A two variable linear equation means an equation having two variables. It is usually represented as ax+by =c. We can solve a two variable linear equation in many ways.
If the linear equation is only given, to solve it we have to calculate the x-intercept and y-intercept. It is one way of solving a two variable linear equation. Lets look into an example.
2x+5y = 19
The x intercept is when y=0,
then, 2x+ (5×0) = 20
2x = 20, x=10
y intercept is when x=0, then
2×0 + 5y = 20
5y = 20, y= 20/5 =4
So, by solving the equation, we get x=10 at x intercept and y=4 at y intercept.
If one the values are given , we can substitute it in the equation to calculate the other variable.
In the equation, 2x+3y= 12, if y=2, we can calculate by substituting.
2x + (3×2) = 12
2x = 12-6
2x = 6
x =3
So when y=2 then x=3.
Constraints are the restrictions on the domain of a linear equation, like a number of days or students should be a positive integer.
So, we can solve a two variable linear equation through different ways.
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jake has 16 toy cars. lydia has five fewer toy cars than jake. how many toy cars do they have in all?
For counseling groups, it is recommended that the number of members for groups of children, __________, as compared to counseling groups for adults.
decrease
The number of members for counseling groups of children should generally be smaller as compared to counseling groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. Smaller groups also allow for more individualized attention and support.
The recommended number of members for counseling groups of children should generally be smaller than that of groups for adults. This is because children may feel overwhelmed in larger group settings and may not be able to adequately express themselves. This can lead to a lack of engagement and little benefit from the group counseling sessions. Smaller groups also allow for more individualized attention and support, which is important for young people to feel comfortable expressing their thoughts and feelings. Additionally, smaller groups can help create a more intimate environment for participants to safely share their experiences and feelings with one another. As such, reducing the size of the group for counseling sessions with children can help ensure a more successful therapeutic experience.
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The graph below is a transformation of x^2
Give the function in the graph below
G(x)= ?
I first put it as G(x)=(x-2)^2-1
But what I put it at was wrong
The equation of the graph is g'(x) = -(x + 2)² - 1
How to determine the equation of the functionFrom the question, we have the following parameters that can be used in our computation:
g(x) = x²
From the graph, we can see that the graph is inverted
This means that
g'(x) = -x²
Next, the graph is shifted left by 2 units
This implies that
g'(x) = -(x + 2)²
Lastly, the graph is shifted down by 1 unit
So, we have
g'(x) = -(x + 2)² - 1
Hence, the equation is g'(x) = -(x + 2)² - 1
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Listed below are student evaluation ratings of courses, where a rating of 5 is for "excellent." The ratings were obtained at one university in a state. Construct a confidence interval using a % confidence level. What does the confidence interval tell about the population of all college students in the state?
Question content area bottom
Part 1
What is the confidence interval for the population mean ?
The 95% confidence interval for the population mean is given as follows:
(3.64, 4.18).
It tells that we are 95% sure that the true population mean rating is between these two bounds.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 15 - 1 = 14 df, is t = 2.1448.
The remaining parameters for this problem are given as follows:
[tex]\overline{x} = 3.91, s = 0.48, n = 15[/tex]
Hence the lower bound of the interval is of:
[tex]3.91 - 2.1448\frac{0.48}{\sqrt{15}} = 3.64[/tex]
The upper bound of the interval is of:
[tex]3.91 + 2.1448\frac{0.48}{\sqrt{15}} = 4.18[/tex]
Missing InformationThe sample is given as follows:
3.9
3.1
3.7
4.4
3.2
4.1
3.3
4.4
4.3,
4.4
4.5
3.9
3.2
4.2,
4.0
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A polling organization contacts 1398 teenagers who are 13 to 17 years of age and live in the United States and asks whether or not they had attended a concert this past year. What is the population in the study? A. Teenagers who are 13 to 17 years of age and have attended a concert. B. Teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age and live in the United States and have attended a concert. D. Teenagers who are 13 to 17 years of age. What is the sample in the study? A. Teenagers who are 13 to 17 years of age and live in the United States. B. The 1398 teenagers who are 13 to 17 years of age and live in the United States. C. Teenagers who are 13 to 17 years of age. D. The 1398 teenagers who are 13 to 17 years of age and have attended a concert.
