The rate at which a rumor spreads through a town of population N can be modeled by the equation dt/dx = kx(N−x) where k is a constant and x is the number of people who have heard the rumor. (a) If two people start a rumor at time t=0 in a town of 1000 people, find x as a function of t given k=1/250. (b) When will half the population have heard the rumor?

Answer:

Step-by-step explanation:

Since ABCD is a parallelogram, we know that its opposite sides are parallel. That is, AB is parallel to CD and BC is parallel to DA.

To prove that AB = CD, we can use the fact that opposite sides of a parallelogram are congruent. That is, AB is congruent to DC. So, we can write:

AB = DC

Similarly, to prove that BC = DA, we can use the same fact. That is, BC is congruent to AD. So, we can write:

BC = AD

Therefore, we have proven that AB = CD and BC = DA, which shows that the opposite sides of the parallelogram ABCD are congruent.

ADC & BCD are congruent triangles (by SAS postulate). Since triangle ADC & BCD are congruent according to the SAS postulate, we may utilize CPCTC to determine that section AC is equal to segment BD.

In arithmetic progression, the triangles 3: 4: 5 are the only ones with edges. Pythagorean triple-based triangles are Herodian, which means they have integer areas and sides.

The easiest approach I've found to know for sure if an aspect is 90 degrees is to use the 3:4:5 triangle. According to this rule, a triangle is said to be a right triangle if one of its sides is 3 and the other is 4.

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Answer: y = -2x -3

Step by step explanation

First, we find the gradient of the line 4x + 2y = 10 by making y the subject of the formula.

4x + 2y = 10

2y = 10 - 4x which is the same as 2y = -4x + 10

Divide each term by 2

2y/2 = -4x/2 + 10/2

y = -2x + 5

From the equation, the gradient (coefficient of x) is -2

Since the line is parallel to 4x+2y=10, therefore the gradient of the lines are the same

The equation of the line can be gotten from y - y1 = m(x -x1)

where y1 = 5, x1 = -4 and m = -2

Therefore subtitiuiting into y - y1 = m(x -x1)

y - 5 = -2(x-(-4))

y - 5 = -2(x + 4)

y - 5 = -2x - 8

y = -2x -8 + 5

y = -2x -3

you can see that the gradients are the same (coefficent of x = -2)

The slope of the graph f(x) = 3x² + 7 at (-2, 19) is -12

The slope of a graph is the derivative of the graph at that point.

Since we have tha graph f(x) = 3x² + 7 and we want to find its slope at the point (-2, 19).

To find the slope of the graph, we differentiate with respect to x, since the derivative is the value of the slope at the point.

So,  f(x) = 3x² + 7

Differentiating with respect to x,we have

df(x)/dx = d(3x² + 7)/dx

= d3x²/dx + d7/dx

= 6x + 0

= 6x

dy/dx = f'(x) = 6x

At (-2, 19), we have x = -2.

So, the slope f'(x) = 6x

f'(-2) = 6(-2)

= -12

So, the slope is -12.

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Answer:

height = 7 yards

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the 2 parallel bases

here b₁ = 12 , b₂ = 9 and A = 73.5 , then

[tex]\frac{1}{2}[/tex] h(12 + 9) = 73.5 ( multiply both sides by 2 to clear the fraction )

h(21) = 147

21h = 147 ( divide both sides by 21 )

h = 7 yards

Answer:

79.2ft

Step-by-step explanation:

(9+9+10.3+10.3+10+10+10.3+10.3)ft

79.2ft

Answer:

t=7.7 s

Step-by-step explanation:

h=ut+1/2gt²

-76=113t+1/2(-32)t²

-76=113t-16t²

16t²-113t-76=0

[tex]t=\frac{113\pm\sqrt{(-113)^2-4 \times 16 \times(-76)} }{2 \times 16} \\t=\frac{113 \pm\sqrt{12769+4864} }{32} \\t=\frac{113 \pm\sqrt{17633} }{32} \\t=\frac{113+\sqrt{17633} }{32} \approx 7.68~s \approx7.7 s\\or\\t=\frac{113-\sqrt{17633} }{32} \approx~-0.62 ~s \approx-0.6~s[/tex]

negative~sign~rejected.

The value of f⁻¹(3) is 1/3. The value of f⁻¹(12) is -14/3. The complete table is:

X 0 1 2

f(x) 2 5 8.

A function is a mathematical rule that assigns a unique output or value for each input or value in a set. It is a relationship between two sets of numbers, called the domain (input) and range (output), such that each input value is associated with exactly one output value. A function is usually denoted by a letter such as f, and its input is represented by x, while its output is represented by f(x). The concept of a function is a fundamental one in mathematics and has many applications in various fields, including physics, engineering, economics, and more.

