If the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity, approaching either infinity or -infinity.
It is given that, the first number is 2 and the last number is 18,
a = 2
L=18
n=5
a₅=5
a₅=a+(5-1)d
18=2+4d
4d = 18-2
4d = 16
d= 16 / 4
d=4
The terms of the sequence are,
a₁=2
a₂=2+4=6
a₃=6+4=10
a₄=10+4=14
a₅=14+4=18
Thus, if the first number is 2. The last number is 18. The sequence of five numbers will be 2,6,10,14,18.
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The sum of two numbers is 122. The second number is 25 less than twice the first number. Find the number.
B.
The scale of figure A to figure B is 1 to 2. If the area of figure A is 7 ft2, what is the area of figure B?
OA. 3.5 ft²
OB. 35 ft²
OC. 14 ft²
OD. 28 ft²
8x +1312x + 7X == [?]Enter
The two angles given in the problem lie the opposite of each other with respect to the transversal line. This means that these two angles are supplementary angles. The sum of the two angles will be equal to 180 degrees, hence, we can set up an equation solving for x. We have
[tex]8x+13+12x+7=180[/tex]Solve for x, we have
[tex]\begin{gathered} 20x+20=180 \\ 20x=180-20 \\ \frac{20x}{20}=\frac{160}{20} \\ x=8 \end{gathered}[/tex]The value of x
Home Liquidators marks up its merchandise 35% on cost. What is the company’s equivalent markup on selling price?
The company’s equivalent markup on selling price is 26%.
What is markup?The markup is the gap between the selling price and the cost of a good or service. It is frequently represented as a percentage of the total cost. To cover the costs of doing business and generate a profit, a markup is added to the overall cost borne by the manufacturer of a good or service.
The following can be deduced based on the information:
Markup on cost = 35%
Cost = 100%
Selling price = 135%
Markup on selling price will be:
= (0.35/1.35 x 100)
= 26%
Therefore, the value is 26%.
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the variables x and y vary inversely. use x=-2 and y=3 to write and equation relating x and y. then find y when x=-1
SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define the variation that occurs in the Question.
Inverse Variation: Inverse variation is the relationship between two variables, such that if the value of one variable increases then the value of the other variable decreases.
STEP 2: Interpret the statements in the question tab
[tex]\begin{gathered} x\text{ varies inversely as y} \\ x\propto\frac{1}{y} \end{gathered}[/tex]STEP 3: Get the constant of variation
[tex]\begin{gathered} x\propto\frac{1}{y} \\ \text{Introducing the constant, we have;} \\ x=k\times\frac{1}{y},x=\frac{k}{y} \\ By\text{ cross multiplication,} \\ x=ky \\ \text{Divide both sides by y} \\ \frac{x}{y}=k \end{gathered}[/tex]STEP 4: Use the given values to get the equation relating x and y
[tex]\begin{gathered} \frac{x}{y}=k,x=-2,y=3 \\ By\text{ substitution,} \\ \frac{-2}{3}=k \\ k=\frac{-2}{3} \\ \\ \text{The equation relating x and y will be:} \\ x=-\frac{2}{3}y \\ x=\frac{-2y}{3} \end{gathered}[/tex]Hence, the equation relating x and y is:
[tex]x=\frac{-2y}{3}[/tex]STEP 5: Find y when x=-1
[tex]\begin{gathered} x=ky \\ \text{Divide both sides by k to get the value of y} \\ y=\frac{x}{k} \\ x=-1,k=-\frac{2}{3} \\ By\text{ substitution,} \\ y=\frac{-1}{\frac{-2}{3}} \\ y=-1\div-\frac{2}{3} \\ y=-1\times\frac{-3}{2}=\frac{-1\times-3}{2} \\ y=\frac{3}{2} \end{gathered}[/tex]Hence, the value of y when x=-1 is 3/2
Transforming the graph of a function by reflecting over an axis
ANSWER:
(a)
(b)
STEP-BY-STEP EXPLANATION:
(a)
We must do the following transformation:
[tex]y=f(x)\rightarrow y=f(-x)[/tex]In this case, reflects f(x) about the y-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(-x,y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-4.2\mright)\rightarrow(4,2) \\ (0,4)\rightarrow(0,4) \\ (4,6)\rightarrow(-4,6) \end{gathered}[/tex]We graph and we have:
(b)
We must do the following transformation:
[tex]y=g(x)\rightarrow y=-g(x)[/tex]In this case, reflects f(x) about the x-axis. The rule that follows the above, is like this:
[tex](x,y)\rightarrow(x,-y)[/tex]We apply the rule to the points of the function and it would be:
[tex]\begin{gathered} \mleft(-7,-2\mright)\rightarrow\mleft(-7,2\mright) \\ \mleft(-4,-5\mright?)\rightarrow\mleft(-4,5\mright) \\ \mleft(4,-1\mright)\rightarrow\mleft(4,1\mright) \end{gathered}[/tex]We graph and we have:
Simplify 3√12 +8✓12 - √6 how
In order to simplify this equation, we are going to start by simplifying the radicals.
