\( \ln \left[\frac{\left(x^{3}-2\right)^{5} \cdot \sqrt{x^{3}}}{2 \cdot \sqrt[3]{(4 x+1)^{7}}}\right]= \)

• The number 4: Because there are four cards with the number four in a regular deck of 52 cards (4 suits each containing a four), the chance of getting a four is 4/52, which may be reduced to 1/13 or about 0.077.

• The number 7 or a Jack: A regular deck of cards has four sevens and four jacks, for a total of eight cards that are either a seven or a jack. Picking a 7 or a Jack has a chance of 8/52, which may be reduced to 2/13 or roughly 0.154. • A red card or a Queen: A normal deck has 26 red cards (13 diamonds and 13 hearts) and 4 queens. to avoid counting them twice, we must remove the two red queens. As a result, the total number of red or queen cards is 26 + 4 - 2 = 28. Picking a red card or a queen has a chance of 28/52, which may be reduced to 7/13, or roughly 0.538. • A Spade or an Ace: A regular deck of cards has 13 spades and 4 aces, but we must deduct the ace of spades to avoid counting it twice. Therefore there are 13 + 4 - 1 = 16 cards that are either a spade or an ace. As a result, the chance of selecting a spade or an ace is 16/52, which may be reduced to 4/13 or roughly.

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The probability that they will all be non fiction is 0.0667. The solution has been obtained by using hyper-geometric distribution.

What is hyper-geometric distribution?

When sampling from a small population without replacement, the hyper-geometric distribution is a discrete probability distribution that determines the likelihood that an event occurs k times in n trials.

The formula is

P (X = x) = h (x, N, n, k) = [tex]\frac{C_{k,x} * C_{N-k, n-x} }{C_{N,n} }[/tex]

We are given

x = 4

N = 10 + 12 = 22

n = 4

k = 12

Substituting this in the formula, we get

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{22-12, 4-4} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = [tex]\frac{C_{12,4} * C_{10, 0} }{C_{22,4} }[/tex]

⇒P (X = 4) = h (4, 22, 4, 12) = 0.0667

Hence, the probability that they will all be non fiction is 0.0667.

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The factorized expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

To factorize the given expression au maximum, (3x+6)(4x−9)+(3x+6)(7x−3)(3x+6)(4x−9)+(3x+6)(7x−3), follow these steps:

Look for common factors in the terms. Notice that (3x+6) is a common factor in all terms.

Factor out the common factor, (3x+6), from each term:

(3x+6)[(4x−9) + (7x−3)(3x+6)(4x−9) + (7x−3

Now simplify the expression inside the brackets:

(3x+6)[(4x−9) + (21x² - 39x - 18x + 27)(4x−9) + (7x−3)]

Distribute the terms inside the brackets:

(3x+6)[(4x−9) + (84x³ - 153x² - 36x² + 63x - 108x + 81) + (7x−3)]

Combine like terms:

(3x+6)[(4x - 9) + (84x³ - 189x² + 9x + 81) + (7x - 3)]

Add the terms inside the brackets:

(3x+6)[84x³ - 189x² + 20x + 69]

So, the factorised expression au maximum is:

(3x+6)(84x³ - 189x² + 20x + 69)

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The location of A using graphs, is at (4, -1).

An organised representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Here in the question,

Coordinates of A= (8,2)

Now it is dilated by a scale factor of 1/2. So,

New coordinates, A' = (8/2,2/2)

= (4,1)

Now the triangle is reflected over the x-axis.

A' now becomes A" which is (4, -1).

Therefore, the new coordinate of A is (4, -1).

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The complete question is:

Triangle ABC is shown on the coordinate plane. Triangle on coordinate plane with vertices A at 8 comma 2, B at 10 comma 6, and C at 4 comma 4. Triangle ABC is dilated by a scale factor of one half about the origin and then reflected over the x-axis. What is the location of A″ after the sequence of transformations? (8, −2) (4, 1) (4, −1) (−4, 1)

If there were 756 students in the school and each student receives 10 pamphlets on the tooth brushing drills, the total number of pamphlets given out, using multiplication operation, is 7,560.

Multiplication operation is one of the four basic mathematical operations.

Multiplication operation involves the number being multiplied (the multiplicand), the multiplier or the number multiplying the multiplicand, and the product, which is the result.

The number of pamphlets given to each student on tooth brushing drills = 10

The total number of students at the school.

