Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
Dividing Polynomials:We use the division of polynomials to find the quotients of two polynomials. Two polynomials can be divided by simply multiplying and dividing by the largest power in each term.
The two different ways to divide polynomials are 1. Long division method and 2. The synthetic division method. The synthetic division method is the quickest way to divide polynomials between these two approaches.
Advantages of performing a Synthetic Division:
Only if the divisor is a linear factor can we use the synthetic division approach. In contrast to the long division method, which uses division and subtraction, the synthetic division approach uses multiplication and addition. There are just a few calculations needed. There is no need for variables to do the calculation.This method is less prone to errors than the polynomial long division method.
Therefore,
We can say
Yes, we can use always the synthetic division for dividing polynomials since it is the easiest way in order to get the quotients of two polynomials.
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Work & Power: Incredibles
Must Show Work!!
Mr. Incredible can push with a force of 5000 N on a train and move it 100 meters in 100
seconds. Dash can push this tiny railcar with a force of 50 N moving it 100 meters in 1
second. Who would you say did more work? Also, who is more powerful? Explain your
answers.
Based on the information, it can be inferred that Mr. Incredible did more work than Dash moving the train car.
How to calculate the work done by Mr. Incredible and Dash?To calculate the work that Mr. Incredible and Dash did moving the train car, we must apply the following mathematical formula:
Work (Joules) = Force (N) * Distance (d)According to the above, we only have to replace the values according to each case.
J = 5,000 * 100J = 500,000J = 50 * 100J = 500According to the above, it can be inferred that Mr. Incredible made more effort than Dash because they did 500,000 J and 500 J of work respectively.
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130 estimated to the nearest integer is
130 estimated to the nearest integer is 130 itself as 130 itself is an integer.
What are Integers?Integers are numbers which includes the set of natural numbers, 0 and the negatives of all those natural numbers.
Set of integers are usually denoted as Z.
A number is normally rounded to the nearest integer when it is decimal.
First we have to look at the tenths place.
When the digit in the tenths place is 5 or numbers greater than 5, then increase digit in the ones place by 1.
If the digit in tenths place is less than 5, then leave the ones place as such.
Suppose that the number is 1.30.
Then the digit in tenths place is 3, less than 5. So leave the digit in one place which is 1, as such.
So 1.30 rounded to the nearest integer is 1.
Here 130 itself is an integer.
Hence 130 rounded to nearest integer is 130.
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The basketball team averaged 68 points per game last
season and average 77 points per game this season.
What is the approximate percent of the increase?
Hi there, here's your answer:
Given, a basketball team averaged 68 points per game in the last season and averaged 77 points per game in the present season.
To find:
The approximate percentage of increase.
Solution:
If 68 points was the average last season, and 77 points was the increase this season, then the number of increase in points is 9.
Also we have that % increase = [tex]\frac{Difference}{Original}[/tex] × 100
Which is [tex]\frac{9}{68}[/tex] × 100 = 0.1323 × 100 = 13.23%
Therefore, the approximate percent increase is 13%.
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2. Andrea and Casey work at a restaurant over the summer. Andrea gets paid $25 when they
work along with an average of $9 in tips every hour. Casey only gets $10 when they work,
but they make an average of $14 in tips every hour. Write a system of equations to determine
how many hours it takes for Andrea and Casey to make the same amount of money? How
much money is it?
Answer:
So Andrea and Casey each make $52 after working for 3 hours.
Step-by-step explanation:
Let's call the number of hours that Andrea and Casey work "x".
The amount of money that Andrea makes in a given hour can be represented as 25 + 9x.
The amount of money that Casey makes in a given hour can be represented as 10 + 14x.
We want to find the number of hours it takes for Andrea and Casey to make the same amount of money, which we can represent as:
25 + 9x = 10 + 14x
To solve for x, we can isolate x by subtracting 10 from both sides of the equation:
15 + 9x = 14x
Next, we can isolate 9x by subtracting 14x from both sides of the equation:
15 = -5x
Finally, we can divide both sides of the equation by -5 to solve for x:
-3 = x
So it takes 3 hours for Andrea and Casey to make the same amount of money. To find the amount of money, we can plug in x = 3 back into either of the equations:
Andrea's equation: 25 + 9x = 25 + 9 * 3 = 25 + 27 = 52
So Andrea and Casey each make $52 after working for 3 hours.
