Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
Define median.When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.
Here,
(48, 51, 65, 71, 61, 45, 48, 72, 74, 66, 43, 47, 70, 66, 45) sample data; sample mean, x = 58.133; sample size, n = 15; standard deviation, s = 11.6;
Standard deviation equals sd/√(n)
where, n = sample size and sd = standard deviation
Margin of error is equal to t alpha/2 and the standard error is (11.6/√( (15)) = 2.995. (standard error)
where ta/2 is the t-table level of significance, alpha is 0.05 from the standard normal table, the two-tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145, and the margin of error is 2.145 * 2.995, which equals 6.425. The confidence interval for this margin of error is [58.133 6.425] = [51.708, 64.558].
being that,
sample data: (48 , 51 , 65 , 71 , 61 , 45 , 48 , 72 , 74 , 66 , 43 , 47 , 70 , 66 , 45 )
sample mean, x =58.133
standard deviation, s =11.6
sample size, n =15
level of significance, alpha = 0.05
from standard normal table, two tailed value of |t alpha/2| with n-1 = 14 d.f is 2.145
we use CI = x ± t a/2 * (sd/ √((n))
where,
x = mean
sd = standard deviation
a = 1 - (confidence level/100)
ta/2 = t-table value
CI = confidence interval
confidence interval = [ 58.133 ± t a/2 ( 11.6/ sqrt ( 15) ]
= [ 58.133-(2.145 * 2.995) , 58.133+(2.145 * 2.995) ]
= [ 51.708 , 64.558 ]
Therefore , the solution of the given problem of median comes out to be
confidence interval = [ 51.708 , 64.558 ].
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which equation represents the lime that is parallel to y=3 and passes through (-2,-8)?
A. x=-2
B. x=3
C. y=-8
D. y=3x -2
The line that parallels y = 1/2 x + 8 and goes through the point (-2, 2) is represented by the equation y = 1/2 x + 3.
What do you meant by x=-2 and x=3?
The entire time, the x-coordinate -2 is shown. A function is NOT what this is. A number is multiplied three times by itself to form a cube. The symbol for the cube of a number is x. 3.
To increase an integer to the third power is to cube it. A function is an equation with just one solution for every value of y in the equation. A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
A function, in general, is a relationship between two variables. In other words, the relationship x = y2 is not a function.
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Using the collected data above what would be a reasonble rough estimate of a ratio of how many cubic inches per orange?
given the farmer's market wanted o use a box that had the dimensions, approximately how many oranges should fit?
The ratio is 17.14 cubic inch per orange and 168 oranges for given dimensions.
What is volume?In three dimensions, everything takes up some space. What is being measured here is the area's volume. The volume of an object is the area occupied inside its three-dimensional boundaries. It is referred to as the object's capability on occasion.
The amount required to fill an object can be determined by finding its volume, for example, how much water is required to fill a bottle, aquarium, or water tank.
Given
dimensions of box 20 x 13 x 12, 12 x 12 x 12 and 20 x 10 x 6
volume of box 1 = 20 x 13 x 12 = 3120 cubic inches
volume of box 2 = 1728 cubic inches
volume of box 3 = 20 x 10 x 6 = 1200 cubic inch
oranges in box 1 = 96
oranges in box 2 = 53
oranges in box 3 = 37
and radius of orange = 32./2 = 1.6 inches
volume of each orange = 4/3πr³
volume of each orange = 4/3(3.14)(1.6)³
volume of each orange = 4/3(3.14)(4.096)
volume of each orange = 17.14 cubic inches
here one orange will cover 17.14 cubic inches.
7. let the dimension of box is 15 x 12 x 16
volume of box is = 15 x 12 x 16 = 2880 cubic inches
the number of oranges in box will be 2880/17.14 = 168 oranges
Hence there will be 17.14 cubic inch per orange volume is covered, and 168 oranges will be in box for given dimensions.
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Question 7 is incomplete the missing dimensions are 15 x 12 x 16.
Which of the following best describes X on the scatter plot below?
The option that best describes X on the scatterplot is;
C: Outlier
How to Interpret a scatterplot?Let us first define the terms in the given options before we analyze the scatterplot.
1) Negative correlation is defined as a relationship between two variables whereby one variable increases while the other decreases, and vice versa.
2) A nonlinear relationship is also referred to as nonlinear association, and it exists when a constant change in the independent variable does not result in a constant change in the dependent variable.
3) An outlier is defined as a data point that differs significantly from other observations.
4) Clusters are small populations that a wider population is divided into.
Now, from the scatter plot, we see that X is isolated from the plotted points which tells us that it differs greatly from the other points and as such it fits the definition of an outlier.
