On April 1, a patent with an estimated useful economic life of 12 years was acquired for $115,200. In addition, on December 31, it was estimated that goodwill of $36,500 was impaired.

Answer:

this is the answer:

Step-by-step explanation:

Hope it helps:

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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Kareem uses 300 milliliters of Solution B.

Let's assume Kareem uses "x" milliliters of Solution B.

Since Kareem uses twice as much Solution A as Solution B, he would use 2x milliliters of Solution A.

Solution A contains 10% alcohol, so the amount of alcohol from Solution A is (2x)(0.10) = 0.2x milliliters.

Solution B contains 15% alcohol, so the amount of alcohol from Solution B is (x)(0.15) = 0.15x milliliters.

The resulting mixture has 105 milliliters of pure alcohol, which is the sum of the alcohol from Solution A and Solution B:

0.2x + 0.15x = 105

Combining like terms:

0.35x = 105

Dividing both sides by 0.35:

x = 105 / 0.35

x = 300

Therefore, Kareem uses 300 milliliters of Solution B.

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Height is considered to be on an interval scale.

In the same town, the height of men can be measured using a ratio scale of measurement. A ratio scale is the most informative and precise measurement scale as it possesses all the properties of the other measurement scales: nominal, ordinal, and interval scales.

With a ratio scale, height measurements have a meaningful zero point, which represents the absence of height. Additionally, the scale has equal intervals, allowing for the comparison of the differences in height between individuals accurately.

To measure the height of men in the town, a standard measuring instrument such as a stadiometer or a measuring tape would be used. These tools provide precise measurements in units like centimeters or inches.

By collecting height data from a representative sample of men in the town and calculating various statistical measures such as the mean, median, and standard deviation, it becomes possible to understand the distribution and characteristics of the heights.

It is important to note that height can vary among individuals due to various factors such as genetics, nutrition, and overall health. Therefore, the collected data may exhibit a range of heights, with some individuals being shorter or taller than the average height for men in the town.

Overall, using a ratio scale to measure the height of men in the town provides a comprehensive and precise understanding of their height distribution, enabling researchers and policymakers to analyze and interpret the data effectively.

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Answer:

b. 12 cm

Step-by-step explanation:

The perimeter of any shape is the sum of the lengths of its sides.

We can call the three sides of a triangle a, b, and c.  Thus, the perimeter, P is given by the formula:

P = a + b + c

Thus, we can plug in 3 for a, 4 for b, and 5 for c to find P, the perimeter of the triangle in centimeters:

P = 3 + 4 + 5

P = 7 + 5

P = 12

Thus, the perimeter is 12 cm (answer b.).

The total number of votes casted by the residents of the city is 6,633.

Given that,  the ratio of yes votes to no votes was 5 to 6.

This means that for every 5 yes votes, there were 6 no votes.

Also given that, there were 3618 no votes.

Since the ratio of yes votes to no votes is 5 to 6, we can set up the following proportion:

5/6 = x/3618

Where x is the number of yes votes

Solving for x:

6x = 5 × 3618

6x = 18090

Divide both sides by 6

x = 18090/6

x = 3015

Therefore, the total number of votes will be:

Number of yes votes + number of no votes

= 3015 + 3618

= 6,633

Therefore, the total number of votes is 6,633.

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Answer:

Step-by-step explanation:

Since there are an even number of values in the data set (20), the median is the average of the two middle values. In this case, the two middle values are 14 and 18. The median is therefore (14 + 18) / 2 = 16.

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

The present value of the annuity is approximately `7032.08. The correct answer is option (d) None of these.

To find the present value of an annuity, we can use the formula:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where PV is the present value, PMT is the periodic payment, r is the interest rate per period, and n is the number of periods.

In this case, the periodic payment is `200, the interest rate is 5% (or 0.05) converted quarterly, and the number of periods is 10 years, which equals 40 quarters.

