3. Suppose that the supply and demand for milk are given by the following equations where Q is the quantity in units of milk and P is the price per unit of milk:
Supply of Milk: Q = 0.50P – 3
Demand for Milk: Q = 27 – 0.30P

Algebraically (mathematically) determine the equilibrium price and quantity in the milk market. Show all work. (6 pts.)

Answer:

Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).

Step-by-step explanation:

We can use proportionality to solve this problem. Since the price of apples is directly proportional to the number of apples, we can set up a proportion:

2 apples / Rs 48 = x apples / Rs 1098

To solve for x, we can cross-multiply and simplify:

2 * Rs 1098 = 48 * x

Rs 2196 = 48x

x = Rs 2196 / 48

x = 45.75

Therefore, Rs 1098 can buy 45.75 apples (or approximately 45 apples, since we cannot buy a fractional part of an apple).

The program to find the divisible values gives the number of multiples of 2 between 3 and 8 inclusive is 3

To check if an integer is divisible by x, you could divide it by x and check if the remainder is 0.

If the remainder is 0, then the integer is divisible by x and therefore is a multiple of x.

We can use this concept to find the number of multiples of x between low and high inclusive.

If low is 3, high is 8, and x is 2, then we can check if each number between 3 and 8 is divisible by 2.

3 is not divisible by 2, so it is not a multiple of 2.

4, however, is divisible by 2, so it is a multiple of 2.

5 is not divisible by 2, so it is not a multiple of 2.

6, however, is divisible by 2, so it is a multiple of 2.

Then 7 is not divisible by 2, so it is not a multiple of 2. 8 is divisible by 2, so it is a multiple of 2.

Therefore, the number of multiples of 2 between 3 and 8 inclusive is 3 (4, 6, and 8).

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Value of limit expression

[tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]  [tex]=\dfrac{5}{9}[/tex]

Value of limit expression

[tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex] [tex]= \dfrac{1}{7}[/tex]

In mathematics, the limit is the value that the function approaches as the input approaches the value. Limits are essential in calculus and mathematical analysis and are used to define continuity, derivatives and integrals  

Given

[tex]a) \lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{sin6\theta}[/tex]

[tex]sin\theta = \theta - \dfrac{\theta^{3}}{3!} + \dfrac{\theta^{5}}{5!} + .......[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{6\theta - \dfrac{(6\theta)^{3} }{3!} +\dfrac{(6\theta)^{5} }{5!}- ......}[/tex]

[tex]\dfrac{10}{3} \lim_{\theta \to 0} \dfrac{\theta}{(6\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{\theta}{(\theta)(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex][tex]\dfrac{10}{3\times6} \lim_{\theta \to 0} \dfrac{1}{(1 - \dfrac{(6\theta)^{2} }{3!} +\dfrac{(6\theta)^{4} }{5!}- ......)}[/tex]

[tex]\dfrac{10}{3\times6} \times \dfrac{1}{(1 - \dfrac{(0)^{2} }{3!} +\dfrac{(0)^{4} }{5!}- ......)}[/tex]

[tex]=\dfrac{5}{9}[/tex]

[tex]b)\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]

[tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x^{2} + 6x - x -6}[/tex][tex]\lim_{x \to 1} \dfrac{(x -1) - \dfrac{(x - 1)^{3}}{3!}-\dfrac{(x - 1)^{5}}{5!} - ......}{x(x + 6) - 1(x +6)}[/tex][tex]\lim_{x \to 1} \dfrac{(x - 1)(1 - \dfrac{(x - 1)^{2}}{3!}-\dfrac{(x - 1)^{4}}{5!} - ......)}{(x- 1)(x +6)}[/tex]

[tex]\dfrac{(1 - \dfrac{(1 - 1)^{2}}{3!}-\dfrac{(1 - 1)^{4}}{5!} - ......)}{(1 +6)}[/tex]

[tex]=\dfrac{1}{7}[/tex]