Here,

To find the values of f(x), we substitute the given values of x in the function f(x) = 3x + 2:

X 0 1 2

f(x) 2 5 8

To find f⁻¹(3), we first replace f(x) with 3 in the equation f(x) = 3x + 2:

3 = 3x + 2

Solving for x, we get:

x = 1/3

Therefore, f⁻¹(3) = 1/3.

To find f⁻¹(-12), we replace f(x) with -12 in the equation f(x) = 3x + 2:

-12 = 3x + 2

Solving for x, we get:

x = -14/3

Therefore, f⁻¹(-12) = -14/3.

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Answer:

24 different lunches

Step-by-step explanation:

There are three choices for the beverage, two choices for the appetizer (soup or salad), and four choices for the sandwich. Therefore, using the multiplication principle of counting, the number of different lunches possible is:

3 choices for beverage x 2 choices for appetizer x 4 choices for sandwich = 24 different lunches.

A. To find the intervals on which g is increasing, we need to find the derivative of g and determine where it is positive. Taking the derivative of g, we get:

g'(x) = 4x^3 - 12x^2 + 12x - 4

To find the critical points, we set g'(x) = 0 and solve for x:

4x^3 - 12x^2 + 12x - 4 = 0

Dividing by 4, we get:

x^3 - 3x^2 + 3x - 1 = 0

(x - 1)^3 = 0

So x = 1 is the only critical point. To determine where g is increasing, we need to test a value in each of the intervals (-∞, 1) and (1, ∞). For example, if we plug in x = 0, we get:

g'(0) = -4 < 0

So g is decreasing on the interval (-∞, 1). If we plug in x = 2, we get:

g'(2) = 20 > 0

So g is increasing on the interval (1, ∞). Therefore, g is increasing on the interval (1, ∞).

B. To find the intervals on which g is concave upward, we need to find the second derivative of g and determine where it is positive. Taking the derivative of g', we get:

g''(x) = 12x^2 - 24x + 12

To find the critical points, we set g''(x) = 0 and solve for x:

12x^2 - 24x + 12 = 0

Dividing by 12, we get:

x^2 - 2x + 1 = 0

(x - 1)^2 = 0

So x = 1 is the only critical point. To determine where g is concave upward, we need to test a value in each of the intervals (-∞, 1) and (1, ∞). For example, if we plug in x = 0, we get:

g''(0) = 12 > 0

So g is concave upward on the interval (-∞, 1). If we plug in x = 2, we get:

g''(2) = 12 > 0

So g is concave upward on the interval (1, ∞). Therefore, g is concave upward on the intervals (-∞, 1) and (1, ∞).

C. To find the value of k for which g has 5 as its relative minimum, we need to set g'(x) = 0 and solve for x:

4x^3 - 12x^2 + 12x - 4 = 0

Dividing by 4, we get:

x^3 - 3x^2 + 3x - 1 = 0

(x - 1)^3 = 0

So x = 1 is the only critical point. To find the corresponding value of k, we plug in x = 1 and set g(1) = 5:

g(1) = 1^4 - 4(1)^3 + 6(1)^2 - 4(1) + k = 5

Simplifying, we get:

k = 6

Therefore, the value of k for which g has 5 as its relative minimum is 6.

We can be 95% confident that the mean duration of imprisonment, p, of all political prisoners with chronic PTSD is somewhere between 19.4 months and 46.1 months.

Therefore the answer is A.

A confidence interval is a range of values that is likely to contain the true population parameter (in this case, the mean duration of imprisonment for political prisoners with chronic PTSD). The confidence level (in this case, 95%) indicates the percentage of times that the interval will contain the true population parameter in repeated sampling.

Option A correctly interprets the confidence interval by stating that we can be 95% confident that the true mean duration of imprisonment for political prisoners with chronic PTSD falls between 19.4 months and 46.1 months. This means that if we were to take many random samples of political prisoners with chronic PTSD and calculate the mean duration of imprisonment for each sample, 95% of the resulting confidence intervals would contain the true population mean.

Option B is incorrect because a confidence interval does not give the probability of the population parameter being in a particular range. It only gives the probability that the interval will contain the true population parameter if the sampling and estimation process is repeated many times.

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For the given CDF of X, the pmf of X at 1,3,4,6 and 12 is written as :

P(X = k) = 0.30 for k = 1 , P(X = k) = 0.10 for k = 3,

P(X = k) = 0.05 for k = 4 , P(X = k) = 0.15 for k = 6,

P(X = k) = 0.40 for k = 12.

