This is a probability problem. To find the probability of removing two blue counters, we need to calculate the number of possible outcomes of removing two blue counters out of seven counters (3 blue and 4 yellow).
The number of possible outcomes of removing two blue counters is 3C2 = 3! / (2! * (3-2)!) = 3.
So, the probability of removing two blue counters is 3/7C2 = 3/21.
To find the probability of X being equal to 2, we need to calculate the probability of removing two blue counters.
Therefore, the probability of X being equal to 2 is 3/21.
3x-1/2y=5x+4 what is the slope
Answer: The slope of a line in the form y = mx + b can be found by taking the coefficient of x, which is m. In this equation, the slope is not in that form, so we need to isolate y and put it in that form.
Starting with the equation:
3x - 1/2y = 5x + 4
We'll isolate y by subtracting 3x from both sides:
-1/2y = 2x + 4
And then multiply both sides by -2 to solve for y:
y = -4x - 8
So the slope of the line is -4.
Step-by-step explanation:
let f be the continuous function defined on [-4,3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above. Let g be the function given by g(x) =
Answer: no exact answer
Step-by-step explanation:
A jar contains 70 L of juice. It is poured into
glasses, each of 150 mL capacity. How many glasses
are completely filled with the juice and how much juice
is left in the jug?
First, we need to convert the volume of the juice in the jar from liters to milliliters, since the volume of the glasses is given in milliliters.
1 liter = 1000 milliliters
So, 70 liters = 70 * 1000 = 70,000 milliliters
Next, we'll divide the volume of the juice in the jar by the volume of each glass to find out how many glasses can be filled with the juice.
70,000 milliliters ÷ 150 milliliters/glass = 466.67 glasses (rounded to the nearest whole number)
Therefore, 466 glasses can be filled completely with the juice.
Finally, we can find out how much juice is left in the jar by subtracting the total volume of the juice used to fill the glasses from the volume of the juice in the jar.
70,000 milliliters - (466 glasses x 150 milliliters/glass) = 70,000 milliliters - 69900 milliliters = 800 milliliters
So, 800 milliliters of juice is left in the jar.
What does it mean when someone writes (n k) or n choose k?
"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula."
What is n Choose k Formula?C (n, k) represents "n select k" (or) [tex]_n C_k[/tex] (or) (n k) . A binomial coefficient is another name for it. It is used to determine how many different ways there are to choose k distinct items from n distinct items.
The combination formula is another name for the n select k formula (as we call a way of choosing things to be a combination). Factorials are used in this formula.
The n Choose k Formula is:
C (n , k) = n! / [ (n-k)! k! ]
"Choose" means "select". Finding the number of possible methods to choose k items out of n items is done using the "n choose k formula." We occasionally prefer choosing than ordering things.
When preparing for a trip, for instance, you decide to bring five of your ten brand-new clothes. There are several ways you can achieve this; it doesn't matter what sequence you choose them in, but it does matter which dresses you picked.
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please help! I'm struggling a lot with this domain and range.
=====================================================
Explanation:
The domain is the set of allowed x inputs.
In this case, we can plug in anything but x = 2 because of the vertical asymptote here.
This means the domain is the interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] that notation basically says "start with the entire real number line. Then poke a hole, or remove, 2 from the number line".
------------
The range is the set of possible y outputs. In this case, the domain and range lead to the same interval notation since we're kicking out "2" each time. This time we focus on the horizontal asymptote. The curve gets closer and closer to these dashed lines but never actually reaches them.
Since [tex](-\infty,2) \cup (2,\infty)[/tex] is one of the possible ways to represent the range, one of the answers is choice A.
The interval notation [tex](-\infty,2) \cup (2,\infty)[/tex] is too vague because it's not clear if we're talking about the domain or range. The notation [tex]\left\{\text{y}|\text{y} \in \text{R}, \ \text{y} \ne 2\right\}[/tex] is more specific. It says "y is a real number such that it cannot equal 2". In other words "y can be anything but 2". This tells us that choice D is another answer.