[tex]\sqrt[]{12}=\sqrt[]{2^2\cdot3}=\text{2}\sqrt[]{3}[/tex]Now we have the radicals simplified and we are going to replace them on the equation that we already have.
[tex]\begin{gathered} 3\cdot(2\sqrt[]{3})+8\cdot(2\sqrt[]{3})-\sqrt[]{6} \\ 6\sqrt[]{3}+16\sqrt[]{3}-\sqrt[]{6} \\ 22\sqrt[]{3}-\sqrt[]{6} \end{gathered}[/tex]Question 6 of 25Simplify the radical expression below.이히O A.A.v28O B.9O c.NIC3
We need to simplify the next given expression:
[tex]\sqrt{\frac{2}{9}}[/tex]We can rewrite it as:
[tex]\sqrt{\frac{2}{9}}=\frac{\sqrt{2}}{\sqrt{9}}[/tex]Solve each square root:
√2 =√2
√9 = 3
Then, the result is:
[tex]=\frac{\sqrt{2}}{3}[/tex]Hence, the correct answer is option A.
Which of the following are maximum and minimum points of the function y = 2 cos x -1?
The graph of the function is shown below
From the options provided
Option A is correct because the maximum and minimum values are satisfied
Find the exact value of sin,cos, and tan for the angle while simplifying all roots.
We can solve these values using the next triangle:
First, we need to label the sides using the angle of 30 degrees.
- The largest side is always the hypotenuse, h = 1.
- The opposite side is opposite to the angle, opp = 1/2.
- The adjacent side is between the angle of 30 degrees and the right angle,
adj = √3/2.
Now, we can solve the trigonometric expressions:
For sin:
sin θ = opposite side / hypotenuse
sin 30 = (1/2) / 1
sin 30 = 1/2
For cos:
cos θ = adjacent side / hypotenuse
cos 30 = (√3/2)/1
cos 30 =√3/2
For tan:
tan θ = opposite side / adjacent side
tan 30 =(1/2) / (√3/2)
Simplify the fractions:
tan 30 = 1/√3
JCPenney sells jeans for $49.50 that cost $38.00. What is the percent markup on cost? Check the cost.
The percent markup of the jeans is 30.2%
How to calculate the markup on cost ?
The selling price of the jeans is $49.50
The cost price is $38
Markup can be described as the difference between the selling price and the cost price of a product
The markup can be calculated by subtracting the cost price from the selling price
= 49.50 - 38
= 11.5
The percent markup can be calculated as follows
11.5/38 × 100
= 0.302 × 100
= 30.2%
Hence the percent markup is 30.2%
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You have the option of loaning money to one friend who promises to pay simple interest or to another friend who promises to pay the same APR but compound the interest. Which would you choose, and why?
I would loan my money to the one who pays the compound interest.
