives the volume of the solid.
![The Function F And G Are Given By [tex]f(x)=x^2[/tex] And [tex]g(x)=-^1_2 X+5[/tex].Let R Be The Region](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/ggEzoWmKybVU6E5yxmAhM4iPrwjkmIdz.png)
Answers
As you've pointed out, R is a different region that I originally thought. The area of R can be computed using either
[tex]\displaystyle \int_0^2 x^2 \, dx + \int_2^{10} -\frac x2 + 5 \, dx[/tex]
or
[tex]\displaystyle \int_0^4 (10-2y)-\sqrt y \, dy[/tex]
Either way, you've gotten the correct area for part (a).
For part (b), we can use part of the integral with respect to [tex]y[/tex] above. The horizontal distance between the curves [tex]y=x^2[/tex] and [tex]y=-\frac x2+5[/tex] is obtained by first solving for [tex]x[/tex],
[tex]y=x^2 \implies x=\sqrt y[/tex]
[tex]y=-\dfrac x2+5 \implies x = 10-2y[/tex]
so the length of each cross section is [tex]10-2y-\sqrt y[/tex].
The height of each cross section is [tex]3y[/tex].
Then the volume of the solid is
[tex]\displaystyle \int_0^4 3y \left(10-2y-\sqrt y\right) \, dy = \boxed{\int_0^4 -6y^2 + 30y - 3y^{3/2} \, dy}[/tex]
The instructions don't say to evaluate, but if you're looking for practice the volume ends up being 368/5, or 73 3/5.
![The Function F And G Are Given By [tex]f(x)=x^2[/tex] And [tex]g(x)=-^1_2 X+5[/tex].Let R Be The Region](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/M1Nx3qF6H3zIbmOtytCKXpjyebsahFPB.jpeg)
Related Questions
Find the surface area of the regular pyramid.
A square pyramid. The length of the base is 1 inch. The height of each triangular face is 2 inches.
Answers
Answer:
Love helping people so here's the answer :)
Step-by-step explanation:
A square pyramid has 5 faces: 1 square base and 4 triangular faces. The surface area of the pyramid is the sum of the areas of all its faces.
The area of the square base is 1 * 1 = 1 square inch.
The area of each triangular face is (1/2) * base * height = (1/2) * 1 * 2 = 1 square inch.
Since there are 4 triangular faces, the total area of the triangular faces is 4 * 1 = 4 square inches.
Therefore, the surface area of the pyramid is 1 + 4 = 5 square inches.
Jayda is older than her 12-year-old sister. Write an inequality for j, Jayda's age.
Answers
The inequality states that Jayda's age (j) is greater than 12 i.e., j > 12.
Let j represent Jayda's age.
Since Jayda is older than her 12-year-old sister, we can write the inequality:
j > 12
Thus, the inequality states that Jayda's age (j) is greater than 12.
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I need help with this math
Answers
Answer:
500 and 4.3
Step-by-step explanation:
A decigram is one-tenth of a gram and a kilometer is one-thousandth of a meter. Using this information, we must multiply the given amounts by the values.
5000 × 0.1 = 500
4300 × 0.001 = 4.3
Thus, the answers [in order] are 500 and 4.3
Hope this helps and feel free to ask any questions.
The owner of a computer store estimates profits using
the equation P = 4x² - 15x - 20 where P is the profit, in
dollars, and x is the number of
computers sold.
What is the estimated profit when 60 computers are
sold?
$26,400
$15,320
O $14,400
$13,520
$13,480
Answers
Answer:
(e) $13,480
Step-by-step explanation:
You want the estimated profit from selling 60 computers, if the profit from selling x computers is P = 4x² -15x -20.
ProfitPut 60 where x is in the profit equation and do the arithmetic.
The result is an estimated profit of $13,480.
__
Additional comment
To simplify evaluation, the polynomial can be written in "Horner form:"
P = (4x -15)x -20
Evaluating it this way takes fewer math operations and generally involves smaller numbers.