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The missing options are;
A. negative correlation
B. nonlinear association
C. outlier
D. cluster
Which radicals are already in the simplest form?
Therefore , answering the questions, we can state that a factorial radicals is streamlined, or in its most basic form, when the user ’s behalf has no square components.
what is radicals?Radical is the name for the symbol for the scale factor or nth root. Root expressions are expressions that have square roots. Radicand: An expression or value enclosed by a radical symbol. Examples are the radicalism 7, 2y+1, and on and on. Radicals can also be described using the terms below: Equations that contain radicals are known as radical equations. The expression contained within the square root is referred to as the "root expression."
Here,
We refer to a sum of squares radical as being simplified or in its purest form when the radicand contains no square components.
The simplest form of a radical also exists when the user ’s behalf is not a fraction.
so that radical = 2√x / x
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Prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0
The proof that if if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0 is made by contradiction in this problem.
What is a proof by contradiction?Proof by contradiction is different of traditional proof because it accepts a single example showing that a statement is false, instead of having the need to derive a general relationship for all input values.
For this problem, we must assume the case in which at least one of the terms is non-zero, hence we assume that A is non-zero, hence the expression would be given as follows:
A² + B² + C² = 0
A² = -(B² + C²)
This means that the square of A would be negative. However, the square of a number is always a non-negative number, hence this equation above is a contradiction.
This contradiction was used to prove that if a, b, and c are real numbers such that A^2 + B^2 + C^2 = 0, then A = B = C = 0.
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Given that f(x)=√x, describe the function of g(x)
shown on the graph.
The function is represented by the equation
g(x)=√x +
The function g(x) has a domain x²
The function g(x) has a range y ≥
Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.
Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.
And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.
I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.
Step-by-step explanation:
An octagon has a perimeter of 27 feet. If the sides of the octagon shrink by a scale factor of 8/9, what will the perimeter of the new octagon be
The perimeter of the new octagon be 24 feet.
What is the perimeter of octagon?A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.
There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.
The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.
Given that the perimeter of an octagon is 27 feet
so the length of its side is 27/8 feet
if the side of the octagon shrink by a scale factor of 8/9
The side of new octagon is (27/8) * (8/9)
The side of new octagon is 3 feet.
So the perimeter of new octagon is 8 * side
⇒ the perimeter of new octagon = 8 * 3 feet
⇒ the perimeter of new octagon = 24 feet
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find the value of x !!
thanks :)
According to question as both side are equal so it is an isosceles triangle and the value of X is 18.
What are the properties of Isosceles Triangle?An isosceles triangle is a triangle with two sides of equal length. Some properties of an isosceles triangle include:
The two equal sides are called the legs of the triangle and the remaining side is called the base.The angle between the legs is always equal to the angle between the base and one of the legs.The altitude (perpendicular line segment from a vertex to the opposite side) bisects the base of the triangle.The median (line segment from a vertex to the midpoint of the opposite side) and the altitude from the same vertex to the opposite side are also congruent.The circumcenter (center of the circle that passes through all three vertices) of an isosceles triangle is always located at the midpoint of the line connecting the two vertices of the congruent sides.The line that is bisecting the angle between the congruent sides (also known as the angle bisector) also bisects the side opposite to that angle.so In this triangle ,
The mid point on horizontal side is given and 5m line cut the mid point of both the sides.
both side are equal as it is an isosceles triangle.
and given in the question,
side/2 =9
and one side is equal to x.
and both sides are equal,
therefore
side = 9*2 = 18
so the value of x = 18.
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What is x + y when x = 4 and y = -5
Answer:
x + y = -1
Step-by-step explanation:
4 plus -5 is equivalent (equal to) the equation 4 - 5 which equals -1
Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. How many acorns does frank have in the other hand?
The number of acorns that Frank have in the other hand will be 14.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.
Since Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand.
When Frank has 5 on one hand, the number of acorns that Frank have in the other hand will be:
= 10 + 9 - 5
= 14
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Complete question
Ella has the same number of acorns as frank. Ella has 9 in one hand and 10 in the other hand. Frank has 5 on one hand. How many acorns does frank have in the other hand
Miguel rode his bike to work which was 15 miles from home. However he was too tired to ride back so he got a ride in a
car from a co-worker. He spent a total of 2 hours traveling. The average speed of traveling by car was 3 times faster
than on his bike. What was Miguel's average speed on his bike and in the car?