So either y < 2 or y > 2 which represents us being below the horizontal asymptote or above it respectively.
The third and final answer is choice E.
Find the equation of the parabola whose equation of the tangent at vertex is [tex]3x - 4y = 5[/tex] and focus at the point [tex](1, 2)[/tex].
Answer: The equation of the tangent to a parabolic curve y = ax^2 + bx + c at the point (h, k) can be expressed as:
y = a(x - h)^2 + k
So, we know the equation of the tangent at vertex of the parabolic curve is 3x - 4y = 5, so the vertex of the parabolic curve is (h, k) = (2, -3/2).
The equation of a parabolic curve with vertex (h, k) and focus (h, k + p) is given by:
y = a(x - h)^2 + k, where a = -1/4p.
So, substituting the values of the vertex (2, -3/2) and the focus (1, 2) into the above equation, we have:
-3/2 = a(2 - 2)^2 - 3/2, so a = -1/4p.
And, substituting the values of the focus (1, 2) into the equation y = a(x - h)^2 + k, we have:
2 = -1/4p(1 - 2)^2 - 3/2, so p = 1/2.
So, the equation of the parabolic curve with focus (1, 2) and vertex (2, -3/2) is:
y = -1/4 * 1/2 * (x - 2)^2 - 3/2.
This is the equation of the parabola that has the equation of the tangent at vertex 3x - 4y = 5 and focus at the point (1, 2).
Step-by-step explanation:
You started a savings account by depositing $4,200. The savings account earns 2.1% APY, compounded monthly. What was the balance in the account after 2 months?
1=Prt
4214.7 is the balance in the account after 2 months .
What does compound and simple interest mean?
A fixed proportion of the principal amount borrowed or lent is what is known as simple interest and is paid or received over a given period of time.
Borrowers are required to pay interest on interest in addition to principal because compound interest accrues and is added to the total amount of interest from earlier periods.
P = $4200
R = 2.1% = 2.1/100 = 0.021 =
T = 2 month = 2/12 = 1/6
I = PRT
= 4200 * 0.021 * 1/6 = 14.7
Amount = P + I = 4200 + 14.7 = 4214.7
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Mr. Jackson had to attend a meeting in San Fransisco 300 miles from his home. He traveled the first 90 minutes at 64 miles per hour. The next hour he traveled 66 miles per hour. If he reached San Fransisco three hours later what was his average speed for the last three hours?
Let's call the average speed for the last three hours "S".
First, we need to find the total distance that Mr. Jackson traveled in the last three hours. He traveled 300 miles in total, and he covered 64 miles in the first 90 minutes, so he had 300 - 64 = 236 miles left to travel.
Next, we need to find the time he spent traveling in the last three hours. If he traveled for three hours, and the first hour he traveled at 66 miles per hour, then he covered 66 miles in the first hour. So, he had 236 - 66 = 170 miles left to travel in the last two hours.
Finally, we can use the formula for average speed: distance divided by time. The total distance he traveled in the last three hours was 170 miles, and the time he spent traveling was 2 hours, so his average speed for the last three hours was:
S = 170 miles / 2 hours = 85 miles per hour
So, Mr. Jackson's average speed for the last three hours was 85 miles per hour.
Answer:
68 mph
Step-by-step explanation:
Let's call the average speed for the last three hours "S".
The total distance traveled for the last three hours is 300 - 64 * 1.5 = 300 - 96 = 204 miles.
So, over the last three hours, Mr. Jackson covered a distance of 204 miles at a speed of S.
The time it took him to cover that distance is 3 hours.
We can use the formula distance = speed * time to find S:
204 = S * 3
Solving for S:
S = 68 mph
So the average speed for the last three hours was 68 mph.
to identify the point in a distribution at which 50% of scores fall above and 50% fall below a given score, which measure of central tendency would you report? group of answer choices mode mean median average
The median is the point in a distribution where 50% of the scores fall above and 50% fall below a certain score.