The proof shown needs several statements and reasons filled in.
Given the angle bisector, the statements and reasons for the proof are explained.
What is an angle bisector?A bisector splits a given line or angle into two equal parts. A straight line is said to be an angle bisector if it divides a given angle into two equal measures. Such that on comparison, the sum of the angles formed is equal to the measure of the bisected angle.
The statements and reasons for the proof are given below;
STATEMENT REASONS
1. MK bisects <HKO and <HMO Given
2. m<HMK = m<OMK and m<HKM = m<OKM Definition of angle bisector
3. HK ≅ KO, and HM ≅ OM Congruent side property
4. ΔHMK ≅ ΔOMK Angle-Angle-Side theorem
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Louise is planning to renovate her house. She intends to spend no more than $30 000. She has
$20 000 to invest in an account that pay 4.28% compounded monthly. How long will it take
Louise to meet her goal? Show your work. Round your answer to the nearest tenth of a year.
Answer:
Step-by-step explanation:
To determine how long it will take for Louise to reach her goal of $30,000, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A is the amount of money Louise will have after "t" years,
P is the initial investment of $20,000,
r is the annual interest rate of 4.28%,
n is the number of times the interest is compounded per year (12 times per year), and
t is the number of years.
We can rearrange this formula to solve for t:
t = (log(A/P)) / (log(1 + r/n))
Plugging in the values:
t = (log(30000/20000)) / (log(1 + (0.0428/12)))
t = 5.97 years
Rounding to the nearest tenth of a year, Louise will need to wait 6.0 years in order to reach her goal of $30,000.
what is the order of processes that support the central dogma?
The order of processes that support the central dogma are:1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
The central dogma of molecular biology describes the flow of genetic information within a biological system. The method by which DNA instructions are translated into useful products is known as the "Central Dogma." Francis Crick, who discovered the structure of DNA, first put up the idea in 1958.
The order of processes that support the central dogma are:
1.DNA replication: the process by which DNA makes a copy of itself.
2.Transcription: the process by which RNA is synthesized from a DNA template.
3.Translation: the process by which proteins are synthesized from RNA templates.
In summary, the central dogma can be described as follows: DNA is replicated to make more DNA, DNA is transcribed into RNA, and RNA is translated into proteins.
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14) For y=-7, when x = -35, what is the constant of variation and what is the direct-variation equation?
Is (x + 2) a factor of the polynomial:x4 +
x³ - 2x² + 3x + 7, and what was the
remainder?
Answer:no
Step-by-step explanation:
3. Find the coordinates of the center and the measure of the radius for a circle whose equation is
x²+(y-5)² = 9
Answer:
Radius is 3 units
Center is (0,5)
Step-by-step explanation:
Compared to the standard form of the equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], we have a center of [tex](h,k)\rightarrow(0,5)[/tex], and a radius of [tex]r=3[/tex].
Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
10y - 14x² + 3x - 4x² + 4y - 6
Answer: -18x² + 3x +14y - 6
10y - 14x² + 3x - 4x² + 4y - 6
- 14x²- 4x² + 3x + 10y + 4y -6
-18x² + 3x +14y - 6
bearing is measured from reference line clockwise or counter-clockwise. group of answer choices true false
Bearing is measured from reference line clockwise or counter-clockwise - FALSE.
A bearing is an angle that is calculated clockwise from the north.
The vertical angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.
Angles are measured in comportments clockwise from north.
The direction of north must be identified before taking a bearing measurement.
The math exam question will typically include this north direction. The required angle is then measured in a clockwise fashion. Since all bearings must be reported in three figures, we must begin the three-figure bearing with zero if the angle measured is less than 100 degrees.
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If one bottle holds 750 mL of lemonade how much lemonade will 24 bottles hold tell me two answers
The total volume of lemonade held by 24 bottles would be 18,000 mL (750 mL x 24) or 24x 0.75 liters = 18 liters.
And it would be to express the total volume in terms of the volume of one bottle. You can say that 24 bottles of lemonade is equal to 18 times the volume of one bottle, or 18 x 750 mL = 18,000 mL. This can also be written as 24 x 0.75 liters = 18 liters. This can also be expressed as 18 liters, since 1 liter is equal to 1000 mL.