Answer:
Bike: 10 miles per hour
Car: 30 miles per hour
Step-by-step explanation:
He spent: 2h/(1+3) = 0,5h by car and 0,5h x 3 = 1,5h by bike
The car is: 15 miles/ 0,5h = 30 miles/h
The bike is: 15 miles/ 1,5h = 10 miles/h
Jamie has 18/5 cups of frosting she uses 2/5 cups of frosting for each cupcake how many cupcakes will Savannah be able to frost
Answer:
9
Step-by-step explanation:
18/5 ÷ 2/5 = 18/5 x 5/2 = 9
the mass liquid having a density of 1.40 g and a
volume of 3090 ml
The mass of the liquid is 4326 grams.
How to find the mass of a liquid?The liquid has a density of 1.40 g/ml and the volume of the liquid is 3090 ml. Therefore, the mass of the liquid can be calculated as follows:
The density of a liquid is a measure of how heavy it is for the amount measured. The liquid density is defined as its mass per unit volume.
Therefore,]
density = mass / volume
cross multiply
mass = density × volume
density = 1.40 g/ml
volume = 3090
Therefore,
mass of the liquid = 1.40 × 3090
mass of the liquid = 4326 grams.
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Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.
To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.
To calculate the slope of the line connecting two points, you can use the following formula:
slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.
Step-by-step explanation:
Tyler is 30 years younger than Naeste 9years ago
Answer:
i dont understand this question but i think maybe 21
Step-by-step explanation:
30-9 =21
Answer:
21
Step-by-step explanation:
solue, giving all solutions between 0 and 360 degrees 8 (COS X)² - 10 COS X+3=0
Step-by-step explanation:
please refer to the sketch
Find the slope of the line that passes through (4, 10) and (1, 11).
Answer:
-1/3
Step-by-step explanation:
What is the equation of the line that passes through the point (-4,-4) and has a
slope of -3/4?
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- \cfrac{3}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +4= -\cfrac{3}{4} (x +4) \\\\\\ y+4=-\cfrac{3}{4}x-3\implies {\Large \begin{array}{llll} y=-\cfrac{3}{4}x-7 \end{array}}[/tex]
Answer:
y = -3/4x - 7
Step-by-step explanation:
Given: slope = m = -3/4
Plug this value into the standard slope-intercept equation of y = mx + b.
y = -3/4x + b
To find b, we want to plug in a value that we know is on this line: in this case, point (-4, -4). Plug in the x and y values into the x and y of the standard equation.
-4 = -3/4(-4) + b
To find b, multiply the slope and the input of x(-4)
-4 = 3 + b
Now, subtract 3 from both sides to isolate b.
-7 = b
Plug this into your standard equation.
y = -3/4x - 7
This is your equation.
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What are the dimensions of this shape in terms of the dimensions of the circle?
The diameter or radius of the circle is the dimension of a circle.
What is a circle?The circular line is drawn equidistant from the center point of a circle, which is a two-dimensional geometry object on a plane.
A geometrical rule states that the dimension of an object with n dimensions is n+1. For instance, a square is made up of line segments that are 1d and a cube is built up of squares that are 2d. The circle is therefore 2d or two-dimensional space since it is made up of 1d diameters.
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Answer:
The length of the parallelogram is half of the circumference of the circle, and its height is equal to the radius of the circle.
Step-by-step explanation:
Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).
Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:
F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)
We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:
105 = (R + F) * 3
Now we can substitute the first equation into the second equation:
105 = (R + (R + 5)) * 3
Simplifying and solving for R, we get:
R = 20 mph
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).
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-20 POINTS- Find the value of X
X=[?]
Answer:
x=1252x^2
I'm not sure if I'm 100% correct
Sorry.
I need help completing the square
The formula needed to transform a quadratic polynomial or equation into a perfect square with an additional constant is known as the square formula. It is expressed as, [tex]ax^2 + bx + c = a(x + m)^2 + n[/tex], where, m and n are real numbers.
What does math's "completing the square" mean?When a square is complete, a quadratic is written in the shape of a squared bracket, and if necessary, a constant is added. A good example is [tex]x^2 + 6x + 7[/tex] . First, let's note that [tex](x + 3)^2 = (x + 3)(x + 3) = x^2 + 6x + 9. x[/tex] because this is two more than our expression.
Quadratic Equation: What Is It?The polynomial equations of degree two in one variable of type[tex]f(x) = ax^2 + bx + c = 0[/tex] and with a, b, c, and R R and a 0 are known as quadratic equations. It is a quadratic equation in its general form, where "a" stands for the leading coefficient and "c" for the absolute term of f(x).
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At American Eagle a shirt is on sale from 25 to 15 what is the percent of change for the shirt
Answer:
Percent change = 15 - 25/25 × 100% = -10/25 × 100 = -40%
Step-by-step explanation:
Answer:
5 percent
Step-by-step explanation:
divide 25 by5 which gives you percent
When you are solving a compound inequality, how can you express the solution?
Please give your rationale.