In a distribution, the median is the number that separates the top 50% of scores from the bottom 50% of scores. When the data is organised from lowest to highest, it is the midway value.
The mode is the most common value in a distribution, and it is not always the same as the median. The mean is the total of all scores divided by the number of scores, and it is impacted by outliers or extreme values in the data. Depending on the context, the term "average" can refer to either the mean or the median. When individuals say "average" without any qualification, they typically mean the mean.
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autocorrelation a. should cross-section or time-series multiple regressions be checked for autocorrelation? b. explain what autocorrelation is. c. what is the name of the test for determining if a regression has autocorrelation? d. how do you correct for autocorrelation?
The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).
a. Both cross-section and time-series multiple regressions should be checked for autocorrelation.
b. Autocorrelation is the correlation of a variable with itself over successive time periods. In the context of a regression, it is the correlation between the residuals or errors of a regression model over successive time periods.
c. The Durbin-Watson test is used to determine if a regression has autocorrelation.
d. Autocorrelation can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model. This is known as the autoregressive model. The formula for calculating the autoregressive coefficient is: AR(t) = ρ * AR(t-1), where ρ is the correlation coefficient.
The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).
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For some reason, Brainly keeps saying that the question I'm asking hurts their feelings though I am just typing out the question from the screenshot. please take a look
There is part A and Part B.
1) Note that the ratio of the Area of the Trapezoid to that of the Triangle is 3:1 (Option D)
2) No. Ivan is not correct. He multiplied the base by the length of the side of the parallelogram to get 99cm the correct answer, however, is 90cm.
What is the rationale for the above response?1) To determine the ratio of the Trapezoid to that of the Triangle, we need to first find the Areas of both.
a) To find the area of a trapezium, we use the formula:
Area = (1/2) × (sum of the parallel sides) × (height)
In this case, the trapezium has bases of length 9 cm and 18 cm, and a height of 10 cm. So, we can substitute these values into the formula to get:
Area = (1/2) × (9 + 18) × 10
Area = (1/2) × 27 × 10
Area = 135 square cm
Therefore, the area of the trapezium is 135 square cm
b) To find the area of an isosceles triangle, we can use the formula:
Area = (1/2) × base × height
In this case, the base of the triangle is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:
Area = (1/2) × 9 × 10
Area = 45 square cm
Therefore, the area of the isosceles triangle ACE is 45 square cm.
c) To find the ratio of the area of the trapezium to that of the isosceles triangle, we need to calculate the area of the isosceles triangle using the given dimensions and then divide the area of the trapezium by the area of the triangle.
The ratio of the area of the trapezium to the area of the triangle is:
Ratio = Area of trapezium / Area of triangle
Ratio = 135 / 45
Ratio = 3
Therefore, the ratio of the area of the trapezoid to that of the triangle is 3:1.
d) Note that the area of a parallelogram is given by the formula:
Area = base x height
In this case, the base of the parallelogram is 9 cm and the height is 10 cm. So, we can substitute these values into the formula to get:
Area = 9 cm x 10 cm
Area = 90 square cm
Therefore, the area of the parallelogram is 90 square cm, not 99cm as indicated by Ivan.
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please help meeeeeeeeeee
The number of pet-owners that are in the union of cat owners and other pet owners is given as follows:
20 pet-owners.
How to obtain the union of two sets?The set representing the union of two sets is composed by all the elements that belong to at least one of the sets.
Hence the union of pet-owners that are in the union of cat owners and other owners is composed as follows:
1 + 1 + 3 + 6 = 11 cat owners.7 + 2 = 9 other owners who are not cat owners.Hence the total number is given as follows:
11 + 9 = 20.
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Simplify the expression.
-9(a + b) - 3a
Find the area of the semicircle.