Regardless of how you choose to express the answer, both methods give us the same result: 24 bottles of lemonade hold a total of 18,000 mL or 18 liters of the beverage. This information can be useful in various contexts, such as for planning a party or for ordering supplies for a lemonade stand. It's important to note that while both answers give the same result, they present the information in different ways. The first answer provides the total volume of lemonade held by all 24 bottles, while the second answer provides the number of times the volume of one bottle is contained within the total volume. Both answers provide useful information and the choice of which one to use may depend on the specific context in which the question is being asked.
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Suppose that the amount of algae in a pond doubles every 5 hours. If the pond initially contains
10 pounds of algae, how much algae will be in the pond after 20 hours?
Answer:
160 pounds of algae
Step-by-step explanation:
10 times 2 is 20 ( first 5 hours )
20 times 2 is 40 (10 hours)
40 times 2 is 80 (15 hours)
80 times 2 is 160 ( 20 hours)
there would be 160 pounds of algae
Mallory's Border Collie had 23 puppies in 4 litters. Determine the rate for a ratio of the two different quantities
Answer:
4/23
Step-by-step explanation:
I Did The Quiz :)
If x - 2/3 = 1/2 then
Answer:
x=7/6
Step-by-step explanation:
add 2/3 to both sides
Please find the missing side length using trig!
The length x of the right triangle is 8.66 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, the side of the right triangle can be found using trigonometric ratios as follows:
Hence,
tan 60° = opposite / adjacent
where
opposite side = x
adjacent side = 5
Therefore,
tan 60° = x / 5
cross multiply
x = 5 tan 60°
x = 5 × 1.73205080757
x = 8.66025403784
x = 8.66 units
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Find the midpoint M of the line segment joining the points A = −6, 1 and B = −2, 7.
Answer:
M (-4; 4)
Step-by-step explanation:
A ( -6; 1), B ( -2; 7)
M (midpoint) = ( ?; ?)
Midpoint coordinates formulas are
x = (x1 + x2) / 2
y = (y1 + y2) / 2
xM = (xA + xB) / 2 =
= (-6 + (-2)) / 2 = (-6 - 2) / 2 = -8 / 2 = -4
yM = (yA + yB) / 2 =
= (1 + 7) / 2 = 8 / 2 = 4
M (-4; 4)
given f(x)=2x^{2}+4 find f(3)
Answer: 22
Step-by-step explanation:
f(x) is basically the y of the function and we sent x=3. go back to the function and plug in 3 in the x. then solve 3^2=9 2x9=18 18+4=22 BOOOM MATHH
Given G is the midpoint of EH, FG= GI, Prove triangle EFG= triangle HIG
If G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG
What are Similar Triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .
Given G is the midpoint of EH,
FG≅ GI,
We need to Prove triangle EFG= triangle HIG
∠E and ∠H are right angles, FG≅ GI from given.
∠E≅ ∠H from given
G is midpoint of EH from given
EG≅ GH by definition of congruent triangles.
triangle EFG≅ triangle HIG by SAS congruence postulate.
Hence, if G is the midpoint of EH, FG= GI, then triangle EFG= triangle HIG
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2) g(x) = 4x + 5
f(x)=-3x²-3x
Find g(x) + f(x)
Answer:
[tex]\huge\boxed{\sf -3x\² + x + 5}[/tex]
Step-by-step explanation:
Given functions:g(x) = 4x + 5
f(x) = -3x² - 3x
Add both functionsg(x) + f(x):= 4x + 5 + (-3x² - 3x)
= 4x + 5 - 3x² - 3x
Combine like terms= 4x - 3x + 5 - 3x²
= x + 5 - 3x²
= -3x² + x + 5[tex]\rule[225]{225}{2}[/tex]
ari thinks the perfect milkshake has 5 55 scoops of ice cream for every 3 33 spoonfuls of caramel. freeze zone makes batches of milkshakes with 10 1010 scoops of ice cream and 7 77 spoonfuls of caramel. what will ari think about the amount of caramel in freeze zone milkshakes?
Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high, since the ratio of ice cream to caramel is much higher than her ideal ratio.