Hence, [tex]\dfrac{5}{9}[/tex] is value of limit expression [tex]\lim_{\theta \to 0} \dfrac{10\theta}{3sin\theta}[/tex]

and [tex]\dfrac{1}{7}[/tex] is value of  expression [tex]\lim_{x \to 1} \dfrac{sin(x -1)}{x^{2} + 5x - 6}[/tex]

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Answer:

Step-by-step explanation:

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We know that the 5th term is 729, so:

a * r^4 = 729

10th term is 3, so:

a * r^9 = 3

r^5 = 3/729

r^5 = 1/243

r = (1/243)^(1/5)

r = 1/3

a * (1/3)^4 = 729

a = 3^7

Therefore, the sequence is:

3^7, 3^6, 3^5, 3^4, 3^3, ...

The 12th term is:

3^2 = 9

An explicit rule for the g(x) will be g(x) = 60,000(1.1)ˣ.

A function is a connection between a number of inputs and a single output. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists. A function is often represented by the expression f(x), where x represents the input.

Given, Stefany's income at her company, Horizon Logistics begins off evolving at a base income of $60,000.

Since Stefany's salary at Horizon Logistics starts at a base salary of $60,000, we can write:

g(1) = 60,000

g(2) = 66,000 = 60,000 + 6000

g(2) = 60,000 + 60000(0.1)

g(2) = 60,000* (1.1)

g(3) = 72600 = 66,000 + 6600 +

g(2) = 66,000 + 66000(0.1)

g(2) = 66,000* (1.1) = 60,000 (1.1)²

And so on

thus, we can formulate the function for g(x)

such that

g(x) = 60,000(1.1)ˣ

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Circumcenter is term describes point N .

What are circumradius and circumcenter?

The center of a triangle's circumcircle is known as the circumcenter. The radius of that polygon's circumscribed circle is known as the circumradius.

                         A polygon's circumcenter is marked by the circumcenter point of the circumcircle. The circle that encircles a polygon from all of its vertices is known as its circumcircle, and its circumcenter is where that circle begins.

We have been given an image of a triangle KLM  and we are asked to choose the term that describes point N.

We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.

Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM .

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The requried Kristen travels 9.5 miles to work. Option D is correct.

Speed is defined as when an object is in motion, the distance covered by that object per unit of time is called speed.

Here,
We can use the formula distance = rate x time to solve this problem.

When Kristen is biking, her rate is 10 mph and her time is 1/4 hour. So her distance traveled is:

distance = rate x time

distance = 10 mph x 1/4 hour

distance = 2.5 miles

When Kristen is on the train, her rate is 28 mph and her time is another 1/4 hour. So her distance traveled on the train is:

distance = rate x time

distance = 28 mph x 1/4 hour

distance = 7 miles

Therefore, the total distance Kristen travels to work is the sum of the distances she traveled while biking and on the train:

total distance = distance biked + distance on train

total distance = 2.5 miles + 7 miles

total distance = 9.5 miles

So Kristen travels 9.5 miles to work.

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The 90% confidence interval for the mean number of books people read is (-16, 38.6).

To construct a 90% confidence interval for the mean number of books people read, we first need to find the critical value (z*) that corresponds to a 90% confidence level. This can be found using a z-table or calculator. The critical value for a 90% confidence level is 1.645.

Next, we need to calculate the margin of error (ME) using the formula ME = z* x SE, where SE is the standard error. In this case, SE = 16.6 books, so ME = 1.645 x 16.6 = 27.3 books.

Finally, we can construct the 90% confidence interval by adding and subtracting the margin of error from the sample mean (x overbar). The confidence interval is:

(x overbar - ME, x overbar + ME) = (11.3 - 27.3, 11.3 + 27.3) = (-16, 38.6)

This means that we are 90% confident that the true mean number of books people read is between -16 and 38.6 books.

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The volume of the triangular prism is 137.2 units cube.

