Answer:
The Factor Theorem and Synthetic Division are not the same. The Factor Theorem states that if a polynomial f(x) has a root c, then x - c is a factor of f(x). Synthetic Division is a way of dividing a polynomial by a binomial.
Step-by-step explanation:
To use Synthetic Division, you first need to find the coefficients of the polynomial. Then, you set up the synthetic division table with the binomial on top and the coefficients of the polynomial on the bottom. Starting with the first coefficient, you multiply it by the first term of the binomial and write the product below the coefficient. Then, you add the two numbers below the product and write the sum below that. Continue until you reach the end of the binomial. The remainder at the bottom of the table is the remainder when f(x) is divided by x - c.
If the remainder is 0, then x - c is a factor of f(x).
Can you answer this please with workings out
Answer:
a) 640 ml
b) 40 ml
Step-by-step explanation:
The ratio of lime to lemonade for the fizzy drink is 5 : 3 or as a fraction that would be
[tex]\dfrac{\text{Lime juice}}{\text{Lemonade}}= \dfrac{5}{3}[/tex]
[tex]\text{Therefore the ratio of lemonade to lime }\\\\ = \text{reciprocal of $ \dfrac{5}{3} $} }\\\\= \dfrac{3}{5}[/tex]
Part a)
For all 400 ml of lime juice we would need
[tex]\dfrac{3}{5} \times 400 \;ml = 3 \times 80 = 240 \;ml[/tex]
Total amount of fizzy drink that can be maade
= amount of lime juice + amount of lemonade
= 400 + 240
= 640 ml
This is the answer to Part a)
Part b)
If Gianni has only 280 ml and is using all 400 ml of lime juice then the amount of lemonade used as calculated in part 1) is 240ml
That means the amount of lemonade left over = 280 - 240 = 40 ml
whats the answer to this problem on imagine math?
even a process that is functioning as it should will not yield output that conforms exactly to a standard. why not? multiple choice question. nonrandom variation natural variation measurement error standards change
Even a process that is functioning as it should will not yield output that conforms exactly to a standard because of natural variation.
The natural variation is the variability in the output of a system that is caused by factors that are not controlled.This type of variation is also known as common cause variation.
The output of the system is changed by natural variation in such a way that it deviates from a fixed standard. Despite this, natural variation is usually present in any system, and it cannot be entirely eliminated.
There will always be some variation, and it is vital to understand how much of it is acceptable. The output of the system may be brought back into conformity with the standard by removing the cause of special cause variation.
Measurement errors can be caused by a variety of factors, including incorrect equipment calibration, user error, or environmental factors.
These errors may be distinguished from natural variation and special cause variation because they are caused by the measurement process rather than the system itself.
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what moves beyond excel graphs and charts into sophisticated analysis techniques such as controls, instruments, maps, time-series graphs, and more?
Answer:
Data Visualization Tools
Step-by-step explanation:
SOMEONE PLS HELP MY LITTLE SISTER ON THIS QUESTION
Answer: 56448² ft
Step-by-step explanation:
7 x 4 x 18 x 4 x 7 x 4 = 56448 and square it to get 56448² and then add the unit to get 56448 ft² :)
is it possible that all solutions of a homogeneous system of ten linear equations in twelve variables are multiples of one fixed nonzero solution? discuss.
Yes, it is possible for all solutions of a homogeneous system of ten linear equations in twelve variables to be multiples of one fixed nonzero solution.
This occurs when the rank of the matrix of coefficients of the system is less than the number of variables, in this case 12. In this case, the system has infinitely many solutions, all of which can be expressed as a multiple of one nonzero solution.
To illustrate this concept, consider the following system of two equations in three variables:
[tex]2x + y + 3z = 0[/tex]
[tex]3x + y + 2z = 0[/tex]
The matrix of coefficients for this system is:
[tex][[3, 1, 2][/tex]
[tex][2, 1, 3]][/tex]
The rank of this matrix is 2, which is less than the number of variables, 3. Therefore, this system has infinitely many solutions, all of which can be expressed as a multiple of the following nonzero solution:
[tex](x, y, z) = (2, -3, 1)[/tex]
In other words, any solution [tex](x, y, z)[/tex] of the system will be of the form [tex](2a, -3a, a)[/tex], where a is any real number. This concept can be generalized to systems of ten linear equations in twelve variables.
In conclusion, when the rank of the matrix of coefficients of a homogeneous system of linear equations is less than the number of variables, then all solutions of the system are multiples of one fixed nonzero solution.
