Answer:
1/60
Step-by-step explanation:
For each cake, there is a 1/20 chance to find the gold ring since it is in one of the 20 slices. The probability for each cake is independent of each other, so we multiply
1/20 x 1/20 x 1/20
=1/60
Activity
After an intensive search, Philip has narrowed his choices to four houses. Now he wants to buy the one that fits his budget. He has saved $40,000
for the down payment. Use the fixed-rate calculator to find the monthly payment for each house.
House Purchase Price Monthly Payment Affordability
A
$250,000
B
$200,000
C
$195,000
D
$180,000
Answer:
A
Step-by-step explanation:
A
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?
Let c stand for the number of cousins Sawyer has.
Which bar model represents the problem?
Hazel C
Sawyer с с
Sawyer 8
8
Hazel 8 8
Sawyer C
Hazel
с с
8
Hazel 8
Sawyer 8 8
с
Sawyer has 4 cousins given that Hazel has 2 times as many cousins as Sawyer.
How many cousins does Sawyer have?From the question, we have the following parameters that can be used in our computation:
Hazel has 8 cousins. Hazel has 2 times as many cousins as Sawyer.Using the above as a guide, we have the following:
Hazel = 2 * Sawyer
Let c stand for the number of cousins Sawyer has.
So, we have
Hazel = 2 * c
Substitute the known values in the above equation, so, we have the following representation
2 * c = 8
Divide by 2
c = 4
Hence, the number of cousins Sawyer has is 5
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The football players had to sell DEVIL FOOTBALL t-shirts to raise money for their next uniforms.They charged $14 for short sleeve shirts and $17 for long sleeve shirts. At the end of the fundraiser, they had sold 24 shirts and had made $378. How many of each type of shirt did they sell?
Use
S as the number of short sleeve shirts and
L as the number of long sleeve shirts.
PLS HELP
Answer:
Let's set up a system of equations to solve for S and L:
S + L = 24 (they sold a total of 24 shirts)
14S + 17L = 378 (the total amount made from selling the shirts was $378)
We can solve for one variable in the first equation and substitute it into the second equation:
S = 24 - L
14(24 - L) + 17L = 378
336 - 14L + 17L = 378
3L = 42
L = 14
So they sold 14 long sleeve shirts. We can substitute this value back into the first equation to solve for S:
S + 14 = 24
S = 10
Therefore, they sold 10 short sleeve shirts and 14 long sleeve shirts.
Study this table.
X
-3
-2
0
4
y
-2
0
4
12
Which best describes the function represented by the data in the table?
O linear with a common ratio of 2
Olinear with a common first difference of 2
O quadratic with a common ratio of 2
O quadratic with a common first difference of 2
The Function is linear with a common first difference of 2.
We have,
x y
-3 -2
-2 0
0 4
4 12
For the first set of points
m=(0-(-2))/(-2--3)
m = (0+2)/(-2+3)
m= 2/1 = 2
For the second set of points
m = (4-0)/(0-(-2))
m = 4/(0+2)
m = 4/2 = 2
For the third set of points
m = (12-4)/(4-0)
m = 8/4
m = 2
Thus, the function is linear with a common first difference of 2.
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I'm very confused on this question.
The value of angle x is determined as 107⁰.
What is the x?
The value of angle x is calculated by applying principle of intersecting chord theorem.
The intersecting chord theorem states that half of the difference between the arc of two intersecting chords is equal to the tangent angle.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠MNP = ¹/₂( arc MLP - arc MP )
x = ¹/₂ [(360 -73) - (73)]
x = ¹/₂ (287 - 73 )
x = ¹/₂ (214)
x = 107⁰
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I need help I can't ask my teacher about this because I am sick so I need help learning to solve this.
Answer: x = 20
Step-by-step explanation:
[tex]\frac{3}{5} x - \frac{1}{4} x = 7\\12x-5x=140\\7x=140\\x=20[/tex]
Find the value of the trig function indicated.
3)
tan 0
13
12
0pls help
The value of the identities are;
1. tan θ = 5/12
2. cot θ = √7/3
How to determine the identitiesTo determine the value of the identities, we need to take note of the different identities;
sinetangentcotangentsecantcosecantcosineFrom the information given, we need to take note that;
tan θ = opposite/adjacent
cot θ = inverse of tangent identity
cot θ = adjacent/opposite
then,
1. tan θ =
Opposite = 5
Adjacent = 12
tan θ = 5/12
2. cot θ = 4√7/12 = √7/3
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Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
The equations to solve the length of the room is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
c) ( y + 25 ) ( y - 30 ) = 0
Given data ,
Let the area of a rectangular room is 750 square feet.
