How do you solve the equation 2x+3y=6?
Which ordered pairs are solutions to the equation 2x+3y=6?

The solution for x to the expression x + 13 = 21(x + 10) is given as follows:

x = -9.85.

The expression for this problem is defined as follows:

x + 13 = 21(x + 10)

Before solving for x, we must apply the distributive property at the left side of the expression, hence:

x + 13 = 21x + 210

Now we must isolate the variable x, with every term with x on the left side of the expression and every term without x on the right side, hence:

x - 21x = 210 - 13

-20x = 197

20x = -197

Then the solution is obtained applying the division, which is the inverse operation of the multiplication, hence:

x = -197/20

x = -9.85.

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The equation u×(v + w) = (u × v) + (u × w) is generally true as a property of the cross product.

The cross product is a mathematical operation that results in a third vector that is perpendicular to both input vectors.

The equation u×(v + w) = (u × v) + (u × w) is a mathematical expression that relates the cross product of two vectors, v and w, to the cross product of each vector individually with a third vector, u.

In general, the equation is true, as it is a property of the cross product which is property is known as the distributive property.

However, there are certain conditions where the equation is not always true.

Therefore, the correct option is (b).

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The total number of two-person tents taken on the camping trip was 0, and the total number of four-person tents taken on the camping trip was 50.

The total number of tents taken on the camping trip was 60, and the total number of people was 202. We want to determine how many of each type of tent were taken. Let x represent the number of two-person tents and y represent the number of four-person tents. We can use the following equation to solve for x and y:

2x + 4y = 202

After rearranging the equation to solve for x, we get x = (202 - 4y)/2. Substituting this into the equation, we get 2((202 - 4y)/2) + 4y = 202. Simplifying, we get (202 - 4y) + 4y = 202. Then, 0 + 4y = 202. Dividing both sides by 4, we get y = 50.5. Plugging this value into the equation x = (202 - 4y)/2, we get x = (202 - 202)/2, which simplifies to x = 0.

Therefore, the total number of two-person tents taken on the camping trip was 0, and the total number of four-person tents taken on the camping trip was 50.

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Answer:

[tex]5.0043[/tex]×[tex]10^{6}[/tex]

Step-by-step explanation:

1) First right it as a digit

2) Now write as standard form

Have a lovely day :)

The value of the given expression is 12167.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

The given expression is (14+√81)³.

= (14+9)³

= (23)³

= 12167

Therefore, the value of the given expression is 12167.

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Answer:

Below

Step-by-step explanation:

1 mile is 5280 ft

7 x 5280 = 36960 ft^2 for EACH side of the street = 73 920 ft^2 total

4x 4 = 16 ft^2      8ppl / 16 ft^2 = 1 /2  ppl/ft^2

73920 ft^2  *  1/2  ppl / ft^2 = 36 960 people

There are 595 boys at the school.

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

The concept is used in this proportion, multiplication and subtraction.

1. First calculate how many students at the school are girls multiplying the total number of students at the school by the proportion of girls:

1309 × [tex]\frac{6}{11}[/tex]

= 714 girls.

2. Then to find out how many students at the school are boys, subtract the number of girls from the total number of students at the school, that is:

1309 - 714

= 595 boys

Therefore, there are 595 boys at the school.

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The total number of boys in school are calculated by ratios in which total of 1309 students are 595 boys.

The number of boys in the school are found by using ratios and proportions. If two ratios are set equal to each other then they are in proportion. Like for an example if there are 2 girls and 5 boys we could write it as the ratio 2:5 (like for every 2 girls, there are 5 boys)

The concept used here is subtraction and multiplication.

i . Given the number of girls in the school are 6/11 of total number of students in the school , so we can find the number of girls by multiplying the proportion of girls with the total number of students.

6/11 * 1309 = 714 girls.

ii . Then to find the total number of boys in the school, we subtract the number of girls from the total number of students. so, by subtracting the number of girls from total number of students we get number of boys as,

1309-714 = 595 boys

Thus , there are total of 595 boys present in the school

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It is important to ensure that the covariance matrix of the errors is correctly specified in order to obtain valid results and make accurate inferences about the coefficients of the independent variables in a regression model.