The total number of pamphlets given out to the students = 7,560 (756 x 10)

Thus, based on multiplication operation, the total pamphlets were 7,560.

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Answer:

5³×z²*³×x³*³

Answer=125z⁶x⁹

According the question given above The value οf x is 42

The pοlygοnal shape has three sides and three angles are called as a triangle. A triangle's internal angles are always added up tο 180 degrees.

In right triangles, the trigοnοmetric ratiοs οf sine, cοsine and tangent can be used tο find unknοwn angles and the lengths οf unknοwn sides. The sides οf the triangle are knοwn as fοllοws:

Given diagram the three angles οf a triangle is given,

sο the sum οf all three angles is equal tο  180 degrees.

Therefοre, (3x - 20) + (x - 1) + (x - 9) = 180°

By simplificatiοn,

5x - 30 =  180°

5x = 180 + 30

5x = 210

x = 42

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Domain of [tex]f^{-1}[/tex]: R - {-3}   or  (-∞, -3) ∪ (-3, ∞)

Range of [tex]f^{-1}[/tex]: R - {10}     or  (-∞, 10) ∪ (10, ∞)

The domain of a function is the set of all possible input values (also known as independent variables) for which the function is defined. The range of a function is the set of all possible output values (also known as dependent variables) that the function can produce.

Given the function f, state the domain and range of both f and [tex]f^{-1}[/tex], where

[tex]f(x) =\frac{3x+4}{10-x}[/tex]

Domain and range using inequalities,

Domain of f: R - {10}  or  (-∞, 10) ∪ (10, ∞)

Range of f: R - {-3}     or  (-∞, -3) ∪ (-3, ∞)

The inverse does not exist.

[tex]f^{-1} (x) =\frac{10x-4}{x+3}[/tex]

Domain of [tex]f^{-1}[/tex]: R - {-3}   or  (-∞, -3) ∪ (-3, ∞)

Range of [tex]f^{-1}[/tex]: R - {10}     or  (-∞, 10) ∪ (10, ∞)

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The segment cg has a length of 5 before dilation and 10 after dilation, making it the correct result of the dilation.

In mathematics, a dilation is a function f from a metric space M into itself that satisfies the identity d=rd for all points x, y \in M, where d is the distance from x to y and r is some positive real number. In Euclidean space, such a dilation is a similarity of the space.Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape.

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Answer:

Step-by-step explanation:

Based on the description, this study is most prone to differential misclassification of exposure status. The correct answer is A.

The description of the study suggests that the nurses who collected the data were poorly trained in the use of the male pattern baldness scale. This means that they may have misclassified some men as having male pattern baldness when they did not actually have it, and vice versa.

This misclassification of exposure status (i.e., male pattern baldness) is more likely to be differential because the nurses were unaware of the purpose of the study and did not know whether the men were cases or controls. This means that their misclassification of exposure status is likely to be influenced by the outcome (i.e., MI).

For example, if the nurses believed that male pattern baldness was a risk factor for MI, they may have been more likely to classify cases as having male pattern baldness and controls as not having it, even if this was not accurate. This would result in differential misclassification of exposure status, which can bias the study results. The correct answer is A.

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The fractions between 0 and 1, we have represented on a number line, include 1/4, 2/4, and 3/4. All of these have equal intervals of 0.25.

To plot 1/4, 2/4 and 3/4 on the number line, we need to divide the interval between 0 and 1 into four equal parts. Each part will represent 1/4.

We can label the fractions at 0 and 1 as shown below:

0   1/4   2/4   3/4   1

Now we can plot the given fractions on the number line as shown below:

0   1/4   2/4   3/4   1

         o     o     o

        1/4   2/4   3/4

We can divide the fractions to get the difference of intervals. This can be done as follows:

2/4-1/4 = 0.25, also:

3/4-2/4 = 0.25.

Any portion of a whole number that is stated as one number multiplied by another is referred to as a fraction. One-half of something, for instance, is represented by the fraction 1/2. Another approach to represent a portion of a full number is with a decimal.1/2 is same as 0.25 as a decimal.

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The graph that might be made by Johanna is graph (3).

Johanna has two variables: height and petal length. She plotted these variables on a graph to determine the relationship between them.

However, Johanna also found that there is one outlier in her data.

Each point on the graph represents the height and petal length of a single flower in Johanna's garden. The x-axis represents the height of the flower, and the y-axis represents the petal length.

Since there is a weak positive linear association between the two variables, the points on the scatter plot will be generally moving upwards from left to right.