Plugging in these values into the formula, we get:

PV = 200 * (1 - (1 + 0.05)^(-40)) / 0.05

Simplifying the equation, we find:

PV ≈ 200 * (1 - 0.12198) / 0.05

PV ≈ 200 * 0.87802 / 0.05

PV ≈ 35160.4 / 0.05

PV ≈ 7032.08

Therefore, the present value of the annuity is approximately `7032.08.

None of the provided answer options (a), (b), or (c) match this result. The correct answer is (d) None of these.

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The solution of the system of equations is z = -12

The system of equations are:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From equation  (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From equation (2):

2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From equation (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

We then will compare equation (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

and  xy = x + y in equation 1

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8) we now use this in equation 4

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5    ..........................................(9)

We use this in equation  (8)

x = 5(12/5)/7

x= 12/7 .......................(10)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

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Answer:

θ =  60 degrees

If needed in radians:

θ = π/3

Step-by-step explanation:

2cos(θ) = 1

We are solving for theta.

We can divide 2 on both sides.

2cos(θ) = 1

/2             /2

cos(θ) = 1/2

Now we can use Inverse of cosine to isolate theta.

θ [tex]= cos^-^1(1/2)[/tex]

θ =  60 degrees

If needed in radians:

θ = π/3

One bagel costs 485 cents, equivalent to $4.85.

Let t be the price of a piece of toast in cents

Let m be the price of a muffin in cents

Let b be the price of a bagel in cents.

We will form equations to solve:

Multiply Equa 1 by 2:

4t + 2b = 630 --------- (Equ 4)

Subtract Equ 4 from Equ 3:

(t + 2b + 3m) - (4t + 2b) = 725 - 630

-t + 3m = 95

3m - t = 95 --------- (Equ 5)

Multiply Equ 2 by 2:

2b + 4m = 970 ------ (Equ 6)

Add Equ 5 and Equ 6:

(3m - t) + (2b + 4m) = 95 + 970

3m + 2b + 4m - t = 1065

6m + 2b - t = 1065 (------- Equ 7)

Now we have two equations:

Solve Equ 2 for b:

b = 485 - 2m

Substitute b in Equ 7:

6m + 2(485 - 2m) - t = 1065

6m + 970 - 4m - t = 1065

2m - t = 95 ------ (Equ 8)

Subtract Equ 8 from Equ 5:

(3m - t) - (2m - t) = 95 - 95

3m - t - 2m + t = 0

m = 0

Substitute m = 0 into Equ 2:

b + 2(0) = 485

b = 485

Therefore, one bagel costs 485 cents.

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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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The rate of the jet in still air is 1150 miles per hour and what is the rate of the jetstream is 220 miles per hour

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Let a represent the speed of the jet in still air and b represent the speed of the jet stream.

Flying against the jetstream, a jet travels 7440 miles in 8 hours, hence:

a - b = 7440/8

a - b = 930     (1)

Flying with the jetstream, the same jet travels 12,330 miles in 9 hours, hence:

a + b = 12330/9

a + b = 1370    (2)

From both equations, solving simultaneously:

a = 1150, b = 220

The rate of the jet in still air is 1150 miles per hour and what is the rate of the jetstream is 220 miles per hour

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The correct option is (b) For each Additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles.

The given regression equation is: ý = 38.5 - 1.4x where the weight is the explanatory variable.We are to select the conclusion that is true based on this information regarding weight and miles per gallon (mpg).

Solution:Given regression equation is: ý = 38.5 - 1.4x.

Here, explanatory variable is weight (in hundreds of pounds) and mpg is the response variable. Let us see each option.a) For each additional one pound of weight, mpg stays relatively the same.For each additional one pound of weight, the value of x would increase by 1/100 = 0.01.

Putting this value in the given equation, we get: ý = 38.5 - 1.4 (0.01) x 100= 37.1Since the value of ý is a decreasing function of x, a slight increase in x would lead to a decrease in the value of ý. Hence, this statement is false.b) For each additional one hundred pounds of weight, mpg decreases by 1.4 miles.