Standard errors are a measure of the variability of the estimated parameters in a regression model. They are used to test the hypothesis that the coefficients of the independent variables are significantly different from zero, and to construct confidence intervals for the coefficients.

The standard errors of the coefficients in a regression model are based on the assumption that the covariance matrix of the errors (also known as the residuals) is correctly specified. This assumption is crucial for the validity of the standard errors, as it determines the accuracy of the estimates of the coefficients.

The covariance matrix of the errors is a crucial component in the calculation of the standard errors. It represents the variance-covariance structure of the residuals and is used to estimate the precision of the coefficients. If the covariance matrix of the errors is correctly specified, the standard errors will accurately reflect the variability of the coefficients and provide valid results.

However, if the covariance matrix of the errors is not correctly specified, the standard errors will be biased and the hypothesis tests and confidence intervals will not be valid. In such cases, the standard errors will either be too large or too small, leading to incorrect results.

Therefore, it is important to ensure that the covariance matrix of the errors is correctly specified in order to obtain valid results and make accurate inferences about the coefficients of the independent variables in a regression model.

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The area of the Circular pool will be 1256 square feet.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, A pool that is surrounded by the Square shaped Deck.

Let " 20 feet" be the radius of the pool. that makes the side of the deck will be 20 + 20 = 40 feet

From the formula of the area of a circle:

Area of circle= pi * radius^2

In our case,

Area of the pool = 3.14 * 20 * 20

Area of the pool = 1256 Feet square

Area of the square made by deck = Side * side

Area of the square made by deck =  40 * 40 = 1600

Area of deck = area of Square - the area of the circle

Area of deck = 1600 - 1256

Area of deck = 344 Square feet

therefore, The area of the Circular pool will be 1256 square feet.

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The value of m is obtained as follows:

m = 401º.

The cosine function is periodic, meaning that it's behavior is repeated throughout the domain of the function.

For the cosine function, it is positive on the following quadrants.

The point m is the third point that the cosine function passes through the angle of 41º.

Considering that the time time is on the first quadrant of the second lap of the unit circle (each lap is 360º), the value of m is obtained as follows:

m = 360 + 41

m = 401º.

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The ending inventory amount is p68,000: (200 x 65) + (300 x 68) + (150 x 70) - (500 x 68) = 68,000.

1. Calculate the total cost of the beginning inventory: 200 units x p65 = p13,000

2. Calculate the total cost of the first purchase: 300 units x p68 = p20,400

3. Calculate the total cost of the second purchase: 150 units x p70 = p10,500

4. Calculate the total cost of the units sold: 500 units x p68 = p34,000

5. Calculate the total cost of the ending inventory amount : (13,000 + 20,400 + 10,500) - 34,000 = p68,000

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The final equation in slope-intercept form is y = x - 3.

The slope of a line is a number that describes the steepness of the line and the direction in which the line is increasing or decreasing. It is defined as the ratio of the change in the vertical distance (y) to the change in the horizontal distance (x) between two points on the line. The slope can be calculated as the rise over run and is often represented by the letter "m". Slope is an important concept in mathematics, particularly in algebra and geometry, as it provides information about the direction and the rate of change of a line.

The equation in slope-intercept form can be found using the pattern in the table. The slope of the line can be found by finding the difference in y-values and dividing by the difference in x-values between two points on the line. In this case, the slope is equal to 1, so the equation can be written as y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, use one of the points from the table and plug in the x and y values into the equation. Using the point (0, -3), we get -3 = 1 * 0 + b, so b = -3. The final equation in slope-intercept form is y = x - 3.

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The proof of the sum of the lengths of the medians of a triangle is greater than half the perimeter is shown below.

In Euclidean geometry, theorem that the sum of any two sides of a triangle is greater than or equal to the third side;

Given:

We have

In ΔABC

let AB = c , BC = a , CA = b and M is the Median

Now, In ΔCMA using Triangle Inequality

b < m + c/2

and,  In ΔCMB using Triangle Inequality

a < m + c/2

Now, adding above two equation we get

a + b < 2m + c  (1)

Similarly we can write for other two medians

a+ c < 2n + b (2)

b+ c < 2o+ a (3)

Now, adding (1), (2) and (3) we get

2 (a+b + c)< 2(m + n+ o) + ( a+ +b+ c)

(m+ n + o)> (a+ +b+ c)/ 2

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Answer:

C: 3

Step-by-step explanation:

Hope this helps!