In conclusion, Johanna's graph is most likely a scatter plot that shows the weak positive linear association between the height and petal length of the flowers in her garden, with one outlier that stands out from the rest of the data.

Hence the correct graph is (3).

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Complete Question:

Johanna measured the height and petal length of all the flowers in her garden. She plotted her results and found that the relationship between the variables suggests a weak positive linear association with 1 outlier.

Which of the following might be the graph Johanna made?

The statement that is correct about the two angles that are said to be linear pair would be = <ABC and <CBD are adjacent angles. That is option A

A linear pair exists between angles that are on a straight line that are formed when two lines intersect eachother leading to the formation of the adjacent angles.

The linear angles are there said to be adjacent angles and the sum of these two angles are always = 180°.

Therefore from the given statements, the correct option about the two angles which are linear paired angles is that they are also adjacent to each other.

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The residual is the difference between the observed etching rate and the predicted etching rate

The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]

The least squares regression equation for predicting the etching rate from the room temperature is given as:

[tex]y=2+\frac{1}{5}x[/tex]

When the room temperature is 25 degrees Celsius, the regression equation becomes

[tex]y=2+\frac{1}{5}*25\\\\y=7[/tex]

The residual is calculated as:

Residual = Observed - Predicted

From the question, the observed etching rate is,

[tex]=\frac{-2um}{min}[/tex]

So, the residual equation becomes-

[tex]r=5\frac{um}{min}-7\frac{um}{min}[/tex]

Evaluate the difference

[tex]r=-2\frac{um}{min}[/tex]

The residual of a room temperature of 25 degrees Celsius is[tex]=\frac{-2um}{min}[/tex]

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Answer:

Below

Step-by-step explanation:

the last equation shows frequency of 5 for  greater than this mass

  the equation before it covers 20 to 30 kg   frequency 11

      so it could be ZERO   or it could be ELEVEN are above 26 kg ....you just cannot tell ....so the MINIMUM frequency would be  5 + ZERO = 5

              and the MAXIMUM would be 5 + ELEVEN = 16

To find the total area of the pool and the walkway, we can add the areas of the pool and the walkway together.

Let's assume that the pool has dimensions of length L and width W, and that the walkway has a uniform width of 2 feet all around the pool. This means that the dimensions of the pool plus the walkway will be (L + 4) feet by (W + 4) feet, since we add 2 feet on each side.

The area of the pool alone is given by L x W. The area of the pool plus the walkway is then given by (L + 4) x (W + 4). To simplify, we can use FOIL (First, Outer, Inner, Last) method to expand the expression:

(L + 4) x (W + 4) = LW + 4L + 4W + 16

Therefore, the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 4L + 4W + 16

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

1.Start by assuming that the pool has dimensions of length L and width W, in feet.

2.Since Mrs. Smith wants to add a 2-foot walkway around the edge of the pool, we need to add 2 feet to both the length and width of the pool to get the dimensions of the pool plus the walkway. This means that the dimensions of the pool plus the walkway are (L + 2) feet by (W + 2) feet.

3.To find the area of the pool alone, we can simply multiply the length by the width: A_pool = L x W.

4.To find the area of the pool plus the walkway, we need to multiply the length and width of the larger rectangle that includes both the pool and the walkway. This rectangle has dimensions of (L + 2) feet by (W + 2) feet. Therefore, the area of the pool plus the walkway is:

A_total = (L + 2) x (W + 2)

5.We can simplify this expression by using the distributive property of multiplication. We first multiply L by W to get LW. Then, we multiply L by 2 and W by 2 to get 2L and 2W, respectively. Finally, we add 2 x 2 = 4 to account for the extra area added by the walkway. Therefore, the total area of the pool plus the walkway can be written as:

A_total = LW + 2L + 2W + 4

6.Finally, we can rewrite this expression as a polynomial in standard form, by rearranging the terms in descending order of degree:

A_total = LW + 2L + 2W + 4

    = LW + 2L + 2W + 0x² + 4

    = 0x² + LW + 2L + 2W + 4

So the polynomial expression that represents the total area of the pool and the walkway is:

A(L,W) = LW + 2L + 2W + 4

where A(L,W) is the total area of the pool and walkway as a function of the pool's length and width.