The population of the given study in the polling organization contacts is given by :
Option B. Teenagers who are 13 to 17 years of age and live in the United States.
Total number of people attended by the polling organization = 1398
1398 are the teenagers .They are in the age group of 13 to 17 years of age.They all live in the United States .It was asked whether they have attended any concert in the past year.Population is represented by all teenagers of United States in the age group of 13 to 17 years of age.
Those who attended the concert represents the sample of particular category.
Therefore, the population of the required study is given by :
Option B. Teenagers belongs to 13 to 17 years of age and live in the United States .
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Convert 4/15 to a decimal and a percent.
The percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given a fraction number 4/15
To convert it into decimals we need to divide 4 by 15
Thus, the Decimal value = 0.2666...
the Decimal value = 0.267
To convert it into a percentage we need to multiply it with 100
So,
The percentage values of the given fraction = 4/15 * 100
The percentage values of the given fraction = 26.67%
Therefore, the percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
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PLEASE HELP I WILL GIVE YOU BRAINLIEST AND 10 POINTS!! SHOW WORK PLS
Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?
we know that in parallelogram, opposite sides are parallel and are of equal lengths. So, we can say that line joining vertices ( 5, -2 ) and ( 6, 2 ) and line joining vertices ( x, y ) and ( 0, 2 ) will be parallel, that is line AB and DC will be parallel and equal to each other in length.We know that interior angles on the same side of a transversal are supplementary. Similarly, ∠B + ∠C = 180°, ∠C + ∠D = 180° and ∠A + ∠B = 180°. Therefore, the sum of any two adjacent angles of a parallelogram is equal to 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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Equate the slopes of the opposite lines with (x,y) as the coordinates of the missing vertex.
How to find vertex of a parallelogram?We are aware that a parallelogram has two opposed sides that are equally long and parallel. As a result, we may infer that the lines connecting the vertices (5, -2) and (6, 2) as well as the lines connecting the vertices (x, y) and (0, 2) will be parallel, making lines AB and DC parallel and of identical length. Interior angles on the same side of a transversal are understood to be supplementary. Similarly, B + C, C + D, and A + B all add up to 180 degrees. As a result, the sum of any two adjacent parallelogram angles equals 180°.The distance formula enables us to calculate the distance between two points on a coordinate grid. If those points have coordinates one, one and two, two, then the distance between them is the square root of two minus one all squared plus two minus one all squared.To learn more about parallelogram refers to:
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4. Write the expression in
words.
h - 3
Answer:
h minus three
Step-by-step explanation:
What is the 10th term of the geometric sequence where a1 = 384 and a7 = 6?
Group of answer choices
6
3
0.75
1.5
Answer:
A resposta correta é 6. Esta sequência geométrica, tem uma razão comum de r = 1/2. O 10º prazo o da sequência pode ser encontrado usando a fórmula an = a1 * r-n1, em de n é o número do prazo. Assim, o 10º prazo é: ano = 384 * (1/2)9 = 384 * (1/512) = 6
write a system of linear equations whose solution is (6,19)
Step-by-step explanation:
[tex] \alpha + \beta = \frac{ - b}{a} = 6 \\ \alpha \beta = \frac{c}{a} = 19 \\ p(x) = k( {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta )) = 0\\ = k( {x}^{2} - 6x + 19) \\ polynomial \: = {x}^{2} - 6x + 19 = 0[/tex]
it takes so much tume to solve and type it here and its so hard so plzzz mark me as brainliest plz .
HELP PLEASE FAST i'm not understanding how to do this (i'll give brainiest to whoever has best answer) The bar below is 7 inches long and divided into 2 equal parts. What is the length of one of those parts? Fill in the blanks in the equation using fractions or mixed numbers to show the length of one of the parts. X 7 inches = inches
The length of each bar is given as follows:
3.5 inches.
As a mixed number, the length of each bar is given as follows:
3 and 1/2 inches.