Either enter an exact answer in terms of pi or use 3.14 for pi and enter ur answer as a decimal
The area of the semi circle is 14.13 units²
What is the area of a semi circle?a semicircle is a one-dimensional locus of points that forms half of a circle. It is a circular arc that measures 180°. It has only one line of symmetry.
The area of a semicircle is the half of the area of a full circle.
The area of a full circle is πr², therefore the area of a semicircle is ½πr²
r = d/2 = 6/2 = 3
A = ½πr²
= 1/2 × 3.14 × 3²
A = 28.26/2
A = 14.13 units²
therefore the area of the semi circle is 14.13 units²
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can someone help pls
Answer:
55
Step-by-step explanation:
Since 1 rectangle is 10 and there are 5, that means the whole length is 50.
Which means with can set the equation equal to 50
[tex]x - 5 = 50[/tex]
Adding 5 gets us
[tex]x = 55[/tex]
Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times.
Robin ride her bike this week 35 miles.
Robin rides her bike 3 miles to school.
She rides home a different way that is 4 miles long.
This week, Robin rode to school and back 5 times.
For one time ride to school from house = Rode to School + Rode To home
For one time ride to school from house = 3 + 4
For one time ride to school from house = 7
Robin rides total of 5 times.
So, For five time ride to school from house = 5 × For one time ride to school from house
For five time ride to school from house = 5 × 7
For five time ride to school from house = 35 miles
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The complete question is:
Robin rides her bike 3 miles to school. She rides home a different way that is 4 miles long. This week, Robin rode to school and back 5 times. How many miles did Robin ride her bike this week?
What is true about a system of two linear equations that has no solution?
Answer: The two lines never intersect
Step-by-step explanation:
An algebraic solution for a system of equations means that the graphs of the two equations intersect at some point. If no such point can be found, it means the graphs never intersect.
A. ) Find the value of each inverse trigonometric ratio in degrees.
B. ) Find the exact value of each inverse trigonometric ratio in radians
It is possible for an angle to have another value whose sine, cosine, or tangent is equal to the given ratio, and this value may be in a different quadrant.
A) To find the value of each inverse trigonometric ratio in degrees, we need to use a calculator or reference table to determine the angle whose sine, cosine, or tangent equals the given ratio.
The inverse sine, cosine, and tangent functions are denoted as [tex]sin^-1, cos^-1, tan^-1[/tex] respectively.
For example, if we are given sin^-1(1/2), we need to find the angle whose sine is 1/2. Using a calculator or reference table, we can determine that the angle is 30 degrees. Therefore, [tex]sin^-1(1/2) = 30degree[/tex]
Similarly, [tex]cos^-1(1/2) = 60 degrees[/tex] and [tex]tan^-1(1) = 45 degrees[/tex] .
B) To find the exact value of each inverse trigonometric ratio in radians, we need to convert the degree value to radians by multiplying by π/180. For example, if [tex]sin^-1(1/2) = 30 degrees[/tex] , we can convert to radians as follows:
[tex]sin^-1(1/2) = 30 degrees = (30\pi/180) radians = (\pi/6) radians[/tex]
Therefore,[tex]sin^-1(1/2) = \pi/6 radians[/tex]
Similarly, [tex]cos^-1(1/2) = 60 degrees = (60\pi/180) radians = (\pi/3) radians[/tex]
and [tex]tan^-1(1) = 45 degrees = (45\pi/180) radians = (\pi/4) radians.[/tex]
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Which ordered pairs are in the solution set of the system of linear inequalities?
y2-3x+2
y< 2x+3
Answer: 2
Step-by-step explanation:
In AOPQ, p = 38 cm, q = 29 cm and 20=39°. Find the length of o, to the nearest
centimeter.