The triangular prism has a height of 8 units. The base of the prism is shown in the image. The volume of the prism can be represented as follows:

volume of a triangular prism = BH

where

Therefore, let's find the base area

B = 1 / 2 b h

let's find b

Hence,

tan 65 = b / 4

cross multiply

b = 4 tan 65

b = 8.57802768204

b = 8.58 units

Therefore,

B = 1 / 2  × 4 × 8.58

B = 17.1560553641

Therefore,

volume of a triangular prism = 17.156 × 8

volume of a triangular prism = 137.248442913

Hence,

volume of a triangular prism = 137.2 units cube

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Yellow makes up approximately 17.32% of the total number of trips.

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 calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

To find the percentage of the total that Yellow makes up, divide the total number of Yellow trips by the overall total number of trips, and then multiply by 100 to convert to a percentage -

Yellow total = 820

Overall total = 4730

Yellow percentage = (820/4730) x 100%

Yellow percentage = 0.1734

Yellow percentage = 17.34%

Therefore, Yellow makes up approximately 17.32% of the total number of trips.

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h(-2) = 3

h(0) = 0

h(5) = 3/4

This can be solved by using the concept of function.

In arithmetic, a function from one set to another, X to Y, allocates precisely one element of Y to each element of X. Both of the set X and the set Y usually known as the function's domain and codomain, respectively. The basic conception of functions was the relationship between fluctuating quantities and other variables.

A function with the name f is defined by the formula y=f(x). This is understood to mean "y is a function of x." The input value, also known as an independent variable, is represented by the letter X. The outcome value, or dependent variable, is denoted by the letter y, or f(x).

This is a piece wise-defined function:

For h(-2):

h(-2) = 3

For h (0):

h(0) = (x + 1)²- 1

h(0) = (0 + 1)² - 1

h(0) = 1 - 1

h(0) = 0

For h(5):

h(5) = -1/4 x + 2

h(5) = -1/4(5) + 2

h(5) = 3/4

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Answer:

length =7 breadth =2

Step-by-step explanation:

l x b = 14, so l= 14/b

2(l+b) =18 , l+b =9

14/b+b=9

[tex]b^ {2}[/tex] -9b+14=0

[tex]b^ {2}[/tex] -7b-2b+14=0

(b-7)(b-2) =0

b= 7 or 2

The volume of the open-topped box expressed as the function is V(x) = x(9 - 2x)(12 - 2x)

From the question, we have the following parameters that can be used in our computation:

Length = 9

Width = 12

Cut out = x

The volume as a function of x is represented as

V(x) = (Length - 2x) * (Width - 2x) * x

Substitute the known values in the above equation, so, we have the following representation

V(x) = x(9 - 2x)(12 - 2x)

Hence, the function si V(x) = x(9 - 2x)(12 - 2x)

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If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, then none of the statements is false.

What is proportion?

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

Since a/b = c/d, are proportional then can cross-multiply to get ad = bc.

Now, evaluate each statement -

A. b/a = d/c

Cross-multiplying, it is obtained that bc = ad, which is true based on the original proportion.

Therefore, this statement is true.

B. a/c = b/d

Cross-multiplying, it is obtained ad = bc, which is also true based on the original proportion.

Therefore, this statement is true.

C. b/a = c/d

This is equivalent to the original proportion, so it is true.

D. (a + b)/b = (c + d)/d

Simplify the equation -

d(a + b) = b(c + d)

da + db = bc + bd

da = bc

Cross-multiplying, it is obtained that da = bc, which is true based on the original proportion.

Therefore, this statement is true.

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16% (percent) of the total planes is made up of Green Planes.

The percentage refers to the ratio of one value or quantity compared to another.

The percentage can be computed as the quotient of the numerator and the denominator multiplied by 100.

Percentage values range from 0% to 100%.

               Car        Plane        Train       Total

Green     120         250           500         870

Blue        150         350           750       1250

Yellow    170         200           450        820

Red       200         300           300        800

Brown   220         450           320        990

Total     860        1550        2320       4730

Green Plane = 250 of 1,550 total planes = 16.13% (250/1,550 x 100)

Green Plane = 250 of 870 Vehicles = 28.74% (250/870 x 100)

Thus, we can conclude that of the 1,550 planes, green planes consist of 16%.

