Consider the following function. - **** - 2x + 9 (a) Find y' = f'(x). F"(x) - X (b) Find the critical values. (Enter your answers as a comma-separated list.) (c) Find the critical points. (smaller x-v
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The critical points are approximately (-1.225, -4.097) and (1.225, 3.097).
To find the derivative of the function f(x) = -2x³ + 9x, we differentiate term by term using the power rule:
(a) Differentiating f(x):f'(x) = d/dx (-2x³) + d/dx (9x)
= -6x² + 9
(b) To find the critical values, we need to find the values of x for which f'(x) = 0.Setting f'(x) = -6x² + 9 to 0 and solving for x:
-6x² + 9 = 06x² = 9
x² = 9/6x² = 3/2
x = ±√(3/2)x ≈ ±1.225
The critical values are x ≈ -1.225 and x ≈ 1.225.
(c)
find the critical points, we substitute the critical values into the original function f(x):
For x ≈ -1.225:f(-1.225) = -2(-1.225)³ + 9(-1.225)
≈ -4.097
For x ≈ 1.225:f(1.225) = -2(1.225)³ + 9(1.225)
≈ 3.097
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Related Questions
Malakia is shopping for a gift exchange. She sees fuzzy socks on sale for $3 dollars each and gloves for $3.50 each. She spends $38 total on these gifts. If malakia gives 4 of her friends gloves, how many friends does she give fuzzy socks to.
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PLEASE HELP I WILL GIVE BRAINALIST
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Answer:
Step-by-step explanation:
Original 873 New 781
The new went down by about 10.5%
873*10.5%= 91.67
873-91.67= 781.33
It decreased 10.5%
Applying PL, construct a symbolicmodel of the logical structure of the following argument. Construct a truth table to determine if the argument is valid. Be sure to state whether the argument is valid or invalid. If the argument is invalid then indicate a row that shows this. (4 points)
Jayco qualifies as a small business if and only if it has sales that are not large enough to influence its environment and it is privately owned by a small group of individuals. Jayco does not qualify as a small business. Therefore, Jayco must not be privately owned by a small group of individuals.
Please use these symbols: ~, v, • , ⊃, ≡
Answers
We can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.
To construct a symbolic model of the argument, let's define the following symbols:
P: Jayco qualifies as a small business.
Q: Jayco has sales that are not large enough to influence its environment.
R: Jayco is privately owned by a small group of individuals.
Now we can represent the statements in symbolic form:
Premise 1: P ≡ (Q • R)
Premise 2: ~P
Conclusion: ~R
To determine if the argument is valid or invalid, we can construct a truth table:
| P | Q | R | P ≡ (Q • R) | ~P | ~R |
|---|---|---|-------------|----|----|
| T | T | T | T | F | F |
| T | T | F | F | F | T |
| T | F | T | T | F | F |
| T | F | F | F | F | T |
| F | T | T | F | T | F |
| F | T | F | T | T | T |
| F | F | T | F | T | F |
| F | F | F | T | T | T |
From the truth table, we can see that there is at least one row where all premises are true (row 7), but the conclusion is false. Therefore, the argument is invalid.
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A ramp was constructed to load a truck. If the ramp is 10 feet long and the horizontal distance from the bottom of the ramp to the truck is 8 feet, what is the height from the ground to the top of the ramp ? A) 3. 0 ft B) 4. 5 ft C) 5. 0 ft D) 6. 0 ft.
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Pythagoras theorem is a basic relationship in geometry between the three sides of a right triangle. The height from the ground to the top of the ramp 6. 0 ft. Option D is correct.
What is the Pythagoras theorem?Pythagoras theorem is a basic relationship in geometry between the three sides of a right triangle.
It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
The given data in the problem will be;
L is the length of ramp= 10 feet
x is the horizontal distance from the bottom of the ramp = 8 feet
h is the height from the ground to the top of the ramp=?
According to Pythagoras theorem,
\(\rm H^2=P^2+B^2 \\\\ \rm l^2=h^2+X^2 \\\\ \rm 10^2=h^2+8^2 \\\\ \rm h=\sqrt{100-64 } \\\\ \rm h=36 \\\\ \rm h=6 ft\)
Hence the height from the ground to the top of the ramp 6. 0 ft. Option D is correct.
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Can someone answer this correctly please and thank you :D
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3x^2+20x+12
pls show work ;-;
Answers
Answer:
\(3 {x}^{2} + 20x + 12 \\ 3 {x}^{2} + 18x + 2x + 12 \\ 3x(x + 6) + 2(x + 6) \\( 3x + 2)(x + 6)\)
Answer:
x = -2/3, x = -6
Step-by-step explanation:
Let's solve the problem,
→ 3x² +20x + 12
→ 3x² + (2x + 18x) + 12
→ 3x(x+6) + 2(x+6)
→ (3x+2)(x+6)
→ x = -2/3, x = -6
Thus, solution is -2/3, -6.