In order to find the probability mass function (PMF) of X, we need to calculate the probability that X takes on each possible value.

Since X can take on any positive integer value, we can start by calculating the probability that X equals each positive integer.

⇒ P(X = 1) = 0.30,

⇒ P(X = 3) = F(3) - F(1) = 0.40 - 0.30 = 0.10

⇒ P(X = 4) = F(4) - F(3) = 0.45 - 0.40 = 0.05

⇒ P(X = 6) = F(6) - F(4) = 0.60 - 0.45 = 0.15

⇒ P(X = 12) = F(12) - F(6) = 1 - 0.60 = 0.40

Therefore, the required PMF of X is: P(X = 1) = 0.30 , P(X = 3) = 0.10 , P(X = 4) = 0.05 , P(X = 6) = 0.15 and P(X = 12) = 0.40 .

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The given question is incomplete, the complete question is

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X = the number of months between successive payments.

The CDF of X is as follows:

F(x) = {0           x < 1

         {0.30 1 ≤ x < 3

         {0.40 3 ≤ x < 4

         {0.45 4 ≤ x < 6

         {0.60 6 ≤ x < 12

         {1        12 ≤ x

What is the pmf of X at 1,3,4,6 and 12?

The standard normal area is the region under the standard normal distribution curve, which has a mean of 0 and a standard deviation of 1. One is equal to the entire area under the normal distribution curve.

To determine the probability for the above intervals using a typical normal distribution table or a calculator with a normal distribution function:

[tex]P(1.22 < Z < 2.15) = 0.1143[/tex]

[tex]P(2.00 < Z < 3.00) = 0.0228[/tex]

[tex]P(-2.00 < Z < 2.00) = P(Z < 2.00) - P(Z < -2.00) = 0.9772 - 0.0228 = 0.9544[/tex]

The number of standard deviations the variable is from the mean is shown by the ensuing Z-score. The chance of detecting a certain value of the variable in a given interval can then be determined using the standard normal area.

Therefore, The symmetry of the normal distribution allows us to use the third interval's coverage of 4 standard deviations to simplify the calculation, as illustrated above.

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Based on the properties of determinants, my conjecture is that the determinant of ka is equal to k raised to the power of the dimension of the matrix multiplied by the determinant of the original matrix a.

My conjecture is that the determinant of a matrix multiplied by a scalar k is equal to the determinant of the original matrix a multiplied by k raised to the power of the number of rows or columns in the matrix.

In other words, if a is an n-by-n matrix and k is a scalar, then:

det(ka) = k^n * det(a)

This conjecture is based on the fact that multiplying a matrix by a scalar k multiplies every entry in the matrix by k. Therefore, the determinant, which is a sum of products of matrix entries, is also multiplied by k^n, where n is the number of rows or columns in the matrix.

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The function g is the result of the transformation, which changes the entire graph of the function f(x) horizontally to the right by 90 units (x).

A transformation in mathematics is a function that converts points or objects between two different coordinate systems. It is a method of altering a geometric figure's location, size, or shape without altering its identity or fundamental characteristics. Translations, rotations, reflections, dilations, and combinations of these operations are all considered transformations. They are frequently used in geometry, algebra, and calculus to examine how functions and equations behave under various circumstances and to address issues in a variety of mathematical and scientific fields.

given

The base function f(x) = 1/x undergoes a transformation that may be seen in the equation of the function g(x) = 1/(x-90):

it moves horizontally to the right by 90 units.

The function g is the result of the transformation, which changes the entire graph of the function f(x) horizontally to the right by 90 units (x).

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Answer:

D.

Step-by-step explanation:

The Amount from contributions = R * n

The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.

Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:

FV = R * [(1 + i)ⁿ - 1] / i

where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.

To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.

Amount from contributions = R * n

To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.

Amount from interest = FV - R * n

Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.

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The final answer is $\frac{1}{12}$.

We need to evaluate the triple integral $\iiint e y , dv$ over the region $e$ bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$, and $x + y = 2$.

To evaluate this triple integral, we can use the limits of integration obtained by considering the intersection of the planes. From the plane equations $x+y+z=1$ and $x+y=2$, we can solve for $z$ and $x$ in terms of $y$ to obtain the limits:

0≤z≤1−x−yand0≤x≤2−y.