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

Answer:

Step-by-step explanation:

4x-22.2=1.90

22.20-4x=1.90

4x + 1.90 = 22.20

Let's call the smaller number "x". Since the larger number exceeds the smaller number by 1, we can call the larger number "x + 1".

The problem tells us that the sum of the numbers is 25, so we can set up an equation:

x + (x + 1) = 25

Simplifying and solving for x:

2x + 1 = 25

2x = 24

x = 12

So the smaller number is 12. To find the larger number, we can use x + 1:

x + 1 = 12 + 1 = 13

So the larger number is 13.

Therefore, the two numbers are 12 and 13.

Answer:

33 inches

Step-by-step explanation:

Use triangle calculator online

Two polygons are similar if and only if all corresponding angles are congruent and all corresponding sides are proportional. The solution has been obtained by using concept of similar quadrilaterals.

What are similar quadrilaterals?

Two quadrilaterals are considered to be similar when two adjacent sides have the same ratio and all three matching angles are equal (the fourth angle automatically becomes equal because the internal angle sum equals 360 degrees).

Two polygons are similar if and only if there is a correspondence among their angles and among their sides so that all corresponding angles are congruent and all corresponding sides are proportional.

Hence, the corresponding angles need to be congruent.

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Answer:

x=-15, y=26

Step-by-step explanation:

Now that we know k is 3/2, we can use the formula to find the value of y when x is 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

A variable is a number in mathematics that can change depending on the issue. Several statements and equations in mathematics use the generic letters x, y, and z. Or to put it another way, a variable is a symbol that denotes an unknowable numerical value. Assume that x + 5 = 10. The term "x" is used here.

Since y varies directly with x, we know that the ratio of y to x is constant. Let's call this constant k. Then we can write:

y = kx

To find k, we can use the first two rows of the table:

When x = 2, y = 3, so:

3 = k(2)

k = 3/2

When x = 10, y = 15, so:

15 = k(10)

k = 3/2 (which matches the previous calculation)

Now we can use k to find y when x = 14:

y = (3/2)(14) = 21

Therefore, when x = 14, y = 21.

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Therefore , the solution of the given problem of expression comes out to be Sunny earned $12x - 15 this week.

Mathematical operations like addition, multiply, and division are necessary. They result in the following when combined: An equation, some information, and a mathematical operator Values, parameters, and arithmetic calculations like additions, subtractions, multiplication and division, and divisions are all found in a statement of fact. Different sentences and words can be contrasted and compared.

Here,

If Sunny worked for x hours and earns $12 per hour, her earnings before the late delivery charge would be:

$12x$

However, since she was charged $15 for the late delivery on Tuesday, her earnings for the week would be:

$12x - 15$

Therefore, Sunny earned $12x - 15 this week.

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The complete question is "Sunny earns $12 per hour delivering cakes. She worked for x hours this week. Unfortunately, she was charged $15 for a late delivery on Tuesday. How much money did Sunny earn this week?"

The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

An equation is a mathematical statement that expresses the equality between two mathematical expressions or values. It is a concise representation of a relationship between two or more variables, which can be represented using symbols or numbers. An equation usually consists of two sides separated by an equal sign, where each side represents a mathematical expression.

Equations are used in various branches of mathematics, science, engineering, and other fields to describe various phenomena and solve problems. They play a crucial role in understanding and describing real-world phenomena, from the laws of physics to the behavior of financial markets. Equations can help us predict outcomes, design solutions, and solve complex problems.

In mathematics, equations are used to solve problems that involve unknown variables. The unknown variables can be found by manipulating the equation to isolate the variable. Solving equations is a fundamental skill in mathematics, and it is often used in fields like physics, chemistry, and engineering.

Equations can be linear or nonlinear, depending on the degree of the variables involved. Linear equations involve variables raised to the first power only, while nonlinear equations involve variables raised to higher powers or are composed of a combination of functions.

In summary, equations are a fundamental tool in mathematics and other fields, which help us describe and understand the relationships between variables and solve problems involving unknown variables.

To find the first positive time at which the particles have approximately the same velocity, we need to find the derivative of the displacement function for each particle, set them equal to each other, and solve for x.