Answer:
When solving a compound inequality, you can express the solution in two different ways: using a union or intersection.
Using a union:
A union represents the solutions that belong to either one inequality or the other, or both. You can express a union using the symbol "or," or by writing the solutions for each inequality separately and combining them using a "union" symbol (∪). For example, if you have the compound inequality "x > 2 or x < -3," you can express the solution as "x ∈ (-3, 2) ∪ (-∞, -3) ∪ (2, ∞)."
Using an intersection:
An intersection represents the solutions that belong to both inequalities. You can express an intersection using the symbol "and," or by writing the solutions for each inequality separately and combining them using an "intersection" symbol (∩). For example, if you have the compound inequality "x > 2 and x < -3," you can express the solution as "x ∈ (-3, 2) ∩ (-∞, -3) ∩ (2, ∞)."
Which method you use to express the solution will depend on the specific inequalities and the type of solutions you are looking for. It is important to carefully consider the inequality symbols (>, <, ≥, ≤) and the use of "and" or "or" in order to determine the correct solution.
When solving a compound inequality, the solution can be expressed in one of two ways: as an interval or as a union of intervals.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
An interval is a set of all real numbers between two given numbers, and is written in the form (a, b) or [a, b], where a and b are real numbers, and a < b. If a and b are included in the interval, then the interval is written as [a, b]; if a and b are not included in the interval, then the interval is written as (a, b).
A union of intervals is a combination of two or more intervals, and is written in the form (a, b) ∪ (c, d) or [a, b] ∪ [c, d], where a, b, c, and d are real numbers, and a < b and c < d.
When solving a compound inequality, it is important to first simplify the inequality by combining like terms, isolating the variable on one side of the inequality, and combining any separate inequalities into a single inequality. Then, the solution can be found by graphing the inequality on a number line, and shading the portion of the number line that represents the solution.
Once the solution is found the solution can be expressed either as an interval or as a union of intervals depending on the inequality. For example, if the inequality is x>1 and x<3, then the solution would be expressed as (1,3) and this is an example of an interval. If it's x>1 and x≥3 then the solution would be expressed as (1,3] U [3,∞) and this is an example of union of intervals.
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what is the evaluation for 4-4y+y-3
Answer:
1-3 y
Step-by-step explanation:
Subtract the numbers 4 AND 3 WHICH WOULD EQUAL REWRITING THE ADDITON SO IT CHANGES THE MINUS SIGN TO A PLUS.
Find the value of the lesser root of x squared -7x +12 =0
Answer:
3
Step-by-step explanation:
x² -7x + 12 =0
by factoring:
(x-4)(x-3) = 0
x = 4
x = 3
3<4
Evaluate this problem
Answer:
78
Step-by-step explanation:
a + 8b = 6 + 8 x 9 = 6 + 72 = 78
Answer: 78
Step-by-step explanation:
value of a=6
value of b=9
a+8b= 6+8*9
as the 8 will be multiplied by 9
6+8*9= 6+72
6+72 = 78
13. The line y = -2x +1 is reflected in the line y = 2. Write the equation of the image.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
What is the line of reflection?A reflection over a line is a transformation in which each point of the initial figure (the pre-image) has an image that is on the opposite side of the reflection line from the original point and is situated at the same distance from the reflection line. The pre-size image's and shape are replicated in a reflection.
The line of reflection is typically expressed as y = m x + b y=mx+by, equals, m, x, plus, b. What need I do to draw the line of reflection? The starting points in the figure are all perpendicularly separated from the line of reflection by the same amount as the starting points in the image.
To reflect a line in the y-axis, we need to negate the slope of the line.
The line y = -2x +1 has a slope of -2 and y-intercept of 1.
After reflecting the line in the y-axis, the slope of the line will be positive 2 and the y-intercept remain unchanged.
so the equation of the image is y = 2x + 1.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answer:
B, C, E
Step-by-step explanation:
Let y = length.
Then, y - 5 = width.
area = length × width
area = y(y - 5)
area = 750
y(y - 5) = 750
y² - 5y = 750
A: y(y + 5) = 750
Since y = length, width must be y - 5, not y + 5, so A does not work.
B: y² - 5y = 750
This is what we got above, so this equation works.
C: 750 - y(y - 5) = 0
750 = y(y - 5)
750 = y² - 5y
This is the same as B and works.
D: y(y - 5) + 750 = 0
y(y - 5) = -750
The area cannot be -750, so this equation does not work.
E: (y + 25)(y - 30) = 0
y = -25 or y = 30
This also works.
Answer: B, C, E
x divided by 6 is what
Answer:x/6
Step-by-step explanation:
Here the value of x is not given and hence the answer to the question is
x/6
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