Let the width of the room is 5 feet less than the length of the room
So , on simplifying , we get
w = l - 5
Area of rectangle = length x width
And , A = l x w
A = l ( l - 5 )
750 = y ( y - 5 )
Therefore , the equation is
a) y² - 5y = 750
b) 750 - y ( y - 5 ) = 0
On simplifying the quadratic equation , we get
c) ( y + 25 ) ( y - 30 ) = 0
Hence , the length of the rectangular room is solved
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The complete question is attached below :
Which equations can be used to solve for y, the length of the room? Select three options.
a) y(y + 5) = 750
b) y² – 5y = 750
c) 750 – y(y – 5) = 0
d) y(y – 5) + 750 = 0
e) (y + 25)(y – 30) = 0
The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 5x + 12. Which of the following shows the area of the rectangle in terms of x? (L ⋅ W)(x) = 24x3 − 30x + 72 (L ⋅ W)(x) = 24x3 − 30x2 + 72x (L + W)(x) = 4x2 + x + 12 (L + W)(x) = 2x2 + x + 12
The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.
Given a rectangle.
Length of the rectangle, L(x) = 6x
Width of the rectangle, W(x) = 4x² − 5x + 12
The formula to find the area of the rectangle is,
Area = Length × Width
Substituting the given length and width,
Area of the rectangle = L(x) . W(x)
= (L . W)(x)
= (6x) (4x² − 5x + 12)
= 24x³ - 30x² + 72x
Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.
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Answer:
(L . W)(x) = 24x³ - 30x² + 72x.
Step-by-step explanation:
How do I find the probability?
Answer:
To find the probability of an event occurring, you need to divide the number of ways the event can occur by the total number of possible outcomes. The probability is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
For example, if you want to find the probability of rolling a 3 on a standard six-sided die, there is only one way to roll a 3 and six possible outcomes (1, 2, 3, 4, 5, 6). So, the probability of rolling a 3 is 1/6 or approximately 0.17.
Keep in mind that the probability of an event occurring is not a guarantee that the event will happen. It only indicates the likelihood of the event happening based on the available information.
Given the figure below, find the values of x and z.
120°
(8x
+ 96).
Answer:
x = 3; z = 60°
Step-by-step explanation:
x:
The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.
Thus, we can solve for x by setting the two angles equal to each other and isolate x:
[tex]120=8x+96\\24=8x\\3=x[/tex]
We can check our answer by plugging in 3 for x and ensure that we get 120:
[tex]120=8(3)+96\\120=24+96\\120=120[/tex]
z:
We see that a horizontal straight line separates the angle measuring 120° and z°. Straight lines create straight angles, which equal 180°.
Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180. Then, we must isolate z:
[tex]120+z=180\\z=60[/tex]
A scientist studying babies born prematurely would like to obtain an estimate for the mean birth weight, μ,
of babies born during the 24th week of the gestation period. She plans to select a random sample of birth
weights of such babies and use the mean of the sample to estimate μ. Assuming that the population of birth
weights of babies born during the 24th week has a standard deviation of 2.8 pounds, what is the minimum
sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number
(and make sure that it is the minimum whole number that satisfies the requirements).
The sample size needed for the scientist to be 95% confident that her estimate is within 0.4 pounds of μ is given as follows:
n = 189 babies.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is defined as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters are given as follows:
[tex]M = 0.4 \sigma = 2.8[/tex]
Then the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
0.4sqrt(n) = 1.96 x 2.8
sqrt(n) = (1.96 x 2.8/0.4)
n = (1.96 x 2.8/0.4)²
n = 189 babies. (rounded up).
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Harold ran 3 miles in 24 minutes. How long would it take him to run 4 miles?
Answer:32 minutes
Step-by-step explanation:
He is running at a rate of 1 mile every 8 minutes. 3 miles in 24 minutes and 4 miles in 32 minutes
You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground. How steep was the ramp? We are missing a side or and angle? Regular or Inverse Trig?
The steepness of the ramp is approximately 56 feet.