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The total area of the deck once will be 575.5 ft²

Mathematically, the area of a rectangular deck can be calculated by using this mathematical expression:

Area of a rectangular deck, A = LW

Therefore, the area of the additional dimension can be calculated as follows;

Area of an additional dimension, A = 23.25 x 14

Area of an additional dimension, A = 325.5 ft².

Now, we can calculate the total area of this deck as ;

Total area = original area + new area

Total area = 250 ft² + 325.5 ft²

Total area = 575.5 ft²

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Answer:

-5m - 10

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

= 1m + 2 - 6m - 12

= -5m - 10

So, the answer is -5m - 10

Answer:

-5(m+2)

Step-by-step explanation:

1/3(3m+6)-2(3m+6)

combine like terms

-5/3(3m+6)

Distribute

-5m - 10

common factor

-5(m+2)

answer:Average velocity is displacement divided by the time over which the displacement occurs. v avg = displacement time = Δ d Δ t = d f − d 0 t f − t 0. Velocity, like speed, has SI units of meters per second (m/s), but because it is a vector, you must also include a direction.

Step-by-step explanation:

The probability of picking a 2 and then picking a number less than 4will be 0.56%

By simply dividing the favοrable number οf pοssibilities by the entire number οf pοssible οutcοmes, the prοbability οf an οccurrence can be determined using the prοbability fοrmula. Because the favοrable number οf οutcοmes can never exceed the entire number οf οutcοmes, the chance οf an event οccurring might range frοm 0 tο 1.

The number οf favοurable οutcοmes tο all pοssible οutcοmes οf an event is the ratiο, which is knοwn as prοbability. The number οf gοοd οutcοmes can be represented by the symbοl x fοr an experiment with 'n' number οf οutcοmes. The fοllοwing equatiοn can be used tο determine an event's prοbability.

Yοu pick a card at randοm. Withοut putting the first card back, yοu pick a secοnd card at randοm.

1/13 chance οf picking a 5.

4/51 chance οf picking a 3 οn secοnd draw.

4/(13*51) οf dοing these sequentially = 0.56%

Hence the prοbability will be 0.56%

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The sοlutiοn οf the given prοblem οf quadrilateral cοmes οut tο be DC  = 12 .

In mathematics, a rectangle is a fοur-sided οbject with fοur cοrners. Either "quad" οr "array οf inventive ideas" are Latin terms that were used tο cοin the phrase (meaning "side"). Fοur cοrners, fοur areas, and fοur cοrners are the three cοmpοnents οf a rectangle. Cοnvex and cοncave are the twο primary varieties οf cοnvex and cοncave fοrms. Cοnvex quadrilaterals alsο include the subdivisiοns οf trapezοids, geοmetric shapes, angles, rhοmbuses, and squares.

Here,

Assuming that ABCD is a trapezοid with parallel sides AB and CD, we can use the knοwledge that the perimeter οf a trapezοid is equal tο the sum οf its οppοsite sides tο cοnstruct the fοllοwing equatiοn:

=> AB = 52 + CD = BC + AD

Assuming AB = 13 and BC = 15, the equatiοn can be simplified as fοllοws:

=>  13 + CD + 15 + AD = 52

=>  CD + AD = 24

=> DC  = 12

Hοwever, we are unable tο determine the length οf DC οr AD withοut additiοnal details regarding the angles οr side lengths οf the trapezοid. As a result, there is nο clear sοlutiοn.

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Complete question:

The probability that a pigeon chosen at random will receive an incorrect test outcome is 103/10,000 = 0.0103, or roughly 1.03%.

Let's assume that there are 10,000 pigeons in the population. Then, 1.5% of them, which is 150 pigeons, are infected with the virus.

Out of these 150 infected pigeons, the test will correctly identify 97% of them, which is 145.5 pigeons. The remaining 4.5 infected pigeons will be incorrectly identified as not having the virus.

Out of the 9,850 uninfected pigeons, the test will correctly identify 99% of them, which is 9,751.5 pigeons. The remaining 98.5 pigeons will be incorrectly identified as having the virus.

Therefore, the total number of pigeons that get an incorrect test result is 4.5 + 98.5 = 103.

So, the probability that a randomly selected pigeon gets an incorrect test result is 103/10,000 = 0.0103 or approximately 1.03%

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Answer:

$6.49

Step-by-step explanation:

The original admission price was $5.50, and it increased by 18%. Let's find 18% of 5.50 and then add it to $5.50, meaning $5.50 would increase by 18% (of itself.)