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if ratios x:y=3:4 and y:z=1:4
find x:y:z
Using the idea of comparable ratio, we may determine x:y:z to be 3:16:1, given as x:y=3:4 and y:z=1:4.
A ratio is what?When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b. An equation wherein two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
Given that y is present in both ratios, we may begin by determining its value:
y = (4/1) * (y/z), multiplied by 4, which is the reciprocal of 1/4.
y = 4(y/z)
y/z = 1/4
z/y = 4/1
We can now find x by using the value of y:
x/y = 3/4 (given)
x = (3/4) * y x = (3/4) * 4(z/y) (simultaneously inserting y/z)
x = 3z
As a result, x:y:z = 3z: 4 is the ratio of x:y:z.
y : z\s= 3 : 4(4) : 1\s= 3 : 16 : 1
So, x:y:z = 3:16:1 is the solution.
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please help!! I need this by the end of tonight..!
Answer:
y=2.05x
Step-by-step explanation:
Figure out what the total cost is for 1 of them then you put that in as your M value, then X stands for number of sheets so 2.05 multiplied by the number of sheets sold you get your Y which is the total cost in dollars for x sheets.
please i need help, i’ve wasted like six papers trying to get this one right
Answer:5
Step-by-step explanation:
angle h and k are equal (because alternate exterior angles are equal)
2x+7=5x-8
8+7=5x-2x
15=3x
15/3=x
5=x
h=2x+7=2*5+7=17degrees
Two important properties of eigenvalues Recall that trace of a square matrix is the sum of the entries in main diagonal Let [ 1 -1 1] C = [-1 2 0] [ 0 -1 2] and [ 1 2 1] A = [ 6 -1 0]
[-1 -2 -1] Enter A and C in MATLAB Find trace of C and A by typing : trace(A) and trace(C) Find eigenvalues of A and C Explain Do you any relation between eigenvalues and trace of of a see matrix? Find det (A) and det(C) Explain Do you see any relation between eigenvalues and determinant of a matrix?
The product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.
To enter matrices A and C in MATLAB, we can use the following commands:
A = [6, -1, 0; -1, -2, -1; 0, -1, 2];
C = [1, -1, 1; -1, 2, 0; 0, -1, 2];
To find the trace of A and C, we can use the following commands:
trace_A = trace(A);
trace_C = trace(C);
The trace of matrix A is 6 - 2 + 2 = 6, and the trace of matrix C is 1 + 2 + 2 = 5.
To find the eigenvalues of A and C, we can use the eig() function in MATLAB:
[eig_vec_A, eig_val_A] = eig(A);
[eig_vec_C, eig_val_C] = eig(C);
The eigenvalues of matrix A are -1, 1, and 6, and the eigenvalues of matrix C are 1, 1, and 2.
There is a relationship between the trace of a square matrix and its eigenvalues. Specifically, the sum of the eigenvalues is equal to the trace of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then trace(A) = λ1 + λ2 + ... + λn. This relationship holds true for both matrices A and C.
To find the determinant of A and C, we can use the following commands:
det_A = det(A);
det_C = det(C);
The determinant of matrix A is 12, and the determinant of matrix C is 5.
There is also a relationship between the eigenvalues and the determinant of a square matrix. Specifically, the product of the eigenvalues is equal to the determinant of the matrix. In other words, if λ1, λ2, ..., λn are the eigenvalues of a square matrix A, then det(A) = λ1 * λ2 * ... * λn. This relationship also holds true for both matrices A and C.
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What are the steps to express 0.15 as a fraction in simplest form ? Order the following from 1-5
Answer:
0.15 expressed as a fraction in its simplest form is 3/20.
Step-by-step explanation:
To express a terminating decimal as a fraction:
Step 1Write the decimal as a fraction by dividing it by 1:
[tex]\boxed{\dfrac{0.15}{1}}[/tex]
Step 2Multiply the numerator and denominator by 10 for every number after the decimal point.
As there are two numbers after the decimal point, multiply the numerator and denominator by 100:
[tex]\boxed{\dfrac{0.15 \times 100}{1 \times 100}=\dfrac{15}{100}}[/tex]
Step 3Find the highest common factor (HCF) of the numerator and denominator.
Factors of 15: 1, 3, 5 and 15.Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100.Therefore, the HCF of 15 and 100 is 5.