How to find the steepness of the ramp?You skateboards down a ramp. The ramp starts at a height of 10 feet and runs 55 feet along the ground.
Therefore, let's find how steeped the ramp is.
Hence, using Pythagoras's theorem,
c² = a² + b²
where
a and b are the other legsc is the hypotenuse sideTherefore,
55² + 10² = c²
c² = 3025 + 100
c² = 3125
square root both sides of the equation
c = √3125
c = 55.9016994375
c = 56 feet
Therefore,
steepness of the ramp = 56 feet
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There are 140 in the seventh grade, and 10% are in the Environmental Club. How many students are in the Environmental Club?
Trigonometry question. Please help me
The apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
What is a rectangular base pyramidIn a rectangular base pyramid, the base is a rectangle and the apex (or top point) is directly above the center of the rectangle.
The apex angle is the angle formed by the edges of the pyramid at the apex. In a rectangular base pyramid, the apex angle depends on the dimensions of the rectangle base and the height of the pyramid. It can be calculated using trigonometric functions.
The apex angles bec and aed formed by the opposite width of the rectangle base are equal.
In conclusion, the apex angle |‹aed| of the rectangular base pyramid is equal to 14°.
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Find the volume of the sphere. Give the answer in terms of Pi and rounded to the nearest cubic foot. the radius is 5 ft.
The volume of the sphere with a radius of 5 feet to the nearest cubic foot is 166.67π feet³.
Given a sphere.
Radius of the sphere = 5 feet
The formula to find the volume of the sphere is,
Volume of the sphere = 4/3 πr³,
where r is the radius of the sphere.
Substituting the given radius,
Volume of the sphere = 4/3 × π × (5)³
= 4/3 × π × 125
= 166.67π
Hence the volume of the sphere is 166.67π feet³.
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peaceful travel agency offers vacation packages each vacation packages includes a city, and a airline.The agency has 6 cities, and 2 airlines to choose from.how many different vacation packages do they offer
Solving the given word problem systematically, Serene Travel Organization offers 12 diverse vacation packages.
How to Solve the Problem?To calculate the overall number of distinctive excursion packages that Quiet Travel Organization offers, we ought to duplicate the number of cities by the number of carriers:
Add up to number of get-away bundles = number of cities x number of airlines
Since the agency has 6 cities and 2 aircrafts to select from, we are able substitute those values within the over equation:
Add up to number of get-away bundles = 6 x 2 = 12
In this manner, Serene Travel Organization offers 12 diverse get-away bundles.
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Please help! I will mark brainiest! I do not understand the parenthesis being added.
Answer:
<4√97,-9√97>
Step-by-step explanation:
First, we need to find the values of A-C and B-D:
A-C = < 3, 6 > - < 7, -3 > = < -4, 9 >
B-D = < 4, -7 > - < 0, 2 > = < 4, -9 >
Next, we need to find the magnitude of A-C, which is denoted by |A-C| and is equal to the square root of the sum of the squares of its components:
|A-C| = √((-4)^2 + 9^2) =√(97)
Now we can substitute all the values into the expression |A-C|(B-D) and evaluate:
|A-C|(B-D) = √(97) * < 4, -9 >
= < 4√(97), -9√(97) >
So the final answer is < 4√(97), -9√(97) >.
1. What would you get in your numerator when you multiply your terms together in the first step in simplifying?
2. What two terms would you combine in the numerator to simplify?
The step in simplifying the expression 3x/(x+5) - 3/(x+6) would result in 3x² + 18x - 3x - 15. The two terms that can be combined in the numerator to simplify are -3x and 18x. So, the correct answer is A), B) and D).
When multiplying the terms together in the first step of simplifying, we would get
3x - 3(x + 5)/(x + 6)
Simplifying this expression would lead to
3x² + 15x - 3x - 15/(x + 6)
Therefore, the answer is option (b): 3x² + 18x - 3x - 15
To simplify the numerator, we need to combine like terms.
To simplify the numerator, we need to combine like terms. The given expression is
3x² + 18x - 3x - 15
Here, the terms 18x and -3x have the same variable (x) and the same power (first power), but they have opposite signs. Therefore, we can combine them by subtracting the smaller value from the larger value. In this case, we have
18x - 3x = 15x
So, the expression simplifies to
3x² + 15x - 15
Therefore, the two terms that we would combine in the numerator to simplify are -3x and 18x, which give us 15x. So, the correct option is B) and D).