Since $e$ is bounded by the planes $x=0$ and $y=0$, we have $0 \leq x \leq 2-y$ and $0 \leq y \leq 2$. Thus, we can set up the triple integral as follows:

Next, integrating with respect to $x$, we obtain∫

02[22−22]

02−∫ 02 [eyx− 2eyx 2 − 2ey 2 x​ ] 02−ydy.Simplifying this expression, we get

∫02(2−522+32)

.∫ 02​ (2ey− 25​ ey 2 + 2ey 3 )dy.

Evaluating the integral, we get the final answer of $\frac{1}{12}$.

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question:-Evaluate the triple integral $\int!!\int!!\int e y ,dv$, where $e$ is bounded by the planes $x = 0$, $y = 0$, $z = 0$, $x + y + z = 1$ and $x + y = 2$.

In summary, both theorems require two pairs of congruent angles, but the AAS Congruence Theorem requires an included side to be congruent while the ASA Congruence Theorem requires a non-included side to be congruent.

A similarity theorem is a statement in geometry that describes a relationship between similar geometric figures. Similar figures are figures that have the same shape but may have different sizes. A similarity theorem states that certain corresponding angles of similar figures are congruent and that the ratio of corresponding sides is constant. This constant ratio is called the scale factor, and it is used to find missing side lengths or to enlarge or reduce the size of a figure. The most commonly used similarity theorem is the AA (angle-angle) theorem, which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Here,

The AAS Congruence Theorem and the ASA Congruence Theorem are both used to prove that two triangles are congruent. However, they differ in the conditions required for the triangles to be congruent.

The AAS Congruence Theorem requires that two pairs of corresponding angles and one pair of corresponding included sides be congruent. This means that if two triangles have two pairs of congruent angles and a side included between them is congruent, then the triangles are congruent.

On the other hand, the ASA Congruence Theorem requires that two pairs of corresponding angles and one pair of corresponding non-included sides be congruent. This means that if two triangles have two pairs of congruent angles and a side not included between them is congruent, then the triangles are congruent.

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If we round up, we get x = 12, which means that 12 students took history and 36 students took mathematics.

A Venn diagram is a graphical representation of sets, often used to show relationships between different sets of data. It consists of one or more circles, where each circle represents a set. The circles are usually overlapping to show the relationships between the sets. The region where the circles overlap represents the elements that belong to both sets. The non-overlapping parts of each circle represent the elements that belong to only one of the sets.

Here,

A. To illustrate the data on a Venn diagram, we need to draw two overlapping circles, one for history and one for mathematics. We can label the regions as follows:

The region where the circles overlap represents the students who took both history and mathematics.

The region outside both circles represents the students who did not take either history or mathematics.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history.

In this diagram, let's assume that x students took history and 3x students took mathematics. Then the total number of students who took the examination is x + 3x = 4x. We can label the regions on the diagram accordingly:

The region where the circles overlap represents the students who took both history and mathematics. Since there are 3x students who took mathematics, and all of them are included in the overlap region, the number of students who took both is 3x.

The region outside both circles represents the students who did not take either history or mathematics. Since there are 46 students in total, and 4x of them took the examination, the number of students who did not take either is 46 - 4x.

The region within the history circle but outside the mathematics circle represents the students who took history but not mathematics. Since x students took history, and 3x took mathematics, the number of students who took history but not mathematics is x - 3x = -2x. However, since we cannot have a negative number of students, we can assume that this region is empty.

The region within the mathematics circle but outside the history circle represents the students who took mathematics but not history. Since there are 3x students who took mathematics, and some of them also took history, the number of students who took mathematics but not history is 3x - 3x = 0. Therefore, this region is also empty.

B. We know that the total number of students who took the examination is 46. Therefore, we have:

x + 3x = 46

4x = 46

x = 11.5

However, since x represents the number of students who took history, it must be a whole number. Therefore, we can round x up or down to the nearest whole number. If we round down, we get x = 11, which means that 11 students took history and 33 students took mathematics.

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Answer:
Jika A adalah 20% lebih banyak dari B, maka dapat dituliskan sebagai:

A = B + 0.2B

Dalam bentuk sederhana, hal ini dapat disederhanakan menjadi:

A = 1.2B

Kita dapat menggunakan persamaan ini untuk mencari persentase B yang lebih kecil dari A. Misalnya, jika kita ingin mengetahui berapa persen B lebih kecil dari A, maka kita dapat menggunakan rumus persentase sebagai berikut:

(B lebih kecil dari A) / A x 100%

Substitusikan nilai A = 1.2B dan kita dapatkan:

(B lebih kecil dari 1.2B) / 1.2B x 100%

Maka:

0.2B / 1.2B x 100%

= 0.1667 x 100%

= 16.67%

Jadi, B adalah 16.67% lebih kecil dari A.