How to obtain the length of each bar?The length of each bar is obtained applying the proportions in the context of this problem.
The bar that is 7 inches long is divided into two equal parts, hence the length of each part is given as follows:
7/2 = 3.5 inches.
The fraction equivalent to a decimal of 0.5 is given as follows:
1/2.
(which is used to construct the mixed number).
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Points B and D are on the perpendicular bisector of ∠ABC. The measure of ∠ABD is 45°. Find the measure of ∠C.
Answer:
Step-by-step explanation:
Given ∠B=45,∠C=55
So, ∠A=180°−45°−55°
=80°
From △ABD,40°+45°+∠ADB=180°
⟹∠ADB=95°
From△ADC,40°+55°+∠ADC=180°
⟹∠ADC=85°.
Write an equation to match this graph.
The equation for the line is y=x+7.
What is a linear equation's solution?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation.
In other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.
Given, the line's points are (2,9), (3,10), (4,11), and (5,12). (6,13)
Assuming that the line's equation is y=x+7, adding the points to the equation results in
(2,9) 9=2+7
(3,10) 10=3+7
The equation is also valid for every point on the graph.
Hence, The line's equation is y=x+7.
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Complete Question -
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system using elimination.
5x + 4y = 12
3x - 3y = 18
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By solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
What is Elimination Method?
To create an equation in one variable using the elimination approach, you can either add or subtract the equations. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
Now solving the both equation by using elimination method;
5x +4y = 12 ----------------------------eq(1)
3x - 3y = 18 ----------------------------eq(2)
Multiply equation (1) by 3 and equation (2) by 4, we get;
15x + 12y = 36
12x - 12y = 72
Now, same equation will beb together;
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
x = 4
Now, we calculate for the y ;
3x - 3y = 18
3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
3y = -6
y = -6/3
y = -2
(x, y) = (4, -2)
So, by solving the system using elimination method 5x + 4y = 12 and 3x -3y = 18 we get x = 4 and y = -2.
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Work with a partner. Baby manatees are about 4 feet long at birth. They
grow to a maximum length of 13 feet.
a. Which of the following can represent a baby manatee's growth?
What does x represent? Explain your reasoning.
x + 4 < 13
x + 4 ≤ 13
x-4> 13.
x-4 ≥ 13
An equation which can represent a baby manatee's growth include the following: B. x + 4 ≤ 13.
The variable x represent the baby manatee's growth after birth.
How to write and solve the required inequality?In order to write and solve an inequality that represents a baby manatee's growth, we would take note of the following important information;
The maximum length is equal to 13 feet.Baby manatees are typically about 4 feet long at birth.Let the variable x represent the baby manatee's growth after birth.Now, we can write an inequality that represents the value of x for which a baby manatee's growth as follows;
x + 4 ≤ 13
By subtracting 4 from both sides of the inequality, we have the following:
x + 4 - 4 ≤ 13 - 4
x ≤ 11
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a 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works tuesday-saturday and rests on sunday and monday. the numbers of agents working every day of a week should be at least given numbers d1; :::; d7. the manager wants to meet this requirement with the minimal possible total number of agents employed, by deciding what will be the days o of the agents. assuming that di are large, so that we can ignore integrality restrictions, formulate manager's problem as an lo program.
A call center required the number of agents is equal to 18.
One of the most frequent themes in quantitative aptitude that is tested in government exams is time and work. One of the subjects that candidates are knowledgeable about even before they begin preparing for competitive exams.
The idea of time and effort is still the same, but there may be some variation in the questions that are posed. The majority of the questions on this topic are 1-2 word problems, but candidates should also be ready for questions about data sufficiency and data interpretation that may come up over the course of their work.
A 24/7 calling center works as follows: every agent works 5 days in a row and has two days rest, e.g., every week works Tuesday Saturday and rests on Sunday and Monday.
total working day of call center = 7
agent's working day =5
so, required the minimal number of agents-
[tex]=\frac{7!}{2!.5!}\\\\=\frac{35}{2}\\\\= 17.5 = 18[/tex]
So, at least required number of agents = 18.