Reannealing curve A is generated by oligonucleotide A, and reannealing curve B is generated by oligonucleotide B. This is because reannealing curves are determined by the sequence, length, and concentration of the oligonucleotides.

Oligonucleotide A and B have different sequences, which will lead to their different reannealing curves. Oligonucleotide A has a higher melting temperature, meaning it will require more energy to reanneal, resulting in a slower reannealing rate.

Oligonucleotide B has a lower melting temperature, meaning it will require less energy to reanneal, resulting in a faster reannealing rate. Therefore, oligonucleotide A will result in reannealing curve A, and oligonucleotide B will result in reannealing curve B.

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Helena would need to babysit at least 4 kids.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given that,

Helena will receive $53 plus $4 per kid for babysitting this afternoon.

Let x be the number of kids that she babysit.

Given the inequality can be written as,

4x + 53 ≥ 68

4x ≥ 68 - 53

4x ≥ 15

x ≥ 3.75 ≈ 4

Hence Helena should babysit 4 kids in order to get at least $68.

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The terms of the following arithmetic series are thus:

1)a₁=6

2)a₂=15

3)a₃=24

4)a₄=33

The following math series is given:

[tex]S_4=[/tex][tex]^4_k_=_1(-3+9k)[/tex]

A list of integers is considered an arithmetic series if there is a consistent difference between any two terms that follow one another in the series.

The total of the terms in an arithmetic sequence with a set number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: in Formula 1 If S denotes the sum of a term-filled arithmetic sequence, then The first and last term values, as well as the total number of terms, are necessary for this formula.

Put k=1 in the given series for a1:

So,

[tex]a_1=-3+9*1\\a_1=6[/tex]

Similarly,

[tex]a_2=-3+9*2\\a_2=15\\a_3=-3+9*3\\a_3=24\\a_4=-3+9*4\\a_4=33[/tex]

The terms of the following arithmetic series are thus:

1)a₁=6

2)a₂=15

3)a₃=24

4)a₄=33

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The value of P(A∪B) is 0.9.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x. The formula to calculate the probability of an event is as follows.

Probability(Event) = Favorable Outcomes/Total Outcomes = x/n

Let us check a simple application of probability to understand it better. Suppose we have to predict about the happening of rain or not. The answer to this question is either "Yes" or "No". There is a likelihood to rain or not rain. Here we can apply probability. Probability is used to predict the outcomes for the tossing of coins, rolling of dice, or drawing a card from a pack of playing cards.

The probability is classified into theoretical probability and experimental probability.

We are given that

a) P(A∩B) = 0.5

b) P(A ∩ B') = 0.3

c) P(A' ∩ B) = 0.1

When all are added, we get P(A∪B)

So,

P(A∪B) =  P(A∩B) + P(A ∩ B')+ P(A' ∩ B) = 0.5 + 0.3 + 0.1 = 0.9

Thus, the value of P(A∪B) is 0.9.

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The taylor series for exp(-ax2) about the value x = 0 to second order in x is given by: [tex]exp(-ax2) = 1 - ax2 + (1/2)a2x4.[/tex]

[tex]f(x) = f(0) + f'(0)x + (1/2)f''(0)x2exp(-ax2) = 1 - ax2 + (1/2)a2x4[/tex]

To find the taylor series for [tex]exp(-ax2)[/tex] about the value x = 0 to second order in x, we can use the general formula for a taylor series given by: [tex]f(x) = f(0) + f'(0)x + (1/2)f''(0)x2.[/tex]

First, we need to find the value of f(0). This is simply the value of the function when x = 0, which is 1.

Next, we need to find the value of f'(0). We can do this by taking the derivative of the given function with respect to x. The derivative of [tex]exp(-ax2) is -2axexp(-ax2)[/tex]. When x = 0, the derivative is 0.

Finally, we need to find the value of f''(0). We can do this by taking the second derivative of the given function with respect to x. The second derivative of[tex]exp(-ax2) is 2a2x2exp(-ax2) - 4a2exp(-ax2)[/tex]. When x = 0, the second derivative is -4a2.