This is because more money would be generated from the compound interest as it is based on the principal (Amount loaned) and also the interest generated from the loan. Unlike simple interest that is only based on the principal.
Fifty people in a room are wearing clothes either in red orwhite or a combination of the two colors. Thirty are wearingonly red and 16 are wearing a combination of both red andwhite. How many are wearing clothes that have white in them?
SOLUTION
We will solve the question using a Venn diagram
Let R represents people wearing clothes that have red
Let W represents people wearing clothes that have white
We have the Venn diagram as follow
So from the Venn diagram small letter w represent those wearing clothes that have only white. So we have that
[tex]\begin{gathered} 30+16+w=50 \\ 46+w=50 \\ w=50-46 \\ w=4 \end{gathered}[/tex]So those for "only" white is 4.
But those wearing clothes that have white in them will be only white plus those wearing combination of red and white. We have
[tex]16+4=20[/tex]Hence the answer is 20
Three cities, A, B, and C, are located so that city A is due east of city B. If city C is located 35° west of north from city B and is 100 miles from city A and 70 milesfrom city B, how far is city A from city B?City Ais 20 miles due east of city B.City A is 35 miles due east of city B.City A is 42 miles due east of city B.City A is 122 miles due east of city B.
Given:
City A is due east of city B.
City C is located 35° west of north from city B.
Distance between city C and city A is 100 miles.
Distance between city C and city B is 70 miles.
The objective is to find the distance between city A and city B.
The above situation can be represented as,
Thus the total angle of ∠B = 90°+35° = 125°.
Now the measure of angle A can be calculated by law of sines.
[tex]\begin{gathered} \frac{AC}{\sin B}=\frac{BC}{\sin A} \\ \frac{100}{\sin125\degree}=\frac{70}{\sin A} \\ \sin A=70\cdot\frac{\sin 125\degree}{100} \\ \sin A=0.573 \\ A=\sin ^{-1}(0.573) \\ A\approx35\degree \end{gathered}[/tex]By the angle sum property of triangle the value of angle C can be calculated as,
[tex]\begin{gathered} \angle A+\angle B+\angle C=180\degree \\ 35\degree+125\degree+\angle C=180\degree \\ \angle C=180\degree-35\degree-125\degree \\ \angle C=20\degree \end{gathered}[/tex]Now, the distance between A and B can be calculated by,
[tex]\begin{gathered} \frac{AB}{\sin C}=\frac{BC}{\sin A} \\ \frac{AB}{\sin20\degree}=\frac{70}{\sin 35\degree} \\ AB=\sin 20\degree\cdot\frac{70}{\sin 35\degree} \\ AB\approx42\text{ miles} \end{gathered}[/tex]Thus, the distance of city A is 42 miles due east of city B.
Hence, option (C) is the correct answer.
Which of the following is equivalent to - sin ¹1?A. sin ¹111OB. - sin(-11)OC. sin(-11)D. sinReset Selection
The correct option is C.
Find the slope of the two points: (-3,-2) & (5, -8)
ter Numerical value ONLY. NO Decimals
*
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-8}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{(-3)}}} \implies \cfrac{-8 +2}{5 +3} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{ 3 }{ 4 }[/tex]
When a stone is dropped in a pond ripples are formed and travel in concentric circles away from where the stone was dropped. The relationship between the time and area if the circles was analyzed and is shown in the computer output.
What is the equation of the least/squares regression line?
When a stone is dropped in a body of water, ripples are created and move outward in concentric rings. The least-squares regression line has the equation Area = 0.010 + 3.141 (Time2).
The least squares regression equation is the equation y=1x+0 that specifies the least squares regression line.
the least squares regression line's y=1x+0 equation.
What is relationship between time and distance?Time (t = d/v) or, alternatively, time = speed/distance (v = d/t).
Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words. An annulus is the space between two concentric circles with dissimilar radii.
Concentric circles are two or more circles with the same center but various radii. Congruent circles are any two or more circles that have the same radius but different centers.