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The average distance between the Sun and Neptune is 4450 x 100 km. Express this distance in AU
with two significant figures.
The distance 4450× 10⁶ km between the Neptune and the sun in AU is 29.75 AU
What is Astronomical unit?The astronomical unit is a unit of length, roughly the distance from Earth to the Sun and approximately equal to 150 million kilometres or 8.3 light-minutes. The actual distance from Earth to the Sun varies by about 3% as Earth orbits the Sun, from a maximum to a minimum and back again once each year.
An astronomical unit is the average distance between the Earth and the Sun. Estimates of this distance have varied over time. It is now defined as exactly 149,597,870.7 kilometers.
if 149,597,870.7 kilometers = 1 AU
then 4450× 10⁶ km = 4450× 10⁶ ÷149,597,870.7
= 29.75 AU
Thefore the distance between the sun and neptune is 29.75 AU
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the quartiles of a dataset are the three values that divide the data into four equal groups, each group representing 25% of the data. the first quartile (q1), also known as the lower quartile, is the value that separates the lowest 25% of the data from the rest of the data. the second quartile (q2), also known as the median, is the value that separates the lowest 50% of the data from the highest 50% of the data. the third quartile (q3), also known as the upper quartile, is the value that separates the lowest 75% of the data from the highest 25% of the data. together, the three quartiles can give a sense of the distribution of the data and the spread of the values
A dataset's quartiles are critical summary statistics that split the data into four equal groups. The first quartile (q1), often known as the lower quartile, splits the data into the bottom 25% and the remainder.
The second quartile (q2), commonly known as the median, splits the data into the lowest and highest 50%. The third quartile (q3), often known as the upper quartile, divides the data into the lowest 75% and the highest 25%. These quartiles give useful information regarding the data distribution and value spread.
The quartiles may also be used to find outliers in the dataset. Understanding the quartiles is an important element of data analysis and may assist inform data-driven decision making.
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The vector u is shown below. Find the component form of u. Round your final answers to the nearest hundredth. ū=( , ) IL 105°
According to the given vector, the component form of u is (−3.87, 1.048)
The term vector in math is known as a quantity or phenomenon that has two independent properties such as magnitude and direction
Here we have given that the value of the following are obtained through the given diagram.
θ = 165°
Then the value of |u| is calculated by using the formula,
=> ∣u∣ = 4θ
When we apply the value on it, then we get,
=> ∣u∣=4
Now, we have to calculate the value of
=> ∣u∣cos165° = −3.864
=> ∣u∣sin165° = 1.035
Then the component form of the vertor u is written as,
=> u = (∣u∣cos165°, ∣u∣sin165°)
When we apply the values on it, then we get the resulting form as,
=> u = (−3.87, 1.048)
Complete question:
The vector u is shown below. Find the component form of u.
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For groups of 80 or more people, a charter bus company determines the rate r (in dollars per person) according to the formula
r = 8 − 0.05(n − 80), n ≥ 80
where n is the number of people.
(a) Express the revenue R for the bus company as a function of n.
(b) Complete the table.
(c) Criticize the formula for the rate. Would you use this formula? Explain your reasoning.
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
(a) R(n) = r(n) * n = (8 − 0.05(n − 80)) * n
(b)
n r (dollars per person) R (dollars)
80 8 640
90 7.5 675
100 7 700
(c) This formula for the rate is not ideal, as it does not take into account factors like the distance traveled or any additional services that the bus company may offer. It also does not account for any additional fees or taxes. I would not use this formula, as it does not provide an accurate representation of the price the bus company should charge for its services.
The formula for rate given is not ideal, as it does not take into account factors like the distance traveled or additional services offered by the bus company. It also does not account for additional fees or taxes. Therefore, it does not provide an accurate representation of the price and should not be used.
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A three-column table is given.
Part A C D
Part 25 35 50
Whole B 56 80
What is the value of B in the table?
44
40
36
30
Answer:
(b) 40
Step-by-step explanation:
You want the value of the "whole" corresponding to a "part" of 25 in the given table.
PartsBased on the relationships in the 2nd and 3rd columns, it appears that the parts on the second line are 5/8 of the whole.