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Parallelogram EFGH, E(-1,5), F(2,8), G(4,4), and H(1,1). Find the perimeter and area of the parallelogram. Round to the tenths place
The requried, perimeter and area of the parallelogram are 18.4 centimeters and 18 square centimeters respectively.
To find the perimeter of parallelogram EFGH, we need to find the length of all four sides and add them up. The distance formula is used to find the length of each side:
EF = √((2-(-1))² + (8-5)²) = √(3² + 3²) = √(18)
FG =√(20)
GH = √(18)
HE = √(20)
Therefore, the perimeter is:
Perimeter = EF + FG + GH + HE = √(18) + √(20) + √(18) + √(20) ≈ 18.4
Similarly,
The area of the parallelogram is given as,
= 18 square centimeters
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50 points. Out of 120 seventh and eighth grade CAVA students there were 30 students that chose Music as their elechive course and the rest chose World Language. There were a total of 60 eighth grade students and 40 of them chose
World Language as their elective.
Use this information to complete the two-way table.
Enter your answer by filling in the boxes to complete the table (6 pts)
Answer:
Based on the informtaion provided, the two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
In this situation there were total 120 seventh and eighth grade CAVA students. And there were a total of 60 eighth grade students.
Total number of students = 120
This means that the number of students in 7th grade : 120- 60 = 60
Out of 120 seventh and eighth grade students, 30 students chose Music as their elechive course.
This means that remaining 120 - 30 = 90 students chose World Language as their elechive course.
Here, 40 eighth grade students chose World Language as their elective.
This means that out of total 90 students 90 - 40 = 50 students of 7th Grade chose World Language as their elective.
Now consider the 8th grade students,
Out of 60 students 40 chose World Language.
So, 60 - 40 = 20 must chose Music as their elective.
Now consider the 7th grade students,
Out of 60 students 50 chose World Language.
So, 60 - 50 = 10 students must chose Music as their elective.
Hence the required two-way table would be,
Music World Language Totals
8th Grade 20 40 60
7th Grade 10 50 60
Total 30 90 120
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Bacteria was put in a petri dish with antibacterial soap. Determine the logarithmic regression of the bacteria. Use either a
calculator or spreadsheet program.
Using the given data, a logarithmic regression equation of the form Bacteria = 447.91 * ln(12) - 1733.1 was found to model the relationship between time and bacteria population. So, the population of bacteria is about 44.1 at 12 hours.
Based on the provided data, we can use a logarithmic regression to model the relationship between time and bacteria population. Here's how to do it using Microsoft Excel
Enter the data into two columns one for time and one for bacteria population. Create a scatter plot of the data. Right-click on one of the data points in the plot and select "Add Trendline."
In the Trendline options, choose "Logarithmic" as the type of trendline. Check the box for "Display Equation on Chart" to show the equation for the trendline.
The resulting equation is
Bacteria = 447.91 * ln(Time) - 1733.1
This equation represents a logarithmic regression of the bacteria population over time.
To use this equation to predict the bacteria population at a specific time, substitute the time value into the equation and solve for the bacteria population. For example, if we want to predict the bacteria population at 12 hours, we can substitute 12 into the equation
Bacteria = 447.91 * ln(12) - 1733.1
Bacteria ≈ 44.1
So we would predict a bacteria population of about 44.1 at 12 hours.
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Julia volunteers at a zoo. She records the number of people in each group of visitors in one day.
Based on Julia's data, if a larger zoo has 600 groups of visitors in a day, how many of them would you expect to be groups of 5 or more?
People in Group 1 2 3 4 5 6 7 8
Frequency
9 52 27 38 16 6 5 7
about
groups
We would expect 138 groups in the larger zoo to have 5 or more people based on the relative frequency of group sizes in Julia's data.
To determine how many groups of 5 or more people we would expect to see in a larger zoo with 600 groups of visitors in a day, we need to use the relative frequency of each group size in Julia's data.
To calculate the relative frequency of each group size, we need to divide the frequency of each group size by the total number of groups:
Group Size Frequency Relative Frequency
1 9 9/150 = 0.06
2 52 52/150 = 0.35
3 27 27/150 = 0.18
4 38 38/150 = 0.25
5 16 16/150 = 0.11
6 6 6/150 = 0.04
7 5 5/150 = 0.03
8 7 7/150 = 0.05
We can see that the relative frequency of groups with 5 or more people is 0.11 + 0.04 + 0.03 + 0.05 = 0.23. This means that we would expect 23% of the 600 groups in the larger zoo to have 5 or more people.