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Test Prep What fraction is represented by the point on the number line?
Answers
The fraction represented by the point between 1 and 2 on the number line is 5/3.
If the point is between 1 and 2 on the number line, we can determine the fraction it represents by considering the distance between the point and the two adjacent integers.
The point A lies between the numbers 1 and 2, which indicates that the whole number part of the fraction is 1.
Also note that the segment between 1 and 2 is divided into 3 equal parts. A lies on the 2nd part, which implies that the fractional part is 2/3.
2
Thus, the point A corresponds to the mixed fraction 1 -
3
2 5
1 - = (1*3)+2 / 3 = -
3 3
So, the fraction represented by the point between 1 and 2 on the number line is 5/3.
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PLS ANSWER WILL GIVE BRAINLIEST IF CORRECT (NO LINKS)
Identify the number of vertices, edges, and faces of the polyhedron. Use your results to verify Euler's formula.
Answers
Answer:
The third option
Step-by-step explanation:
Help pls anyone I’m rlly bad at these
Answers
144.) The value of X if the two angles of the triangle are congruent would be = 4. That is option D.
145.) The equation that should be used to find the value of X would be = 13x -15 = 22x + 9. That is option H.
How to determine the value of X when two triangles are congruent?
For question 144.)
Two triangles are congruent means that the angles are equal to each other. That is;
2.3x +25 = 5.8x + 11
Bring like terms together;
5.8x-2.3x = 25-11
3.5x = 14
X = 14/3.5
= 4.
For question 145.)
When two parallel lines are being cut across by a diagonal line a relationship exists between the angles that are formed.
The two given angles are congruent;
That is;
13x -15 = 22x + 9
Therefore the expression that can be used to calculate X would be = 13x -15 = 22x + 9
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At hollywood connection, edgar plays laser tag 6 minutes for every 8 minutes he plays arcade games. If edgar plays arcade games for 48 minutes. for now many minutes will he play laser tag
Answers
Answer:
36
Step-by-step explanation:
48/8 = 6. 6*6 = 36.
A 3-D jigsaw puzzle becomes a cube with a volume of 1 cubic foot when it is solved. Mr. Ruiz stores several of these puzzles in a storage nook in his classroom. The nook is shaped like a rectangular prism and has a height of 3 feet. A layer of 8 puzzles will completely cover the floor of the nook. What is the volume of the storage nook?
Answers
The volume of the storage nook is 24 cubic feet.
How to find the volume of the storage nookTo find the area of 8 puzzles, we multiply the area of one puzzle by 8:
Area of 8 puzzles = 1 square foot * 8 = 8 square feet
Now, to find the volume of the storage nook, we multiply the area of the floor by its height:
Volume of the nook = Area of the floor * Height
= 8 square feet * 3 feet
= 24 cubic feet
Hence, the volume of the storage nook is 24 cubic feet.
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1. The vertices of APQR are P(1, 3), Q(5, 4) and
R(5, 15). Find the length of the perpendicular
from Q to PR.
Answers
The distance of the perpendicular from Q to line PR is D = 2.2135 units
Given data ,
Let the triangle be represented as ΔPQR
Now , the coordinates are P(1, 3), Q(5, 4) and R(5, 15)
And , the equation of line of PR is given by
Slope m = ( 15 - 3 ) / ( 5 - 1 )
m = 3
y - 3 = 3 ( x - 1 )
Adding 3 on both sides , we get
y = 3x
y - 3x = 0
And , the point is Q(5, 4)
Now , distance of a point to line D = | Ax₀ + By₀ + C | / √ ( A² + B² )
D = | ( 1 ) ( 5 ) + ( -3 ) ( 4 ) + 0 | / √ ( 1 )² + ( 3 )²
D = | 5 - 12 | / √10
D = 7/√10
D = 2.2135 units
Hence , the distance is 2.2135 units
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here is a rhombus.A strait line joining the midpoints of two of its sides are work out the size of angle a
Answers
The size of angle can be expressed as 130 degrees
How can the side of the angle be worked out?Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees.