So 18% of 5.50 = 0.99 ( thats 0.18 x 5.50)

Add the 99 cents (0.99) to $5.50

and then you get $6.49

here is the equation I used:

(5.50 x 0.18) + 5.50

hope this helped :)

Answer:

x = 2, y = -2

Step-by-step explanation:

To solve by substitution, you first need an isolated variable in one equation. Luckily, y is isolated in both equations.

Because y = y, we can set the other sides of the equations equal to each other.

x - 4 = 4x - 10 [substitute]

The next step is to isolate and solve for x

x = 4x - 10 + 4

x - 4x = -6

-3x = -6

x = 2

Next, you substitute x into both equations.

y = (2) - 4

y = -2

y = 4(2) - 10

y = 8 - 10

y = -2

Because both equations work out to the same value, you have the correct answer.

Answer: So get your rump in that chair and study your pp off

Step-by-step explanation:

The weight of the first basket full of apples is 8.66 kilograms more as compare to weight of the second basket.

Number of full of apples basket with Tommy = 2

Weight of first basket full of apples = 18.63 kilograms

Weight of second basket full of apples = 9.97 kilograms

Weight of first basket is greater than the weight of the second basket.

More weight in first basket

= Subtract the weight of the second basket from the weight of the first basket

⇒ More weight in first basket  = Weight of first basket - Weight of second basket

⇒ More weight in first basket = ( 18.63 - 9.97 ) kilograms

⇒ More weight in first basket = 8.66 kilograms

Therefore, the first basket weighed 8.66 kilograms more than the second basket.

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The Solution of the matrix for (x, y) is (-1, 5) that is:  [tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-1\\5\end{array}\right][/tex]

A matrix is described by its elements, which are the numbers or symbols that make up the matrix, and its dimensions, which indicate how many rows and columns there are in the matrix. A matrix's inverse is a matrix that yields the identity matrix when multiplied by the original matrix. A matrix's inverse is denoted by and only applies to square matrices (matrices with an equal number of rows and columns).

[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]

find the inverse matrix for the matrix

[tex]\left[\begin{array}{ccc}4&2\\-4&2\end{array}\right][/tex]

Find the determinant,

determinant = 4 × 2 (-4) × 2 = 16

Inverse matrix is

[tex]1/16 \left[\begin{array}{ccc}4&2\\-4&2\end{array}\right]^T = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right][/tex]

So, the solution of the equation is

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = 1/16 \left[\begin{array}{ccc}2&-2\\4&4\end{array}\right] \left[\begin{array}{ccc}6\\14\end{array}\right][/tex]

On solving,

Therefor, The Solution for (x, y) is (-1, 5).

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Answer:

m = - 1

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,0) (0, -2)

We see the y decrease by 2, and the x increase by 2, so the slope is

m = -2/2 = -1

So, the slope is -1

Answer:

m = - 1

Step-by-step explanation:

Kylie changed the ratio of blue to yellow in her paint mixture from 5:3 to 3:4, making the colour more yellowy. She could have started with either 3.5 litres of blue and 2.1 litres of yellow, or 7 litres of blue and 4.2 litres of yellow. She could have added either 0.7 litres of blue and 3.5 litres of yellow, or 1.4 litres of blue and 7 litres of yellow to achieve the new ratio.

The new colour is more yellowy than the first colour because the ratio of blue to yellow has changed. Initially, the ratio was 5:3, or 5 parts blue to 3 parts yellow. After Kylie added more blue and 5 times as much yellow than blue, the ratio changed to 3:4, or 3 parts blue to 4 parts yellow. This means yellow is now the majority colour, which makes the final colour more yellowy than the first.

To calculate the amount of blue and yellow in the new mixture, we can use the equation:

Blue : Yellow = 3 : 4

Therefore, the amount of blue needed is 3/7 of the total, and the amount of yellow is 4/7 of the total.

2a) How many litres of each colour could Kylie have started with?

Possibility 1: Kylie could have started with 3.5 litres of blue and 2.1 litres of yellow (3.5 : 2.1 = 5 : 3).

Possibility 2: Kylie could have started with 7 litres of blue and 4.2 litres of yellow (7 : 4.2 = 5 : 3).

2b) How many litres of each colour could Kylie have added?

Possibility 1: Kylie could have added 0.7 litres of blue and 3.5 litres of yellow (0.7 : 3.5 = 3 : 4).

Possibility 2: Kylie could have added 1.4 litres of blue and 7 litres of yellow (1.4 : 7 = 3 : 4).

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