To calculate the actual number of groups with 5 or more people, we multiply the total number of groups by the relative frequency:
Number of groups with 5 or more people = 600 x 0.23 = 138
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What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
The slope of the line that contains the points (-3, -1) and (3, -10) is -3/2.
Given two points.
We have to find the slope of the line.
Slope of a line passing through (x, y) and (x', y') is,
Slope = (y' - y) / Ix' - x)
Here two points are,
(-3, -1) and (3, -10)
Slope = (-10 - -1) / (3 - -3)
= -9 / 6
= -3/2
Hence the slope of the line is -3/2.
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Use substitution. What is the solution to the system of equations? Use the drop-down menus to explain your answer. y = 12 x + 2 2y = x + 4 The system of equations has Choose... . The two equations represent Choose... .
Find the x intercept of the line 1x -2y =23
Answer: x=23
Step-by-step explanation:
Answer: 23
Step-by-step explanation:
When you have a value on the x-axis, your y=0
plug in y=0 to find your x-intercept
1x-2(0)=23
1x=23
x=23
Simplify 6/15 x 55/10
2.2 in decimal form.
eleven fifths
Qd=50-4Px+0.5I+10Py-2Pz
Answer:
The equation Qd = 50 - 4Px + 0.5I + 10Py - 2Pz represents the demand function for a certain good X, where Qd is the quantity demanded, Px is the price of X, I is the consumer's income, Py is the price of another good Y, and Pz is the price of another good Z.
To solve for the equilibrium price and quantity, we need to find the point where the quantity demanded equals the quantity supplied. However, without information on the supply function or market conditions, we cannot find the equilibrium price and quantity.
We can use the demand equation to determine the effect of changes in the independent variables on the quantity demanded for the good. For example, an increase in the price of X (Px) would lead to a decrease in the quantity demanded (Qd), while an increase in the price of Y (Py) or a decrease in the price of Z (Pz) would lead to an increase in the quantity demanded (Qd). An increase in income (I) would also lead to an increase in the quantity demanded (Qd).
Note that it is important to understand the context and assumptions underlying the demand function in order to make accurate economic predictions or decisions based on it.
Step-by-step explanation:
cost minimal of logistic form factory to
warehouse mathematical problem
Answer:
To calculate the minimal cost of logistics from a factory to a warehouse, you would need to consider various factors such as the distance between the factory and the warehouse, the mode of transportation, the weight and volume of the goods being transported, the number of trips required, and any applicable taxes or fees.
To formulate this as a mathematical problem, you could use linear programming, which is a method for optimizing a linear objective function subject to linear equality and inequality constraints.
Let's say we have a factory that produces goods and a warehouse that stores those goods. We want to transport the goods from the factory to the warehouse in a cost-effective way. Let's assume that there are three transportation options available: truck, train, and ship. Each option has a different cost per unit of distance traveled, and a different maximum weight and volume capacity.
Let x1, x2, and x3 be the number of units transported by truck, train, and ship, respectively. Then, the objective function we want to minimize would be:
C = 10x1 + 8x2 + 6x3
where C is the total cost of transportation.
Next, we would need to set up constraints based on the transportation options and the available resources. For example:
Truck capacity: 3x1 <= 15000 (maximum weight capacity of 15000 units for the truck)
Train capacity: 5x2 + 2x1 <= 40000 (maximum weight capacity of 40000 units for the train)
Ship capacity: 2x3 + 3x1 <= 30000 (maximum weight capacity of 30000 units for the ship)
Distance constraint: 2x1 + 3x2 + 5x3 <= 10000 (maximum distance of 10000 units for all transportation modes combined)
The above constraints limit the total weight transported, the capacity of each mode of transport, and the total distance that the goods are transported.
Finally, we would need to add non-negative constraints to ensure that all variables are greater than or equal to zero:
x1 >= 0, x2 >= 0, x3 >= 0
Once we have set up this linear programming problem, we can use optimization techniques to solve for the values of x1, x2, and x3 that minimize the cost of transportation while satisfying all of the constraints.
Step-by-step explanation:
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