Answer:
Step-by-The length of o in the triangle AOP can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and opposite angle C, the following formula holds:
c^2 = a^2 + b^2 - 2ab cos(C)
In this case, a = 38 cm, b = 29 cm, and C = 39°. The length of o can be found by rearranging the formula and solving for c:
c^2 = 38^2 + 29^2 - 2(38)(29) cos(39°)
c = sqrt(38^2 + 29^2 - 2(38)(29) cos(39°))
Using a calculator, we can find that c ≈ 47.3 cm, to the nearest centimeter, o = 47 cm.step explanation:
what is the difference between assignment and equality? during assignment, the result of the calculation on the right side of an equals sign is assigned to a variable on the left of the equals sign. equality is a logical test that evaluates whether two values are equivalent. assignment is a logical test that evaluates if two values are equivalent. during equality, the result of the calculation on the right side of an equals sign is set to a variable on the left of the equals sign. assignment and equality perform the same action. none of the above
During assignment, the result of the calculation on the right side of an equals sign is assigned to a variable on the left of the equals sign. Where as, equality is a logical test that evaluates whether two values are equivalent.
In the given question, the first option is correct among the four.
An assignment operator assigns the result of the calculation on the right side of an equals sign to a variable on the left of the equals sign. It is indicated by ' = '.
Example: s = 4 + years, then the operator assigns the value of the sum of 4 and years to the variable s.
On the other hand, equality is a logical test that evaluates whether two values are equivalent or not. It is indicated by ' == '. The results obtained by this operator is either true or false.
Example: If f == s, it checks whether the value stored in f equals the value stored in s. If they are equal it returns output as true else false.
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What is the perimeter, p, of a rectangle that has a length of x 8 and a width of y − 1? p = 2x 2y 18 p = 2x 2y 14 p = x y − 9 p = x y 7
The perimeter of the given rectangle is option (b) 2x + 2y + 14.
Perimeter is a mathematical term used to describe the distance around the boundary of a two-dimensional shape.
In this case, we are given a rectangle with a length of x+8 and a width of y-1, and we are asked to find its perimeter, p.
To find the perimeter of a rectangle, we need to add up the lengths of all four sides. In a rectangle, opposite sides are equal in length, so we can simplify the calculation by multiplying the sum of the length and width by two. This gives us the formula:
perimeter = 2(length + width)
Substituting the given values for the length and width of our rectangle, we get:
p = 2(x+8 + y-1)
p = 2(x+y+7)
Simplifying further, we get the answer:
p = 2x + 2y + 14
Therefore, the correct option is (b).
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Complete Question:
What is the perimeter, p, of a rectangle that has a length of x + 8 and a width of y − 1?
a) p = 2x + 2y + 18
b) p = 2x + 2y + 14
c) p = x + y − 9
d) p = x + y + 7
Convert (-z-2)^2 into a quadratic trinomial and (-n+4)^2 and (-m-10)^2
(please help)
The quadratic trinomial of the given expressions are z² + 4 + 4z, 16 + n² - 8n, m² + 100 + 20m respectively.
What do you understand by Quadratic Trinomial?A trinomial is an algebraic expression that has three terms. An algebraic expression consists of variables and constants of one or more terms.
A polynomial is an algebraic expression that has one or more terms and is written as [tex]a_0x^n + a_1x^{ n - 1} + a_2x^{n-2} + ...+ a_n x^0[/tex] in the standard form. Where [tex]a_0, a_1, a_2, ....,a_n[/tex] are constants and n is a natural number.
A quadratic trinomial is a type of algebraic expression with variables and constants. It is expressed in the form ax² + bx + c, where x is the variable and a, b and c are non-zero real numbers. A quadratic trinomial also describes the discriminant D where it defines the quantity of an expression and it is written as D = b² - 4ac.
Given:
(-z - 2)²
⇒ [-(z + 2)]²
⇒ (z)² + (2)² + 2(z)(2)
⇒ z² + 4 + 4z
(4 - n)²
⇒ (4)² + (n)² - 2(4)(n)
⇒ 16 + n² - 8n
(-m - 10)²
[-(m + 10)]²
⇒ (m)² + (10)² + 2(m)(10)
⇒ m² + 100 + 20m
So, the expressions are converted into quadratic trinomial.