Ari's ideal ratio of ice cream to caramel for a milkshake is 5 scoops of ice cream for every 3 spoonfuls of caramel. Freeze Zone's milkshakes, however, have a ratio of 10 scoops of ice cream for every 7 spoonfuls of caramel, which is significantly higher than Ari's ideal ratio. Therefore, Ari will likely think that the amount of caramel in Freeze Zone milkshakes is too high. The higher ratio of ice cream to caramel means that the milkshake will be sweeter, and may not have the desired balance of flavors that Ari prefers. Ari may also think the milkshake is too heavy or overly sweet, since the extra caramel creates a consistency that is different from what she is used to. Ultimately, Ari will likely think that the amount of caramel in Freeze Zone's milkshakes is too high for her liking.
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What is the length of the short leg of a 30-60-90 triangle if the long leg has a length of 8√3?
The ratio of the sides' lengths of a triangle with sides of 30-60-90 is:
short leg : long leg : hypotenuse = 1 : √3 : 2
Consequently, the triangle's short leg's measurement is 8.
What exactly is a triangle?A triangle is a 3-sided shape with 3 vertices. The angles of the triangle are formed by the connection of the 3 sides end to end at a single point. The triangle's three angles sums up to 180 degrees.
What are the three primary sorts of triangles?Triangles can be divided into three varieties based on the lengths of their sides, which are:
Scalene.
Isosceles.
Equilateral.
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Greta has two pet lizards, Draco and Lizzy. For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets. Last week, Greta fed Draco 77 crickets.
Greta feeds Lizzy 56 crickets when she feeds Draco 77.
What do you understand by Proportion?Proportion, in general is referred to as a part, share or number considered in comparative relation to a whole.
According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b
Given:
For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Let solve it by an equality
[tex]\frac{11}{8} = \frac{77}{x}[/tex]
We want to solve for x.
We can do so by finding how much larger the second fraction is than the first.
In this case, 77 is 7 times larger than 11.(77/11 = 7)
So, we know that x must be 7 times larger then 8( because the fractions are proportinal)
Since x is 7 times larger than 8, we can use 7 times 8 to find the value.
7 times 8 i s56
56 crickets for Lizzy.
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x is 7 times larger than 8, we can use 7 times 8 to find the value, 7 times 8 is 56. Greta feeds Lizzy 56 crickets while she feeds Draco 77.
What is the Proportion?
Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole.
According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a: b or a/b
Given:
For every 11 crickets Greta feeds Draco, she always feeds Lizzy 8 crickets.
Let solve it with an equality
11/8 = 77/x
We want to solve for x.
We can do so by finding how much larger the second fraction is than the first.
In this case, 77 is 7 times larger than 11.(77/11 = 7)
So, we know that x must be 7 times larger than 8( because the fractions are proportional)
Hence, x is 7 times larger than 8, we can use 7 times 8 to find the value.
7 times 8 is 56.
56 crickets for Lizzy.
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Jack works at a party supply store. He sold 750 balloons in the last 15 days. What was his selling rate in balloons per day
his selling rate is: 750 balloons / 15 days = 50 balloons per day . To calculate Jack's selling rate in balloons per day, we need to divide the total number of balloons he sold by the number of days he worked.
This means that Jack sold an average of 50 balloons per day over the last 15 days. This information is useful for several reasons. For example, the party supply store might use this information to evaluate Jack's performance and determine whether he is meeting their expectations. It might also be useful for forecasting future sales, since if Jack continues to sell balloons at a rate of 50 per day, we can estimate how many balloons he will sell in a future period of time by multiplying the number of days by 50. In this case,
Jack sold 750 balloons in 15 days, so his selling rate is: 750 balloons / 15 days = 50 balloons per day
It's important to note that the selling rate of 50 balloons per day is an average, and it's possible that Jack's sales varied from day to day. For example, he might have sold more balloons on some days and fewer on others. However, by calculating the average selling rate, we get a general sense of how many balloons Jack sold per day over the course of the last 15 days.
In conclusion, Jack's selling rate in balloons per day over the last 15 days was 50 balloons. This information provides insight into Jack's performance and can be used to make informed decisions about future sales.
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Which of the following rational functions is graphed below?