3) Determine the following values given f(x) = 1.
a) f(1/2)
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Answer:
f(1/2) = 1
Step-by-step explanation:
Wht is the y-intercept of the line describes by the equation below?
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Answer:
(0,7)
Step-by-step explanation:
This is in the form
y = mx+b where m is the slope and b is the y intercept
y = -5x +7
The slope is -5 and the y intercept is 7
(0,7)
Answer:
(0,7)
Step-by-step explanation:
y=mx+b
y=-5x+7
so y intercept is (0,7)
The speed of a car traveling on a straight road increases from 63 m/s to 75 m/s in 4.2 s. What is the car's acceleration
Answers
Answer:
2.857m/s^2
Step-by-step explanation:
Acceleration (a) is the change in velocity (v) over the change in time (t), represented by the equation a = v/t.
Using logarithms, you determined the of 7 solutions ranging from strong acid to neutral to strong base.
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Logarithms are a useful tool in determining the acidity or basicity of a solution. pH is a measure of the concentration of hydrogen ions in a solution and is calculated using the formula pH = -log[H+].
A solution with a pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.
Using logarithms, we can determine the pH of 7 solutions ranging from strong acid to neutral to strong base. To do this, we need to measure the concentration of hydrogen ions in each solution and then use the formula above to calculate the pH.
For example, if we have a solution with a hydrogen ion concentration of 0.001 M, we can calculate the pH as follows:
pH = -log(0.001) = 3
This solution would be considered a strong acid, as it has a pH below 7. Similarly, a solution with a hydrogen ion concentration of 10^-7 M (which is the same as a concentration of 1x10^-7 M) would have a pH of 7 and would be considered neutral.
Finally, a solution with a hydrogen ion concentration of 10^-11 M would have a pH of 11 and would be considered a strong base.
In summary, using logarithms, we can determine the acidity or basicity of a solution by calculating its pH. A pH of 7 is considered neutral, while a pH below 7 indicates acidity and a pH above 7 indicates basicity.
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Takyra has n nail polish colors. Samantha has 4 more than twice the number of nail polish colors. In terms of n,
how many nail polish colors does Samantha have?
3n - 4
3n +4
2n +4
2n x 4
Answers
Answer: 2n+4
Step-by-step explanation:
"(4 more than) twice the number" is 2x
"4 more (than twice the number)" is +4
Put them together: 2n + 4
Kray sells personalized photo frames. She charges $12 for the frame plus $0.25 for each letter the customer wants to engraved on the frame. Which function represents the relationship between the number of letters engraved on a frame, n, and the total cost of a frame, c,? 15 points
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Answer:
c=0.25n+12
Step-by-step explanation:
Please help and give an explanation. I’m struggling
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Answer:
y = 1/3x -4
Step-by-step explanation:
The y intercept is -4 as you can see in the graph. To find the slope look at the graph and find where it perfectly intercepts. It goes up one block and to the right three. So the slope is 1/3 . Since the line is going up to the top right it’s a positive slope.
6. What is the domain of this function?
(0, 2), (1, 3), (2, 4), (3,5), (4, 6)
Answers
\(\large \underline\mathcal{ » \: QUESTION \: : }\)
6. What is the domain of this function?
(0, 2), (1, 3), (2, 4), (3,5), (4,6)
the domain is the set of all the values x of while the range is the set of all the value of y
\( \tt \:1.) (0, 2), (1, 3), (2, 4), (3,5), (4, 6)\)
\( \tt \: DOMAIN = ({{0,1,2,3,4}})\)
\( \tt \: RANGE (2,3,4,5,6)\)
Eli has a number cube. Each side has a different number: 1, 2, 3, 4, 5, or 6. Eli will roll the number cube once. What is the probability he will roll a 4?
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Answer:
E. is the correct^
Step-by-step explanation:
plz need this asap ONLY ANSWER IF YOU KNOW IT will give brainliest
Answers
Answer:
1 would be your y axis
Step-by-step explanation:
1. so the y axis is up and down
2. the x axis is horizontal side to side
3. the x axis is 0
4. the y axis is positive 1
5. So your anwser would be in the format (x,y)
6. It is (0,1)
7. It is positive
8. Plz name me brainliest I would really appreciate it if you need more help just ask me
Thank You
Procter and Gamble (PG) paid an annual dividend of $2.95 in 2018. You expect PG to increase its dividends by 7.4% per year for the next five years (through 2023), and thereafter by 2.6% per year. If the appropriate equity cost of capital for Procter and Gamble is 8.6% per year, use the dividend-discount model to estimate its value per share at the end of 2018.