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Answer:c) 6

Step-by-step explanation:i.e. corresponding to different values of x we are given the values of f(x)

we have to find the value of f(0)

i.e. we have to find the value of f(x) when x=0

As we can see from the table the value of f(x) at x=0 is 6

Answer:

-4(x - 5) + 8x = 9x - 3

Simplifying the left side:

-4x + 20 + 8x = 9x - 3

4x + 20 = 9x - 3

Subtracting 4x from both sides:

20 = 5x - 3

Adding 3 to both sides:

23 = 5x

Dividing both sides by 5:

x = 23/5

Therefore, the equation equivalent to the given equation is:

5x - 23 = 0

Answer:

7. 23      

8. (3 - 8) x 5

Step-by-step explanation:

I think the second one is right but I know the first one is.

Answer:

D

Step-by-step explanation:

Sallys= 2(Jims) -5

Sally's + Jim's = 25

Answer:

Step-by-step explanation:

You want the system of equations that models, "Sally mows 5 less than twice the number of lawns Jim mows, and together they mow 25 lawns."

The letters 's' and 'j' represent the number of lawns that Sally and Jim mow, respectively.

Then "twice the number of lawns Jim mows" is represented be 2j. And 5 less than that is represented by 2j-5. Since this is the number of lawns Sally mows, the equation is ...

  s = 2j -5 . . . . . . . matches only one answer choice (D)

The equation for "together they mow 25 lawns" is ...

  s +j = 25

there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.

The probability of drawing a card from an ordinary deck without replacement can be determined using the concept of conditional probability. Conditional probability is the probability of an event occurring, assuming that another event has already occurred.

In order to calculate the probability that the two cards drawn are not sixes, we can use the formula:

P(A and B) = P(A) x P(B|A)

Where A and B represent two independent events, P(A) is the probability of event A occurring, and P(B|A) is the conditional probability of event B occurring given that event A has already occurred.

The probability of drawing the first card that is not a six is:

P(A) = 48/52 = 0.9231

The probability of drawing the second card that is not a six, given that the first card drawn was not a six, is:

P(B|A) = 47/51 = 0.9216

Therefore, the probability of drawing two cards at random from an ordinary deck of 52 cards and having neither of them be a six is:

P(A and B) = P(A) x P(B|A) = 0.9231 x 0.9216 = 0.8503 or approximately 85%.

This means that there is an 85% chance that the two cards drawn at random from an ordinary deck of 52 cards will not be sixes.

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Answer:

The total number of ways to choose 2 students from a class of 16 is given by the combination formula:

C(16,2) = 16! / (2! * (16-2)!) = (1615) / (21) = 120

This means there are 120 possible pairs of students that could be drawn.

The probability of you and your best friend being chosen is the number of ways that you and your friend can be selected divided by the total number of possible pairs. There is only 1 way to select you and your best friend out of the class of 16, so the probability is:

P(you and your best friend are chosen) = 1/120

Therefore, the probability that you and your best friend will be chosen is 1/120. Option (B) is the correct answer.

Answer:

The probability of choosing one specific student out of 16 is 1/16. After one student is chosen, there are 15 students left, so the probability of choosing the second specific student out of the remaining 15 is 1/15. The probability of both events happening is the product of the probabilities: (1/16) x (1/15) = 1/240. However, there are two ways that the students can be chosen (your friend first, then you or you first, then your friend), so we need to multiply the probability by 2: 2 x (1/240) = 1/120. Therefore, the probability of you and your best friend being chosen is 1/120. Answer: 1/120.

According to bayes therom the conditional probability thst x is greater than 26 is zero.

Bayes' theorem may be used to compute the conditional probability that x is greater than 26 if x is less than or equal to 12.

P(x > 26 | x 12) = P(x > 26 plus x 12) / P(x > 26 plus x 12) (x 12).

Because x cannot be more than 26 and less than or equal to 12, the numerator of the preceding formula is zero. As a consequence, the conditional probability is equal to zero:

P(x > 26 | x ≤ 12) = 0

This means that knowing x is less than or equal to 12 does not inform us if x is more than or less than 26.

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The functions that have all real numbers for their range are the ones in the option B.

Remember that for a function y = f(x), we define the range as the set of possible outputs of the function, that is, possible values of y.

Here we can see a lot of functions, first, the option with the absolute value function can be discarded because we know that:

|x| ≥ 0

So it never takes negative values.

We also can discardthe option with the sine and cosine, because the range of these two functions is [-1, 1].

The only remaining option is B, and the range of these 3 functions is (-∞, ∞), so that is the correct option in this case.

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