Substituting these values into the taylor series formula, we get:

[tex]exp(-ax2) = 1 -ax2 + (1/2)a2x4[/tex]

The taylor series for exp(-ax2) about the value x = 0 to second order in x is given by: [tex]exp(-ax2) = 1 - ax2 + (1/2)a2x4.[/tex]

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Calculating the probability of a mean time watching television falling between 2 and 3 hours requires knowledge of the population's distribution of time spent watching television.

The probability that a random sample of adults will result in a mean time watching television on a weekday of between 2 and 3 hours can be determined by using the standard normal distribution. This requires knowledge of the population's mean and standard deviation for time spent watching television. If these values are not known, they can be estimated using a sample from the population. The calculated probability assumes that the population's distribution of time spent watching television is normal. If this assumption is not met, alternative methods may be used to estimate the probability.

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The distance between the two points is 5.4 meters.

What is coordinate ?

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

The distance between two points in a rectangular coordinate system can be calculated using the Pythagorean theorem, which states that the distance between two points is the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates.

Given the two points (1.8, 3.0) and (4.5, -1.7), the distance can be calculated as follows:

d = √((4.5 - 1.8)^2 + (-1.7 - 3.0)^2) = √(2.7^2 + 4.7^2) = √(7.29 + 22.09) = √29.38 = 5.4

So, the distance between the two points is 5.4 meters.

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The distance between the two points is 5.4 meters.

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

The distance between two points in a rectangular coordinate system can be calculated using the Pythagorean theorem, which states that the distance between two points is the square root of the sum of the squares of the differences of the x-coordinates and the y-coordinates.

Given the two points (1.8, 3.0) and (4.5, -1.7), the distance can be calculated as follows:

d = √((4.5 - 1.8)^2 + (-1.7 - 3.0)^2) = √(2.7^2 + 4.7^2) = √(7.29 + 22.09) = √29.38 = 5.4

So, the distance between the two points is 5.4 meters.

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The required expression that represents the area of a sector of circle  A is 120/360 × 100π.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr²

From the quesiton, we have circle A with a radius of 10 units.
The angle of the sector is not defined in the question,
Let the angle of sector Ф = 120°

Formula of area of sector = Ф/360 × πr²,

Assign the value in the above expression,
Area of the sector of circle A = 120 / 360 × π (10)²

Area of th sector of circle A = 120/360 × 100π

Thus, the required expression that represents the area of a sector of circle  A is 120/360 × 100π.

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a system of four equations whose solution gives estimates for the temperatures T1; : : : ; T4:

T1 = 1/4(10 + 20 + T2 + T4)

T2 = 1/4(T1 + 20 + 40 + T3)

T3 = 1/4(T1 + T2 + 40 + 30)

T4 = 1/4(10 + T1 + T3 + 30). This is system of equations.

Algebra requires the simultaneous solution of two or more equations. There must be an equal number of equations and unknowns for a system to have a singular solution. The several kinds of linear equation systems are as follows:

Given that,

T1 = 1/4(10 + 20 + T2 + T4)

or, 4T1 - T2 - T4 = 30

similarly for 2nd, 3rd, and 4th nodes we have:

T2 = 1/4(T1 + 20 + 40 + T3)

or -T1 + 4T2 - T3 = 60

T3 = 1/4(T1 + T2 + 40 + 30)

or -T2 + 4T3 - T4 = 70

T4 = 1/4(10 + T1 + T3 + 30)

or -T1 - T3 + 4T4 = 40

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The solution to the system of equations is x = -( 1/3 ) and y = -( 4/3 )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the system of equations be A and B

Now , the first equation is

y = 4x   be equation (1)

And , the second equation is

y = x - 1   be equation (2)

Substituting the value of y in equation (1) , we get

4x = x - 1

Subtracting x on both sides of the equation , we get

3x = -1

Divide by 3 on both sides of the equation , we get

x = -1/3

Substituting the value of x in equation (1) , we get

y = -4/3

Hence , the equations are solved

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Answer:

28 m

Step-by-step explanation:

r = l/a

 = 16/4/7

 = 16*7/4

  = 28

The formula r = (arc length / central angle) is used to calculate the radius of a circle. Consequently, r = (16/4/7) = 4.57 m

1. Multiply the central angle (4/7 rad) by the arc length (16 m).

2. Determine the outcome to determine the circle's radius (r): 16 / 4/7 = 4.57 m

The equation r = (arc length / central angle) can be used to calculate the radius of a circle. With the help of this formula, we can determine the radius of a circle given the length of an arc and its central angle. In this instance, the centre angle is 4/7 rad, and the arc length is 16 m. Divide the arc length by the central angle to get the radius: 16 / 4/7 = 4.57 m. The circle's radius is 4.57 m as a result.