Answers
The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.
First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)
where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:
PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.
To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:
Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22
After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.
In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.
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Find the range of the function
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Answer:
y€ R : y greater than or equal to 1
I USED ALL MY POINTS! PLEASE HELP ME ASAP!!!
Mrs. Jackson wants to tile a wall to serve as a splash guard above a basin in the basement. She plans to use equal-sized tiles to cover an area that measures 48 inches by 36 inches. She does not want to cut any of the tiles. What is the least number of tiles she could use?
Answers
Answer:
e
Step-by-step explanation:
50 and 40
Answer:
1728
Step-by-step explanation:
have a good day
Shape T is reflected in the line x = -1 to give shape R.
Shape R is reflected in the line y = -2 to give shape S.
Describe the single transformation that will map shape T to shape S.
Answers
Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. The sum of the transformations can be referred to as a single transformation.
How would you describe a single transformation reflection?Imagine putting a mirror on the page and adding a reflection. You must identify the line in which the shape is mirrored when describing a reflection. Every point of a shape will be separated from the line of reflection by the same amount as the reflected point is separated from the line.
There are occasions when a shape is altered in more than one step, such as when a rotation is followed by a reflection. Typically, the sum of the transformations can be referred to as a single transformation.
Enlargements are a particular kind of transformation where the original shape's size is altered by multiplying it by a scale factor to make it bigger or smaller. To employ a center of enlargement, lines must be drawn from the center via the original shape's vertices. They are known as ray lines.
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Evaluate the expression 6.2 - (-9.1).
Answers
Answer: 15.1
Step-by-step explanation: subtracting a negative (ex. 1 - (-1)) just change to addition (prev. ex. would be 1+1) (also adding decimals is like adding normal numbers just remember the place values
Which of the following is a solution of y - x < -3?
(6, 2)
(2, 6)
(2, -1)
Answers
Answer:
(6, 2)
Step-by-step explanation:
You can do trial and error with this question. Lets try (6, 2) first.
2 - 6 < -3
-4 < -3
This equation is true so you can tell from this it is (6, 2).
A marketing firm obtained random samples of 20 people in five regions of the country to investigate the level of interest in a new product. People in the sample were asked to rate their level of interest on a scale from 1 to 10, with 1 being the least amount of interest and 10 being the greatest. The histograms show the results for each region. The graph for which region displays data for level of interest with the least standard deviation?.
Answers
Without the histograms, there's no specific region as an answer. However, you can follow these steps to determine the region with the least standard deviation in level of interest based on the provided data.
To determine the region with the least standard deviation in level of interest, we need to analyze the histograms for each region. Standard deviation is a measure of how spread out the data is. The region with the least standard deviation will have data points that are more closely clustered around the mean (average) level of interest.
1. Examine the histograms for each region.
2. Look for the region where the data points are more tightly grouped around the mean level of interest. This indicates less variability and a smaller standard deviation.
3. Identify the region with the least standard deviation in level of interest.
To determine the region with the least standard deviation in the level of interest, examine the histograms for each region and identify the one where data points are tightly clustered around the mean level. Calculate the standard deviation for each region and select the region with the smallest value, indicating a more concentrated and less variable distribution of the level of interest.
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calculate the coefficient of variation for a sample of cereal boxes with a mean weight of 340 grams and a standard deviation of 5.2 grams.? 0.15% A
1.53% B
15.29% C
0.65% D
Answers
The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean, and then multiplying by 100 to express it as a percentage.
In this case, the mean weight is 340 grams, and the standard deviation is 5.2 grams.
CV = (Standard Deviation / Mean) * 100
CV = (5.2 / 340) * 100
CV ≈ 1.53%
Therefore, the correct answer is option B: 1.53%.
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Given two events, a and b, with probabilities p(a) = 0.40 and p(b) = 0.20, calculate the indicated probabilities given the additional piece of information
Answers
Answer:
0.60
Step-by-step explanation:
becouse of two probability within added gives the above answer
Find x if AB = x-6, BC = 7,
and AC= -8 + 2x.
Answers
Answer:
9
Step-by-step explanation:
set up the equation: ab+bc=ac
(x-6) + 7 = (-8+2x)
Step 1: Simplify both sides of the equation.
x−6+7=−8+2x
x+−6+7=−8+2x
(x)+(−6+7)=2x−8(Combine Like Terms)
x+1=2x−8
x+1=2x−8
Step 2: Subtract 2x from both sides.
x+1−2x=2x−8−2x
−x+1=−8
Step 3: Subtract 1 from both sides.