Considering the given figure, if we look at the right top triangle we can deduced that it is an isosceles, then the supplementary angle of angle α can be calculated as
(180 - 80)/2
= 50 degrees.
Hence, α = 180 - 50
= 130 degrees.
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HELP Plsssssssssssss
Answers
Answer:
[tex]9^{\frac{1}{8}x }[/tex]
Step-by-step explanation:
The function in the question
[tex]\sqrt[4]{9} ^{\frac{1}{2}x }[/tex]
is equivalent to
[tex]9^{(\frac{1}{4})(\frac{1}{2} x) }[/tex]
where you multiply the powers and get the final answer
[tex]9^{\frac{1}{8}x }[/tex]
g working. In a class of 75 students, 45 students study French and 25 students study Ara only. If 10 students study both Arabic and French, (I)illustrate the information on a Venn
; (ii)how many students study (a) only French (b) only one subject;(c) neither Arabic nor French.
Answers
Answer:
(i) Attached below. You can copy what I drew
(ii) (a) 35, (b) 60, (c) 5
Step-by-step explanation:
We're told that 25 students study Arabic only and 10 students' study both French and Arabic. Thus, this leaves 40 other students, as 75 - (10 + 25) = 40.We know that 45 students study French and this includes those who study French only and those who study both French and Arabic. Thus, we can subtract the number of students who study both languages from the number of students who study French (generally) to find the number of students who study French only: 45 - 10 = 35.(a) Thus, 35 students study French only.
Thus, we've sorted 70 students so far as 35 + 10 + 25 = 70.To find the number of students who studied neither Arabic nor French, we can subtract 70 from the total number of students in the class: 75 - 70 = 5.(c) Thus, 5 students' study neither Arabic nor French
We can check our work by making sure that:the number of students who study French only + the number of students who study both French and Arabic + the number of students who study Arabic only + the number of students who study neither Arabic nor French equals 75:
35 + 10 + 25 + 5 = 75
45 + 30 = 75
75 = 75
Thus, our numbers are correct.
(b) Also, the number of students who study only subject is 60, as 35 (number of students studying French only) + 25 (number of students studying Arabic only) = 60
I attached a picture of a diagram that you can use and I'll explain what everything means:The box represents the set, which is represented by the letter S in the top-left corner of the pictureF represent the number of students who studied French only, which is why I wrote 35 in this circleThe 10 represents the number of students who study both Arabic and French and likes between the F circle and the A circle A represents the number of students who studied Arabic only, which is why I wrote 25 in this circleThe 5 outside the circles but inside the box represents the number of students who study neither Arabic nor FrenchA researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The required sample size for the confidence interval and given margin of error is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
[tex]\pi = 0.5[/tex]
Then the sample size for M = 0.04 is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575 \times 0.5[/tex]
[tex]\sqrt{n} = \frac{2.575 \times 0.5}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2[/tex]
n = 1037.
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Given the arithmetic sequence an with a1=−10 and d=−2, find a3.
Answers
The value of a3 in the Arithmetic sequence with a1 = -10 and d = -2 is -14.
The value of a3 in the arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1) * d
Where:
- an is the nth term in the sequence
- a1 is the first term of the sequence
- d is the common difference between consecutive terms
- n is the position of the term we want to find
In this case, we are given that a1 = -10 and d = -2. We want to find the value of a3, which corresponds to the third term in the sequence (n = 3).
Plugging in the values into the formula, we have:
a3 = a1 + (3 - 1) * d
= -10 + 2 * (-2)
= -10 - 4
= -14
Therefore, the value of a3 in the arithmetic sequence with a1 = -10 and d = -2 is -14.