Concentric circles are those that share a common center but have differing radii. It is described as two or more circles with the same center, in other words.
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Find f such that the given conditions are satisfied. f(x)=x2-3x + 12, f(0) = 9 O f(x) = 1x2 - 4x² + 12x +9 O O f(x) - x-x2 + 12x + 1 f(x) = 3x3-4x2 + 12x + 1 O f(x) = 3x - x? + 12x + 9
To find f(x) we will do an integration
[tex]\begin{gathered} f^{\prime}(x)=x^2-3x+12\text{ } \\ f(x)=\int (x^2-3x+12) \end{gathered}[/tex][tex]\int (x^2-3x+12)=\frac{x^3}{3}-\frac{3x^2}{2}+12x+c[/tex]To find c substitute x by 0 and y by 9 because f(0) = 9
[tex]\begin{gathered} f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+c \\ f(0)=\frac{1}{3}(0)^3-\frac{3}{2}(0)^2+12(0)+c=9 \\ c=9 \end{gathered}[/tex]The function f(x) is
[tex]f(x)=\frac{1}{3}x^3-\frac{3}{2}x^2+12x+9[/tex]Answer D
find the explict formula for 15, 12, 9, 6
Given:
15, 12, 9, 6
To write the explicit formula, use the form:
[tex]a_n=a_1+d(n-1)[/tex]Where
a1 = first term = 15
d = common difference = 12 - 15 = -3
n = number of terms
Therefore, the explicit formula is:
[tex]\begin{gathered} a_n=15-3(n-1) \\ \\ a_n=15-3n+3 \\ \\ a_n=18-3n \end{gathered}[/tex]ANSWER:
[tex]a_n=18-3n[/tex]What is the total population of the four cities shown in the table? Express your answer in scientific notation and in standard form.
Scientific notation is a way of writing large or small numbers that have many digits in a simplified form. The index of the base 10 exponents indicates the number of digits there are after the decimal dot.
The table shows the population of 4 cities of Texas, Houston, San Antonio, El Paso, and Corpus Christi.
To determine the total population of all cities you have to add them together, the first step is to express each given population in standard form:
Houston:
[tex]2.3\cdot10^6[/tex]This notation indicates that there are 6 digits after the decimal dot, the first one is 3 and the other five digits are zero. The positive index indicates that this number is greater than 1, so to write the number in the standard form you have to erase the decimal dot:
[tex]2.3\cdot10^6=2300000[/tex]San Antonio:
[tex]1.5\cdot10^6[/tex]The notation indicates that there are 6 digits after the decimal point, the first one is 5 and the other five digits are zero. The positive exponent indicates that this number is greater than 1, so you have to erase the decimal dot:
[tex]1.5\cdot10^6=1500000[/tex]El Paso:
This population is already given in the standard form
[tex]680000[/tex]Corpus Christi:
[tex]3.2\cdot10^5[/tex]This notation indicates that there are 5 digits after the decimal dot, the first one is 5 and the next four are zero. The exponent is positive, so as mentioned before, this number is greater than one, and to write it in the standard form you have to erase the decimal dot:
[tex]3.2\cdot10^5=320000[/tex]Now that all values are expressed in the standard form you can add them:
[tex]2300000+1500000+680000+320000=4800000[/tex]In the standard form, the total population of the four cities is 4,800,000 people
To express this value using scientific notation you have to write the decimal dot after the first digit and then count the number of digits after the decimal dot.
When you use scientific notation you have to write only the digits that are different than zero.
There are 6 digits after the decimal dot, so the exponent of the base 10 number will be 6, and the result expressed in scientific notation is:
[tex]4.8\cdot10^6\text{people}[/tex]The value of a collectible coin can be represented by the equation+9 74 where x represents the number ofyears that Consuello has owned the coin and y represents the total value, in dollars, of the coin. What was the valueof the coin when Consuello originally purchased it?