The derivative of the displacement function for particle 1 is:

f'(x) =[tex]-4e^(4[/tex]cos(x))sin(x)

The derivative of the displacement function for particle 2 is:

g'(x) =[tex]-x^2 - x[/tex]

Setting f'(x) equal to g'(x), we get:

[tex]-4e^(4[/tex]cos(x))sin(x) =[tex]-x^2 - x[/tex]

We can solve this equation numerically using a graphing calculator or computer software. The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

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Answer:

[tex]\frac{3}{x+7}[/tex]

Step-by-step explanation:

[tex]\frac{3x-21}{x^{2} -49}[/tex]

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form [tex]x^{2} -a^{2}[/tex]), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

[tex]\frac{3(x-7)}{(x-7)(x+7)}[/tex]

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

[tex]\frac{3}{x+7}[/tex]

volume of a cube = x³

where x the length of the side of the cube

so, the volume = (4.2)³

= 74.088 in³

Answer:

R

Step-by-step explanation:

-1 is exactly between 0 and -2, meaning that the answer is R.

R is the right answer

a) The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = 0.1406

b) The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

The number of possible answers = 4

Let the probability that the answer is correct P ( C ) = 1/4

Let the probability that the answer is wrong P ( W ) = 3/4

Now , probability that the first two guesses are wrong and the third is correct is P ( WWC ) = P ( W ) x P ( W ) x P ( C )

On simplifying , we get

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 3/4 ) x ( 3/4 ) x ( 1/4 )

The probability that the first two guesses are wrong and the third is correct is P ( WWC ) = ( 9/64 ) = 0.1406

And ,

The probability that exactly one correct answer when 3 guesses are made is = P ( WWC ) + P ( WCW ) + P ( CWW )

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 3 x 0.140625

The probability that exactly one correct answer when 3 guesses are made 3 P ( WWC ) = 0.4219

Hence , the probabilities are solved

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The third expression i.e. a(b) + a(c) is not equivalent to the other expressions. The solution has been obtained by using the algebraic expressions.

What is an algebraic expression?

A mathematical phrase is said to as "algebraic" if it contains variables, constants, and algebraic operations (addition, subtraction, etc.).

We are given three expressions.

The first expression is a + b+ c which represents the sum of the three variables.

The second expression is c + b + a which also represents the sum of the three variables but just the order of adding is different.

The third expression is a(b) + a(c) which represents sum of two variables multiplied with the third variable.

Hence, the third expression i.e. a(b) + a(c) is not equivalent to the other expressions.

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The areas and the perimeters of the composite figures are listed below:

Case 1: A = 36 cm² (Right choice: A)

Case 2: p = 30 cm (Right choice: G)

Case 3: A = 46 cm² (Right choice: I)

Case 4: p = 38 cm (Right choice: H)

In this problem we find two composite figures that are result of combining three rectangles, whose perimeters are the sum of all side lengths and whose areas are the sum of the areas of the rectangles. The formulae for the perimeter and the area of a rectangle are, respectively:

Perimeter

p = 2 · (w + l)

Where:

Area

A = w · l

Where A is the area, in square centimeters.

Now we proceed to determine the perimeters and areas according to the case:

Case 1

A = 2 · (3 cm) · (5 cm) + (2 cm) · (3 cm)

A = 30 cm² + 6 cm²

A = 36 cm² (Right choice: A)

Case 2

p = 2 · (3 cm) + 3 · (2 cm) + 2 · (5 cm) + 8 cm

p = 6 cm + 6 cm + 10 cm + 8 cm

p = 30 cm (Right choice: G)

Case 3

A = 2 · (5 cm) · (4 cm) + (2 cm) · (3 cm)

A = 40 cm² + 6 cm²

A = 46 cm² (Right choice: I)

Case 4

p = 2 · (4 cm) + 2 · (5 cm) + 2 · (2 cm) + 3 cm + 13 cm

p = 8 cm + 10 cm + 4 cm + 3 cm + 13 cm

p = 38 cm (Right choice: H)

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