This means that 25 is 5/8 of B, or ...
B = 8/5 × 25 = 40
The value of B in the table is (b) 40.
__
Additional comment
The parts on the first line will be 3/5 of the value of the parts on the second line. The sum of the two parts in each column is equal to the whole.
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can someone give me the answer asap
Answer:
Rise: 2
Run: 1
Slope: 2
At what point does the line intersect the y-axis? (0,-1)
the school marching band has 328 members. Can the band members march in 8 lines, with an equal numberof band members in each line with no members left over? Explain
Answer:
Yes
Step-by-step explanation:
328/8 = 41
Thus if 41 members are in each line, there should be no members left without a spot and it should be equal all across
A line passes through the point (-6, 5) and has a slope of 2 Write an equation in point-slope form for this line. 0 08
The required point-slope form for the given line is y = 3x/2 + 14.
What is equation of line?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change. Draw a sloping triangle connecting the two spots you find on the line.
According to question:
We have,
A line passes through the point (-6, 5) and has a slope of 3/2
Then the equation of line is;
y - 5 = 3/2(x - (-6))
y - 5 = 3/2 (x + 6)
2y - 10 = 3x + 18
2y = 3x + 28
y = 3x/2 + 14
Thus the point slope form of the line is y = 3x/2 + 14.
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What is the result from the expression[tex](6x-3)[/tex] is subtracted from [tex](-3x+2)[/tex]
Answer:
9 x - 5
Step-by-step explanation:
Simplify the following:
6 x - 3 - (-3 x + 2)
-(-3 x + 2) = 3 x - 2:
6 x - 3 + (-2 + 3 x)
Grouping like terms, 6 x - 3 - 2 + 3 x = (6 x + 3 x) + (-3 - 2):
(6 x + 3 x) + (-3 - 2)
6 x + 3 x = 9 x:
9 x + (-3 - 2)
-3 - 2 = -(3 + 2):
9 x + (-(3 + 2))
3 + 2 = 5:
Answer: 9 x - 5
Part A What descriptive words, units, and intervals would you choose to label the x-axis and the y-axis?
Answer:
x on the horizontal axis and y on the vertical axis.
ANYONE GOOD IN MATH PLEASE HELP!
Answer: 15
Step-by-step explanation:
The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15
il 5 star your comment and thanks it and brainlist if u help me
Answer:
the 4 represents how many times 5 can go into 20
Gianna is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Gianna will earn $50 every time one of her songs is played in a commercial and she will earn $100 every time one of her songs is played in a movie. Gianna's songs were played on twice as many commercials as movies and her total earnings on the royalties from all commercials and movies was $800. Graphically solve a system of equations in order to determine the number of commercials, x,x, and the number of movies, y,y, on which Gianna's songs were played.
A graph of each function is shown in the image attached below.
The number of commercials (x) is equal to 8 commercials while the number of movies (y) is equal to 4 movies.
How to write and solve the system of equations graphically?In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of commercials.Let the variable y represent the number of movies.Since Gianna would earn $50 every time one of her songs is played in a commercial and $100 every time one of her songs is played in a movie, an equation which models it is given by;
50x + 100y = 800
Additionally, Gianna's songs were played on twice as many commercials as movies;
x = 2y
Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (8, 4) as shown in the image attached below.
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Which of the following refers to the type of statistical methods used to draw conclusions about the population based on a sample?
Population methods
Sampling methods
Descriptive statistics
Inferential statistics
The type of statistical methods used to draw conclusions about the population based on a sample is called inferential statistic.
Statistical inference refers to the process of generating inferences about a population from a sample or subset of the data. The goal of inferential statistics is to extrapolate from sample data to the population as a whole by comparing the parameters of multiple samples. Two major categories of inferential statistics use distinct strategies to extrapolate information from samples of the population. These are regression analysis and hypothesis testing. Inferential statistics, including hypothesis testing, examines sample data to draw conclusions about the whole population. It entails establishing a null hypothesis and an alternative hypothesis, then doing a statistical test of significance to determine which one is more likely to be correct. The impact of one variable on another can be measured with the use of regression analysis.
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