Given:
The value of a collectible coin can be represented by the equation
[tex]y=2x+9.74[/tex]Required:
We need to find the original purchased value
Explanation:
To find the orginal value we just put
[tex]x=0[/tex][tex]\begin{gathered} y=2*0+9.74 \\ y=9.74 \end{gathered}[/tex]Final answer:
The original value is $9.74
A. Find the zeros in state the multiplicity of each zeroB. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F a small as possible.C. Use both the equation in part B and graph to find the Y intercept
Given the graph of a polynomial function:
We will find the following:
A. Find the zeros and state the multiplicity of each zero
The zeros of the function are the points of the intercept between the x-axis and the graph of the function
as shown, there are 3 points of intersection (3 zeros)
x = -1, multiplicity = 3
x = 1, multiplicity = 2
x = 2, multiplicity = 1
B. Write an equation expressed as the product of factors, of a polynomial function for the graph Using A leading coefficient of 1 or -1 and make the degree of F as small as possible.
Form A, the factors of the function will be:
(x+1), (x-1), and (x-2)
The equation of the function will be:
[tex]f(x)=(x+1)^3(x-1)^2(x-2)[/tex]C. Use both the equation in part B and graph to find the Y-intercept
The y-intercept is the value of (y) when (x = 0)
So, substitute with x = 0
So,
[tex]y=(0+1)^3\cdot(0-1)^2\cdot(0-2)=-2[/tex]So, the answer will be: y-intercept = -2
2. Simba pays $15 per month
for the phone he bought. His cell phone plan costs $49
per month and includes 15GB of
data. He also pays $5 for each additional 1GB
of data he uses over the 15GB limit. Using x to represent the GB of data
he uses over 15 GB, write an equation to represent Simba's monthly cell
phone bill and determine how much he will pay if one month he uses
23GB of data.
The equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
What is an linear equation is one variable?
An linear equation is an equation of degree one. the highest exponent is 1 and one variable is number of variable is 1 in the equation
We are given that, Simba pays $15 per month for the phone he bought. His cell phone plan costs $49 per month.
He pay additional $5 for 1 gb data after 15gb data limit got over
Let the number of gb's used be x
Hence the total bill will be given by the equation
B= 15+49+5x
B= 64+5x
If he uses 23 gb of data the first 15 Gb are covered in his phone plan
And he has to pay $5 for each gb
The total cost is 8*5=$40
Hence the total phone bill is B=64+40
B=$104
Hence the equation can be given as B=64+5x
And the cost of phone bill if he uses 23GB will $104
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Can you please help me with 44Please use all 3 forms such as :up/down, as_,_ and limits
Given:
[tex]h(x)=(x-1)^3(x+3)^2[/tex]The x-intercepts of the given polynomial are
[tex]x-\text{intercepts }=1\text{ (multiplicity 3) and -3 (multiplicity 2)}[/tex]Substitute x=0 in h(x) to find y-intercepts.
[tex]\text{ y-intercepts =}(-1)^3(3)^2=-9[/tex][tex]\lim _{x\to-\infty}h(x)=\lim _{x\to-\infty}(x-1)^3(x+3)^2=-\infty[/tex][tex]as\text{ x}\rightarrow-\infty,\text{ h(x)}\rightarrow-\infty[/tex][tex]\lim _{x\to\infty}h(x)=\lim _{x\to\infty}(x-1)^3(x+3)^2=\infty[/tex][tex]as\text{ x}\rightarrow\infty,\text{ h(x)}\rightarrow\infty[/tex]The graph of the given polynomial h(x) is
The degree of the polynomial is 6=even and the leading coefficient=1=positive.
Both ends of the graph point up.
End behaviour is
up/up.