-5
OA. F(x)=
O C. F(x) =
1
B. F(x) = (x+2)(x-3)
OD. F(x) =
5
x(x - 2)
(x-2)
(x + 3)
1
(x-2)(x+3)
5
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
f(x) = x(x + 5)(x - 2)
x(x + 5)(x - 2) = 0
x = 0, x + 5 = 0, x - 2 = 0
x = 0, -5 and 2
The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
Hence, the graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2
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11 Jack and Sadia work for a company that
sells boxes of breakfast cereal. The
company wants to have a special offer.
Here is Jack's idea for the special offer.
Put 25% more cereal into each box and do not change the price.
Here is Sadia's idea.
Reduce the price and do not change the amount of cereal in each
box.
Sadia wants her idea to give the same value for money as Jack's idea.
By what percentage does she need to reduce the price?
Answer:
20% reduction in price
Step-by-step explanation:
Let the original price of each box be P and original quantity be Q. The unit rate is P/Q
Jack's approach
increase quantity by 25% = 0.25Q
New quantity = Q + 0.25Q = Q(1 +0.25) = 1.25Q
Unit rate = P/1.25Q
Sadia's approach
Reduce price and keep quantity same
Let price reduction be d% = d/100
Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10
Price reduction = P x r = Pr
New price = P - Pr = P(1-r)
Unit rate by this method =P(1-r) /Q
Both unit rates have to be the same if both values are the same
So
[tex]\dfrac{P}{1.25Q} = \dfrac{P(1-r)}{Q}\\\\\dfrac{P}{Q} \cdot \dfrac{1}{1.25} = \dfrac{P}{Q} \cdot (1-r)\\\\[/tex]
Eliminate [tex]\displaystyle {\dfrac{P}{Q}}[/tex] common factor from both sides to get
[tex]\dfrac{1}{1.25} = 1- r[/tex]
[tex]\dfrac{1}{1.25} = 0.8\\\\[/tex]
So we get
[tex]1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\[/tex]
0.2 works out to 0.2 x 100 = 20%
So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%
Rewrite in simplest radical form
how many ounces of a 30% alcohol solution must be added to a 70% alcohol solution to make 50 ounces of a 40% alcohol solution?
To make 50 ounces of a 40 percentage alcohol solution, eight ounces of the 30% solution must be mixed with the 70% solution.
1. Round the two solutions' initial concentrations to the nearest tenth (30% alcohol = 0.3; 70% alcohol = 0.7).
2. Determine the combined solution's overall alcohol content
(30% + 70%): 0.3 + 0.7 = 1.
3. Multiply 50 ounces by 0.4 to get the total amount of alcohol required for a 40% solution:
50 x 0.4 = 20 ounces.
4. Determine how much 30% solution is required to reach the desired concentration. 1 divided by 20 equals 20 ounces.
5. Subtract the quantity of the existing 70% solution:
(50 ounces x 0.7)/20 ounces = 8 ounces.
6. The outcome is that 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.
The original concentrations of the two solutions must first be converted to decimals (30% alcohol = 0.3; 70% alcohol = 0.7) in order to determine how much of a 30% alcohol solution has to be added to a 70% alcohol solution to create 50 ounces of a 40% alcohol solution. The two decimals can then be added to determine the total amount of alcohol present in the combined solution: 0.3 + 0.7 = 1. In order to determine the entire amount of alcohol required for a 40% solution, multiply 50 ounces by 0.4, which results in 20 ounces. The amount of the 30% solution required to reach the specified concentration can be estimated by dividing 20 ounces by 1, which is 20 ounces. Then, 20 ounces must be divided by the amount of the 70% solution that is already present to get 8 ounces. As a result, 8 ounces of the 30% solution are required to create 50 ounces of the 40% solution.
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A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company.
The expected value of the policy for the insurance company: $359.38
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
The expected value of the policy for the insurance company can be calculated as follows:
Expected value = (Probability of survival) x (Annual payment)
= 0.999057 x $360
= $359.38
So, the expected value of the policy for the insurance company is $359.38.
It's important to note that this is just an estimate based on statistical probabilities and does not guarantee the outcome. The actual value could be higher or lower than this estimate, depending on the actual lifespan of the policyholder.
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