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PLEASEEEE HURRYY
On Giana's map of Texas, there is a close up view of the Dallas/Fort Worth area. The map scale is 1 inch = 3.5 miles. From Garland to Mansfield is 52.5 miles. How far apart are these two cities on the map?
Answers
Answer:
The distance between Garland and Mansfield on the map is 15 inches.
Step-by-step explanation:
On Giana's map of Texas, the scale is 1 inch = 3.5 miles. To determine the distance between Garland and Mansfield on the map, we can use the scale to find the corresponding measurement. Given that the actual distance between these two cities is 52.5 miles, we can set up a proportion:
1 inch / 3.5 miles = x inches / 52.5 miles
Cross-multiplying, we have:
3.5 miles * x inches = 1 inch * 52.5 miles
3.5x = 52.5
Dividing both sides by 3.5, we find:
x = 15
Therefore, the distance between Garland and Mansfield on the map is 15 inches.
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Hellooo i’m pretty sure x is 30 but can someone tell me what im meant to write for the reason. Thank youuu
Answers
Answer:
2x and 180 - 5x are complementary angles.
2x + 180 - 5x = 90
-3x + 180 = 90
-3x = -90
x = 30
I am struggling bad Can I get help finding the Domain and Range thank you everyone
Answers
The domain and the range of the graph seen in the figure are X = {- 5, - 4, - 1, 3} (or x ∈ [- 5, 3]) and Y = {- 2, 0, 2, 4} (or y ∈ [- 2, 4]).
How to determine the domain and the range of the graph
Herein we find a graph generated by four points of the form (x, y) set on Cartesian plane. The domain of the graph consists in the set of all x-coordinates of the graph, whereas range is for the set of all y-coordinates.
Domain
X = {- 5, - 4, - 1, 3}
(Interval notation)
x ∈ [- 5, 3]
Range
Y = {- 2, 0, 2, 4}
(Interval notation)
y ∈ [- 2, 4]
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The domain of this emath equation is
Answers
Answer:
x ≥ 5
Step-by-step explanation:
You want the domain of the equation y = √(x -5) -1.
DomainThe domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...
x -5 ≥ 0
x ≥ 5 . . . . . . the domain of this function
__
Additional comment
The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.
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Use technology or a z-score table to answer the question. The odometer readings on a random sample of identical model sports cars are normally distributed with a mean of 120,000 miles and a standard deviation of 30,000 miles. Consider a group of 6000 sports cars. Approximately how many sports cars will have less than 150,000 miles on the odometer? O 300 951 O 5048 O 5700
Answers
Approximately 5048 sports cars will have less than 150,000 miles on the odometer
Mean = 120,000
Standard deviation = 30,000
Total group = 6000
Total Miles = 150,0000
An odometer is a device used to gauge how far a wheeled vehicle has driven. The tool might be mechanical, electrical, or a hybrid of the two.
Calculating the Z score -
z = x - u/a
= 15,0000 - 12,0000/30000
= 30000/30000
= 1
Using the standard normal table, to determine the value -
P ( Z<1) = 0.8413
Calculating the total number of cars -
= P value x total group of cars
= 6000 x 0.8413
= 5047.7 or 5048
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer:
3/8 = (3 + AD)/20
8(3 + AD) = 60
24 + 8AD = 60
8AD = 36
A = 4 1/2
B is the correct answer.
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
I need help with this
Answers
Answer:
B. {1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}
Step-by-step explanation:
The intersection of two sets is a set containing the elements that are present in both sets.
{1, 6, 7, 8} ∩ {6, 8, 9} = {6, 8}
John received $200 dollars for his birthday. He went to Greenbriar Mail and purchased a pair of tennis shoes for $75.00. Then he went to the Cookie Store and bought $10.00 worth of cookies. Going to the car, John looked down and found $20.00 on the ground. How much money does John has now?