Divide the numerator and denominator by the HCF to reduce the fraction to its simplest form:
[tex]\boxed{\dfrac{15 \div 5}{100 \div 5}=\dfrac{3}{20}}[/tex]
Conclusion0.15 expressed as a fraction in its simplest form is 3/20.
Answer:
See below, please.
Step-by-step explanation:
Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.So the order would be:Write 0.15 as the fraction 15/100.Simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF). In this case, the GCF of 15 and 100 is 5.Divide both 15 and 100 by 5. This gives 3/20.The resulting fraction 3/20 is in its simplest form, as 3 and 20 have no common factors other than 1.The final answer is 3/20.Wright a function (eqaution) that can be used to fined y, the total cost, dollars ,of buying x shirts from the local stare
The equation will be :20 + 8.95 × 10 = $109.50
Here the total cost is $109.50.
Total cost refers to the total cost of production, which includes the fixed and variable parts of the cost. In economics, total cost is described as the cost required to produce a product. The total cost consists of two parts and they are: Fixed costs: These are the costs that do not change.
According to the Question:
C = 20 + 8.95× t
This can be read as : The total cost (C) will be $20 (setup fee) plus $8.95 for each t-shirt ordered (t).
The equation will be:
10 shorts would be 20 + 8.95*10, or $109.50.
Complete Question:
A t-shirt company charges a $20.00 set-up fee plus $8.95 for each t-shirt that is screen-printed with a school’s logo. Write a function that can be used to find the total cost, C, for purchasing and screen printing, t, number of t-shirts.
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3 2/5 -1 3/5!!
Please i need help!
Answer:
Step-by-step explanation:
3 2/5 -1 3/5 = 1.8
The equation h=t2−10t+25
represents the path of an eagle as it descends to the ground only to ascend back into the sky. If h
represents the height, in feet, of the eagle t
seconds after beginning its descent, which graph best represents the equation, where 0≤t≤10
Therefore , the solution of the given problem of equation comes out to be the parabola expands upwards, with the vertex being a minimum point.
Equation : What is it?Complex algorithms frequently employ variable words to demonstrate consistency between two conflicting assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this instance, normalization results in b + 7 rather than a singular formula that divides 12 into two components along with is able to be utilized to evaluate data obtained from y + 7.
Here,
A parabolic route taken by the eagle as it soars into the sky and then descends to the ground is shown by the equation
=> h = t² - 10t + 25.
The vertex of the equation, which is provided by the formulas
=> t = -b/2a and h = f(t),
where a, b, and c are the coefficients of the quadratic equation, can then be found in order to graph it.
Here,
=> a = 1, b = -10, and c = 25.
Consequently, the apex is at t = 5 and h = f(5) = 0, respectively.
Given that t² has a positive coefficient, the parabola expands upwards, with the vertex being a minimum point.
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at an after-school program there are 27 boys and 32 girls. what is the ratio of boys to total kids written in 3 ways?
The ratio of boys to total kids can be expressed in three different ways fraction, decimal, and percent which are 27:59, 0.4576 and 45.76% respectively.
First, let's find the total number of kids in the program. The total number of kids in the program is the sum of boys and girls. Total kids = boys + girls = 27 + 32 = 59. Now that we have the total number of kids, we can find the ratio of boys to total kids in three different ways. 1. Fraction: The ratio of boys to total kids can be expressed as a fraction, where the numerator is the number of boys and the denominator is the total number of kids. Boys: Total kids = 27:59 This fraction cannot be simplified.
2. Decimal: The ratio of boys to total kids can also be expressed as a decimal. To find the decimal, divide the number of boys by the total number of kids. Boys/Total kids = 27/59 = 0.4576 (rounded to four decimal places). 3. Percent: The ratio of boys to total kids can also be expressed as a percentage. To find the percentage, multiply the decimal by 100. Boys/Total kids × 100 = 0.4576 × 100 = 45.76%. Therefore, the ratio of boys to total kids can be expressed as a fraction, decimal, and percent as shown above.
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Use fractions strips to help find the difference. Answer your answer in simplest form three and five 1 and two
To find the difference between 3/5 and 1/2 using fraction strips, we can use strips that are divided into fifths and halves, respectively.the difference between 3/5 and 1/2 is 2/10 or 1/5, , the answer in the simplest form is 1/5.
What is the use of fractions strips?First, we'll need to represent each fraction using the fraction strips.
For 3/5, we can use three fifths strips to represent the numerator and put them together to form a whole.
For 1/2, we can use one half strip and cut it into two equal parts to represent the numerator.
Next, we'll need to compare the two fractions by placing them side by side.