I already wrote the answer I just need you to work it out for me please and thank you
Answer:
[tex]A=470\frac{1}{4}ft^2[/tex]Detailed Explanation: The area of the figure provided is the sum of two areas, a rectangle, and a triangle:
The total area is calculated next, and the necessary steps are shown as follows
[tex]\begin{gathered} A=A_1+A_2 \\ A_1=\frac{1}{2}(b\cdot h)=\frac{1}{2}\cdot\lbrack(25ft-22.5ft)\times19.8ft\rbrack \\ A_1=\frac{1}{2}\cdot\lbrack2.5ft\times19.8ft\rbrack=\frac{49.5ft^2}{2}=24.75ft^2 \\ A_1=24.75ft^2 \\ A_2=w\cdot h=22.5ft\cdot19.8ft=445.5ft^2 \\ A_2=445.5ft^2 \\ \therefore\Rightarrow \\ A=A_1+A_2=24.75ft^2+445.5ft^2 \\ A=470.25ft^2 \\ A=470\frac{1}{4}ft^2 \end{gathered}[/tex]used to figure for exercises two through nine period determine whether each pair of lines are parallel or perpendicular. right yes or no
2. q and v are parallel. YES
3. r and s are parallel. NO
4. r and t are parallel. NO
5. s and u are parallel. YES
6. q and s are perpendicular. NO
7. q and v are perpendicular. NO
8. r and s are perpendicular. YES
9. t and v are perpendicular. YES
Todd forgot the first two numbers of his locker combination.The number can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly
Todd forgot the first two numbers of his locker combination. The number can be any number 1 through 6. What is the probability that he will guess the first number correctly and the second number incorrectly?
______________________________________________
Please, give me some minutes to take over your question
________________________________________
The probability that he will guess the first number correctly and the second number incorrectly
1/6 (the first number correctly)
5/6 (the second number incorrectly)
1/6 * 5/6 = 5/36
_________________________________________
Answer
The probability that he will guess the first number correctly and the second number incorrectly is 5/36 = 0.1389 = 13. 89%.
Joyce paid $154.00 for an item at the store that was 30 percent off the original price. What was the original price?
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a shelf is in the shape of a triangle. find the angle of the triangle if the measure of the angles are in the ratio of x:x:4x.x=4x=
ANSWER
30°, 30° and 120°
EXPLANATION
We want to find the measures of the angles of the triangle if the ratio of the angles is x : x : 4x
In other words, the ratio is 1 : 1 : 4
The total angle in a triangle is 180°.
Therefore, we have to find the value of x. To do this, we first find the total ratio:
[tex]\begin{gathered} 1+1+4 \\ =6 \end{gathered}[/tex]Now, find x by apply ratios. x is equal to 1/6 of the total angle of the triangle:
[tex]\begin{gathered} x=\frac{1}{6}\cdot180 \\ x=30\degree \end{gathered}[/tex]Now, find 4x:
[tex]\begin{gathered} 4\cdot x=4\cdot30 \\ =120\degree \end{gathered}[/tex]Therefore, the ratio of angles is:
[tex]30\degree\colon30\degree\colon120\degree[/tex]In other words, the angles are 30°, 30° and 120°.
If an investment grew to $13,500 in 2 years and the interest amount earned was $1,150, calculate the nominal interest rate compounded quarterly.
The nominal interest rate compounded quarterly is 1.33%.
Given,
If an investment grew to $13,500 in 2 years.
and, the interest amount earned was $1,150.
To find the nominal interest rate compounded quarterly.
What is nominal interest rate?
The interest rate before inflation is referred to as the nominal interest rate.
Nominal can also refer to the advertised or stated interest rate on a loan, excluding any fees or interest compounding.
Now, According to the question:
Here given ,
P = $13500
i = ?
A = $1150
t = 2 yrs
n = 4 x 2 = 8
Formula of compound interest ,
A = P( 1 + I )ⁿ
$1150 = $13500 ( 1 + i ) ⁸
$1150 / $13500 = (1 + i)⁸
0.0851 = (1+ i) ⁸
1 +i = 8√.0851
1 + i = 2.33
i = 2.33 -1
i = 1.33 %
Hence, The nominal interest rate compounded quarterly is 1.33%.
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