Answers
Explanation:
Subtract 200 and 75 to and you get 125.
Next, subtract 125 and 10 to get 115.
Then, add 115 and 20 to get $135.
The inverse of a conditional statement is "If a number is negative, then it has a negative cube root.”
What is the contrapositive of the original conditional statement?
If a number is negative, then it does not have a negative cube root.
If a number does not have a negative cube root, then the number is not negative.
If a number has a negative cube root, then the number is negative.
If a number is not negative, then it does not have a negative cube root.
Answers
The contrapositive of the original conditional statement is B. If a number does not have a negative cube root, then the number is not negative.
How to find the contrapositive ?In logic, the contrapositive of a conditional statement is a logically equivalent statement that switches the positions of the hypothesis and the conclusion, while also negating both.
The contrapositive maintains the logical validity of the original statement. If the original statement is true, then the contrapositive is also true, and vice versa. "If a number is negative, then it has a negative cube root." The contrapositive of this statement would be: "If a number does not have a negative cube root, then the number is not negative."
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A bird sanctuary has 14 bags of bird seed. Each bird feeder holds 16 of a bag.
How many bird feeders can be filled with the bird seed?
Answers
k bro i gochu
the answer is 84 man,
do good on ur hw
also can i get a pizza
Help pleaseeeeeeeeee
Answers
16800 cubic inches of concrete is needed to make the stairs
How many cubic inches of concrete is needed to make the stairs?Rectangular prism is a three dimensional shape which consist of six faces. The two faces are at the top and bottom and the other faces are lateral faces.
The given stairs can be divided into 3 rectangular prisms as shown in the image attached.
Volume of a concrete needed = Volume of A + Volume of B + Volume of C
Volume of a rectangular prism = l × w × h
where l is the length, w is the width and h is the height
For A:
l = 40, w = 10 in and h = 7 + 7 + 7 = 21 in
For B:
l = 40, w = 10 in and h = 7 + 7 = 14 in
For C:
l = 40, w = 10 in and h = 7 in
Volume of a concrete needed = (40 * 10 * 21) * (40 * 10 * 14) + (40 * 10 * 7)
Volume of a concrete needed = 8400 + 5600 + 2800
Volume of a concrete needed = 16800 in³
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For what values of x does 5x^2+4x-4= 0
Answers
The values of x that satisfy the equation are x = (-4 + 2√6) / 5 and x = (-4 - 2√6) / 5
What values of x satisfy the given equation?The values of x that satisfy the equation 5x² + 4x - 4 = 0 can be determined using the quadratic formula given below:
x = (-b ± √(b² - 4ac)) / (2a)
From the equation:
a = 5, b = 4, and c = -4.
Substituting these values into the quadratic formula:
x = (-(4) ± √((4)² - 4(5)(-4))) / (2(5))
Simplifying to solve for values of x
x = (-4 ± √(16 + 80)) / 10
x = (-4 ± √96) / 10
x = (-4 ± 4√6) / 10
x = (-4 ± 2√6) / 5
Hence, x = (-4 + 2√6) / 5 or x = (-4 - 2√6)
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At the farmers' market, Tom bought 11/12 of a pound of string beans and 1/2 of a pound of
lima beans. How many more pounds of string beans did Tom purchase?
Write your answer as a fraction or as a whole or mixed number.
pounds
Answers
Answer:
Step-by-step explanation:
5/12 pounds more
For positive acute angles A and B, it is known that SinA= 11/61 and tan B=4/3. Find the value of Cos(A-B) in simplest form.
Answers
For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.
We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).
First, we need to find the value of cosA and sinB:
Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:
cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61
Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:
hypotenuse = √(4² + 3²) = 5
sinB = opposite/hypotenuse = 4/5
Now we can substitute these values into the formula:
cos(A-B) = cosA cosB + sinA sinB
= (60/61)(3/5) + (11/61)(4/5)
= 180/305 + 44/305
= 224/305
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