We can see that the two fractions do not have the same denominator, so we need to find a common denominator to make the comparison easier.
The smallest common multiple of 5 and 2 is 10, so we can represent 3/5 using six tenths strips, and 1/2 using five tenths strips.
We can see that there are two tenths strips that are not shared between the two fractions.
Therefore, the difference between 3/5 and 1/2 is 2/10 or 1/5, , the answer in the simplest form is 1/5.
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10 points if someone gets it right
Patricia jumped 4 times every 14 hours. At that rate, how many would she jump in 35 hours?
Answer:10
Step-by-step explanation: 14/4= 3.5, 35/3.5=10
How do you solve the equation x=1.8x+32
One way to do this is to subtract 1.8x from both sides of the equation, which gives:
x - 1.8x = 32
Simplifying the left-hand side, we get:
-0.8x = 32
To solve for x, we can divide both sides of the equation by -0.8:
x = 32 / (-0.8)
Simplifying, we get:
x = -40
What is the solution to this equation? 125^x-2= (1/25)^3x
The equation 125ˣ⁻² = (1/25)³ˣ when solved for x by the calculations below is 2/3
How to evaluate the equation for xWe can simplify both sides of the equation using the properties of exponents:
125ˣ⁻² = (1/25)³ˣ
Rewrite 125 as 5³ and 1/25 as 5⁻²
(5³)ˣ⁻² = (5⁻²)³ˣ
Simplify the exponents by multiplying:
5³ˣ ⁻ ⁶ = 5⁻⁶ˣ
Now we can see that the equation involves powers of the same base (5).
Therefore, we can solve for x by equating the exponents:
3x - 6 = -6x
Add 6x to both sides:
9x - 6 = 0
Add 6 to both sides:
9x = 6
Divide both sides by 9:
x = 2/3
Therefore, the solution to the equation is x = 2/3.
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The circumference of circle A is 21.99 cm. The circumference of circle B is 51.52 cm. What is the difference between the lengths of the radii to the nearest hundredth? Show all your work and circle your answer.
The difference between the lengths of the radii is approximately 4.70 cm.
What is circle ?
A circle is a two-dimensional geometric shape that is defined as the set of all points in a plane that are at a given distance (called the radius) from a given point (called the center). It can also be defined as the locus of all points that are equidistant from a given point. A circle is a closed curve and its circumference is the distance around the circle.
We know that the formula for the circumference of a circle is:
C = 2πr
Where C is the circumference and r is the radius.
For circle A, we have:
21.99 = 2πr
Dividing both sides by 2π, we get:
r = 3.5
For circle B, we have:
51.52 = 2πr
Dividing both sides by 2π, we get:
r = 8.2
The difference between the radii is:
8.2 - 3.5 = 4.7
Rounding to the nearest hundredth, we get:
4.7 ≈ 4.70
Therefore, the difference between the lengths of the radii is approximately 4.70 cm.
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Write the equation of a line that is parallel to the line x-3y=15 that go through the point (-9,8)
Answer:
eqn of line : x-3y=15
slope1=m= -coefficient of x/coefficient of y=1/3
As lines are parallel slope must be equal.
slope3=m'=1/3
passing points of second line =(0,7)
eqn of line = (y-y')=m(x-x')
=(y-7)=1/3(x-0)
=y-7=1/3x
=1/3x-y+7=0
=x-3y+21=0
Step-by-step explanation:
What is the solution to the equation 2y+4=12?
Answer:
y=4
Step-by-step explanation:
2y+4=12
2y=8
y=4
answer: y=4
Answer:
y=4
Step-by-step explanation:
2y+4=12
2y=8
y=4
how many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die.
The number of distinct sequences of letters is 8 × 26⁷.
How many distinct sequences of letters can you make if each sequence is ten letters long and contains the subsequence die?
We have to find the number of distinct sequences of letters that can be made. Here, the word 'die' can occur in any position of the ten-letter sequence. Therefore, we have to find the number of distinct sequences of seven letters that can be formed, which are not related to the word 'die'. The number of distinct sequences of seven letters that can be formed with no restrictions is:
26 × 26 × 26 × 26 × 26 × 26 × 26 = 26⁷
The word 'die' has three letters, and it can be placed in any of the eight positions of the seven-letter sequence (that is not related to the word 'die'). We have a total of 8 possibilities to choose where to put the word 'die'.Thus, the number of distinct sequences of letters is:
8 × 26⁷ (or) 703, 483, 260, 800.