Finding other circle measures is made easier by knowing the radius of the circle. For instance, using the formula circumference = 2r, we can determine the circumference of a circle if we know its radius. Any circle's circumference can be determined using this formula given its radius. The circumference in this instance would be 2 x 4.57 m, or 28.7 m. Furthermore, we may utilise the radius to get the circle's area by applying the formula area = r2. Any circle's area can be determined using this formula given its radius. The area in this instance would be x 4.572 = 66.3 m2.

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e2020 has 707 digits.

e is the mathematical constant known as the base of the natural logarithm, which means that the logarithm of any number to the base e is its natural logarithm. It is approximately equal to 2.71828, but its decimal representation goes on infinitely without repeating.

Calculating the number of digits in e2020 involves finding the number of decimal places that e extends past 2020. This is calculated using logarithms.

To find the number of digits in e2020, you can calculate 10^(number of decimal places past 2020) and determine the number of digits in the result.

This gives us 10^(707) = e2020, meaning that e2020 has 707 digits.

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Note that in the above scenario, the expert in Geometry of the two students is Miracle. All angles across from each other are NOT vertical angles; NOT all adjacent angles form linear pairs.

Vertical angles have two properties: 1) their sides are defined by the same lines; and 2) they share a vertex but not a side. Vertical angles are equivalent, according to the vertical angle theorem.

A vertex is a place on a polygon where the object's sides or edges meet, or where two rays or line segments intersect. Vertices is the plural of vertex.

In the original image, you can see visually that the angles formed by the lines "intersection of the lines" are not equal because they do not share the same vertex.

See the updated image to see the adjusted intersections and show how it is that the angles are now vertical. Note as well that the newly added angles x and y are also vertical and therefore congruent.

So in the new image:

1 ≅ 3

2≅ 4; and

x ≅ y

With regard to the question, if whether adjacent angles always form linear pairs, as indicated above, this statement is false. This is evidenced by ∠2 and ∠3 in the original image which are adjacent but non-linear.

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The x-intercept is x = -7/2

The y-intercept is when y = 7.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The equation of the graph is -2x + y = 7.

Now,

The x-intercept is when y = 0.

The y-intercept is when x = 0.

So,

-2x + y = 7

Substitute x = 0 and y = 0.

-2 x 0 + y = 7

y = 7

And,

-2x + 0 = 7

-2x = 7

x = -7/2

Thus,

x = -7/2 is the x-intercept.

y = 7 is the y-intercept.

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We can create a committee with 2 women and 2 men in (D) 60 ways.

To find the number of ways to select 2 women out of 4, we can use the combination formula C(4, 2) = 4! / (2! * (4 - 2)!) = 6. Similarly, to select 2 men out of 5, we can use the combination formula C(5, 2) = 5! / (2! * (5 - 2)!) = 10. To find the total number of ways to create a committee with 2 women and 2 men, we need to multiply the number of ways to select women and men: 6 * 10 = 60.

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The pounds of the Earl Grey tea and Orange Pekoe tea are required from selling the new blend versus selling the other types is 225 pounds and 75 pounds.

Let x = amount of Earl Grey tea to mix

so, 300-x = amount of Orange Pekoe tea to mix

After putting the equations together,

6x+4(300-x)=5.5*300

6x+1200-4x=1650

2x=450

x=225

So amount of Earl Grey tea to mix is 225 pounds

amount of Orange Pekoe tea to mix = 300-x

300-225 = 75

So the amount of Orange Pekoe tea to mix is 75 pounds.

Amount of Earl Grey tea to mix=225 pounds

Amount of Orange Pekoe tea to mix=75 pounds

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