−x+1−1=−8−1
−x=−9
Step 4: Divide both sides by -1.
−x/−1 = −9 /−1
x=9
dy ex+y = xy For the following implicity defined curves, find dx
Answers
The derivative dx for the curve defined by the equation dy = ex+y - xy is given by dx = (ex+y - xy - y) / [1 - (ex+y)].
To find dx for the curve defined by the equation dy = ex+y - xy, we can use implicit differentiation.
Taking the derivative of both sides with respect to x, we get:
d/dx(dy) = d/dx(ex+y - xy)
Using the chain rule, we have:
dy/dx = (d/dx)(ex+y) - (d/dx)(xy)
To differentiate ex+y, we use the chain rule again:
dy/dx = (ex+y)(d/dx)(x+y) - (d/dx)(xy)
dy/dx = (ex+y)(1 + dy/dx) - (x)(dy/dx) - y
Next, we isolate dy/dx by moving the terms involving dy/dx to one side:
dy/dx - (ex+y)(dy/dx) = (ex+y) - xy - y
dy/dx[1 - (ex+y)] = ex+y - xy - y
Finally, we can solve for dx:
dx = (ex+y - xy - y) / [1 - (ex+y)]
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Janine sold 428 tickets for the school play. Student tickets were $3 and adult tickets were $5.
Janine’s total ticket sales were $1674. How many student tickets and how many adult tickets were sold ?
Solve this problem using a system of linear equations. Make sure you introduce the two variables
used and explain what they represent, write two equations using the two variables you have chosen,
solve the linear system using substitution OR elimination method, showing ALL steps, and write a
concluding statement in words.
Answers
The system of the equation is written as
x + y = 428
5x + 3y = 1674
the solution:
adult tickets is 195
students tickets is 233
How to write the required equationThe problem is a simultaneous equation of two unknowns with two equations.
The equations are formed as follows
Janine sold 428 tickets for the school play
let the adult ticket be x and student ticket be yx + y = 428
Janine’s total ticket sales were $1674
Student tickets were $3 and adult tickets were $5
5x + 3y = 1674
The simultaneous equation
x + y = 428
5x + 3y = 1674
solving the equation by elimination method
x + y = 428 * 3
3x + 3y = 1284
5x + 3y = 1674
subtraction gives
-2x = -390
x = 195
substitute x = 195 into x + y = 428
195 + y = 428
y = 428 - 195
y = 233
hence adult tickets is 195, while students tickets is 233
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Find the point on the line y=-6/7x+6 that is closest to the
origin.
Type your answer in the form (x,y).
Answers
The point on the line y = (-6/7) x + 6 that is closest to the origin is (2.96, 8.54)
The equation of the line is,
y = (-6/7) x + 6
So each point on the given line can be expressed as (x, (-6/7) x + 6).
So the distance of the point on the line to the origin (0, 0) is given by,
d = √[x² + {(-6/7) x + 6}²]
d² = x² + {(-6/7) x + 6}²
d² = x² + {(-6/7) x}² + 6² + 2 (-6/7)x * 6
d² = x² + 36x²/49 + 36 - 72x/7
d² = 85x²/49 - 72x/7 + 36
Let, z = 85x²/49 - 72x/7 + 36
differentiating the above relation with respect to 'x' we get,
dz/dx = 170x/49 - 72/7
d²z/dx² = 170/49
Now, dz/dx = 0. So,
170x/49 - 72/7 = 0
170x/49 = 72/7
x = (72*49)/(7*170)
x = 252/85
At x = 252/85, d²z/dx² = 170/49 > 0
So, at x = 252/85, z is minimum.
So, at x = 252/85, d² is minimum thus d is minimum.
So, the point is = (252/85, [(-6/7)(252/85) + 6]) = (2.96, 8.54) [Rounding off to nearest hundredth].
Hence the required point is (2.96, 8.54).
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Diego went to a restaurant, and his dinner bill was $24. He paid a total of $28.32. Which equation will help find the percent tip (in decimals), x, that Diego gave the server?
24−24⋅x=4.32
24+24⋅x=28.32
24+24⋅x=4.32
24−24⋅x=28.32
Answers
The equation that represent the percentage is 24 + 24x = 28.32
What is percentagePercentage is a way of expressing a fraction or ratio as a number out of 100. It is often represented by the symbol "%". For example, if there are 20 red balls out of 100 balls in a bag, the percentage of red balls is 20%.
To find the equation that represent the percentage in tip, we can write it as;
Let the amount in tip be represented by x
24 + 24x = 28.32
Solve for x,
x = 0.18 which can be expressed in percentage as 18%
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