The number of distinct sequences of letters is 8 × 26⁷.
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If the measur of BEC is (2x3) and x is 30 which expression could represent the measure of AED
The expression that equals ∠BEC is 3x - 27, and the answer is B.
First, we find the measure of ∠BEC using the given information and the value of x. We get
2x + 3 = 63, which simplifies to x = 30.Then, we use the fact that ∠AED is vertically opposite to ∠BEC, so ∠AED = ∠BEC = 63 degrees.
Finally, we need to find the expression among the given choices that equals 63 when x = 30.
Option A is too large, option C is too large, and option D is too small. Option B gives us
3x - 27 = 3(30) - 27 = 63which matches the measure of ∠BEC. Therefore, the answer is B.
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Complete Question:
If the measure of BEC is (2x+3) and x=30, which expression could represent the measure of AED?
which shape has at least one circular face and no vertices
Answer:
cylinder
Step-by-step explanation:
A cylinder has 2 circular faces and no vertices.
Which results only in a horizontal compression of Y by a factor of 6?
Answer:
Y = 6*y
Step-by-step explanation:
We have Y = b * y by a factor of 6.
That is, b = 6.
now, to find what results only in a horizontal compression of y = b * y by a factor of 6.
By transformation rule, the function would be a horizontal compression f (a * x) if a> 1.
Therefore, knowing the above, the answer would be:
Y = 6 * y
the sum of the numbers (20cba)16 and (a02)16 is ( (click to select) )16 and their product is ( (click to select) )16.
To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.
(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402
(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256
Adding the two decimal numbers together gives us:
131402 + 256 = 131658
To convert this decimal number back to hexadecimal form, we can use the repeated division method.
131658 / 16 = 8228 remainder 10 (A)
8228 / 16 = 514 remainders 4 (4)
514 / 16 = 32 remainder 2 (2)
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.
To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.
131402 x 256 = 33559552
Converting this decimal number to hexadecimal form gives us:
33559552 / 16 = 2097472 remainder 0
2097472 / 16 = 131092 remainder 0
131092 / 16 = 8193 remainder 4 (4)
8193 / 16 = 512 remainders 1 (1)
512 / 16 = 32 remainder 0
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.
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Given m = 2/3 and the point (-5, 5), which of the following is the point-slope form of the equation?
Answer: y -5
Step-by-step explanation:
a random variable x is uniformly distributed between 45 and 150. what is the probability of xbegin mathsize 12px style less or equal than end style60?
The probability of x being exactly 48 when it is uniformly distributed between 45 and 150 is 1/105
Since x is uniformly distributed between 45 and 150, the probability of x taking any particular value in this range is the same. Let this probability be denoted by P(x).
To find P(x = 48), we need to first check if 48 lies within the range of values that x can take. In this case, 48 lies within the range of 45 and 150, so it is a possible value for x.
Since the distribution is uniform, the probability of x taking any particular value between 45 and 150 is given by
P(x) = 1 / (150 - 45) = 1 / 105
Therefore, the probability of x being exactly 48 is
P(x = 48) = 1 / 105
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The given question is incomplete, the complete question is:
A random variable x is uniformly distributed between 45 and 150. what is the probability of x = 48?
how many ways can a person toss a coin 15 15 times so that the number of tails is between 4 4 and 11 11 inclusive?
The number of ways a person can toss a coin 15 times so that the number of tails is between 4 and 11 inclusive is the product of the total number of ways and the sum of probabilities for k=4 to k=11 inclusive.
Binomial distribution refers to the issue of tossing a coin 15 times and getting a specific amount of tails. The following gives the binomial distribution formula:
[tex]P(X=k) = C(n,k) (n,k) * p^k * (1-p)^(n-k) (n-k)[/tex]
Where P(X=k) denotes the likelihood that there will be k tails in n tosses, p is the likelihood that there will be one tail in a single toss, and C(n,k) denotes the number of combinations of n objects that will be picked up k at a time.
The total of probability for k=4 to k=11 inclusive must be calculated in order to find the solution. This is,
P (4), P (5), P (6), P (7), P (8), P (9), P (10) and P (11)
We can figure out and add up each of these probability using the technique above. As an alternative, we can compute the probabilities using a statistical software programme or a binomial probability table.
A person can flip a coin 15 times in a total of 32,768 different ways. By calculating the total number of ways by the sum of probabilities for k=4 to k=11 inclusive, one may get the number of ways that the number of tails is between 4 and 11 inclusive.
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