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please answer asap i need helpp
Answer:
110°
Step-by-step explanation:
]%}}%¶¢{^[€{¢¶¢¶€¶
Answer: 110˚
Step-by-step explanation:
Complementary angles have a sum of 90˚
With this knowledge, we can say <B = 90 - <A = 90 - 20 = 70˚
Supplementary angles have a sum of 180˚
With this knowledge we can say <C = 180 - <B = 180 - 70 = 110˚
∴ Measure of angle C = 110˚
suppose that 5 out of the 19 doctors in a small hospital are general practitioners, 9 out of the 19 are under the age of 50 , and 3 are both general practitioners and under the age of 50 . what is the probability that you are randomly assigned a general practitioner or a doctor under the age of 50 ? enter a fraction or round your answer to 4 decimal places, if necessary.
The probability of being assigned a general practitioner or a doctor under the age of 50 is 11/19 or approximately 0.5789 (rounded to four decimal places).
We are given that there are 5 general practitioners (GPs) out of 19 doctors in the hospital, which means that the probability of being assigned a GP is 5/19.
We are also given that there are 9 doctors under the age of 50 out of the 19 doctors in the hospital, which means that the probability of being assigned a doctor under the age of 50 is 9/19.
However, we need to subtract the probability of being assigned a doctor who is both a GP and under the age of 50 because this group is counted twice in the above probabilities.
We are given that there are 3 doctors who are both GPs and under the age of 50. Therefore, the probability of being assigned a doctor who is both a GP and under the age of 50 is 3/19.
To use the inclusion-exclusion principle, we add the probabilities of being assigned a GP and being assigned a doctor under the age of 50, and then subtract the probability of being assigned a doctor who is both a GP and under the age of 50.
P(GP or Under 50) = P(GP) + P(Under 50) - P(GP and Under 50)
= 5/19 + 9/19 - 3/19
= 11/19
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please help me i dont understand
Answer:
x=15°
∡Q= 75°
Step-by-step explanation:
supplementary angles means the sum of the angles =180°
so, 5x+105°=180°
5x=75°
x=15°
∡Q= 75°
an algebra class has 6 students and 6 desks. for the sake of variety, students change the seating arrangement each day. how many days must pass before the class must repeat a seating arrangement?
Using the concept of arrangements, 720 days must pass before the class must repeat a seating arrangement
The class has 6 students and 6 desks and students change the seating arrangement each day. We are asked to calculate the number of days that must pass before the class must repeat a seating arrangement.
The number of days that must pass before the class must repeat a seating arrangement is equal to the total number of seating arrangements.
Person one has 6 positions to choose from, person 2 has 5 positions to choose from and so on.
Total number of seating arrangements = 6 × 5 × 4 × 3 × 2 × 1
= 720
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2. Order the following decimals from least to greatest.
0.439
0.394
0.441
0.531
0.342
i have exactly ten coins whose total value is $. if three of the coins are quarters, what are the remaining coins?
it would be 5 pennies and two dimes
if 3 are quarters, that is 75 cents. if you add two dimes, it's now 95, and making the total number of coins 5. then you add 5 pennies, you get a total of 100 cents, one dollar, and now have 10 coins. hope its right
3
Type the correct answer in each box. Use numerals instead of words.
Consider this expression.
The equivalent expression to -4x² + 2x - 5(1 + x) is given as follows:
-4x² - 3x - 5.
How to obtain the equivalent expression?The expression for this problem is defined as follows:
-4x² + 2x - 5(1 + x)
To obtain the equivalent expression, we apply the distributive property to -5(1 + x) as follows:
-5(1 + x) = -5 - 5x.
Then the expression is given as follows:
-4x² + 2x - 5 - 5x.
Combining the like terms, we have that the expression is given as follows:
-4x² - 3x - 5.
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