For each additional one hundred pounds of weight, the value of x would increase by 1. Putting this value in the given equation, we get: ý = 38.5 - 1.4 (1) x 100= 24.5For every increase of 100 pounds of weight, mpg decreases by 1.4 miles. Hence, this statement is true.

Therefore, the correct option is (b) For each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles.

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Answer:

0.17

Step-by-step explanation:

Substitute the w for 2 since we are trying to find out how much the dog weighs if it eats 2 cups a day.

c(2)= 0.06(2)+0.05 Multiply

c(2)= 0.12+0.05. Add

c(2)= 0.17 Answer.

The mean number of siblings for the population is 2 siblings.

To get mean number of siblings for the population, we need to calculate the sum of all the responses and divide it by the total number of campers.

The given responses are: [tex]3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1[/tex]

Sum of the responses = 3 + 2 + 0 + 1 + 0 + 2 + 3 + 4 + 1 + 2 + 2 + 1

Sum of the responses = 21

Total number of campers = 12

The mean number of siblings:

= Sum of the responses / Total number of campers

= 21 / 12

= 1.75

= 2.

Full question:

While at summer camp, Mike asked a random camper from each of the 12 cabins how many siblings he or she had. The results below display the responses. 3, 2, 0, 1, 0, 2, 3, 4, 1, 2, 2, 1 If there are 48 campers altogether, use Mike’s data to infer the mean of the population. What is the mean number of siblings for the population rounded to the nearest unit?

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Taylors total years of service is 21 years

Simple interest is an interest charge that borrowers pay lenders for a loan.

Simple interest is expressed as;

I = P× R × T)/100

where I is the interest,

P is the principal

R is the rate and T is the time.

In this case;

I = 1338.75 × 12 = 16065

P = $51,000

r = 1.5%

16065 = 51000× 1.5 × t/100

t = 1606500÷ 1.5 ÷ 51000

t = 21 years

Therefore the total number of years of service Taylor spent is 21 years.

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Answer:

  20°

Step-by-step explanation:

You want to know the measure of external angle 1 in the diagram of a circle, secants, and chord.

The measure of each arc subtended by a chord is shown as 100°. They all have the same measure because the chords are all the same length.

The measure of the remaining arc is ...

  360° -100° -100° -100° = 60°

The measure of angle 1 is half the difference of the measures of the arcs it intercepts:

  angle 1 = 1/2(100° -60°)

  angle 1 = 20°

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The measure of the angle 1 using the appropriate angle theorem is 20°

The measure of the arc subtended by the chord is 100°. Since the length of the chord are equal, then the measure of each arc in the figure is the same.

Since we have three arcs measuring 100°

The measure of the smallest arc would be : (360 - 100) = 60°

Angle 1 = 0.5(100-60) (half the measure of intercepted arc)

Angle 1 = 0.5(40) = 20°

Hence, the measure of angle 1 is 20°

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The correct expression is: 14 - 5 = a.

To find the value of a in the equation a + 5 = 14, we can use inverse operations. Inverse operations are operations that undo each other.

Starting with the equation a + 5 = 14, the inverse operation of adding 5 is subtracting 5. By subtracting 5 from both sides of the equation, we isolate the variable a:

a + 5 - 5 = 14 - 5

This simplifies to:

a = 9

By performing the subtraction, we find that a = 9.

The answer "14 - 5 = a" correctly demonstrates the use of inverse operations to find the value of a. It shows that by subtracting 5 from both sides of the equation, we isolate the variable and determine that a is equal to 9.

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Therefore Table 1 represents the function g(x) obtained by shifting f(x) 5 units down.

To shift a function f(x) 5 units down, we need to subtract 5 from the y-values of f(x) or add a constant -5 to the function. This means that the new function g(x) will be f(x) - 5. In other words, we take the table of values for f(x) and subtract 5 from each of the y-values to get the new table of values for g(x).Let's take a look at the given tables of values and see which one represents the function g(x) obtained by shifting f(x) 5 units down.

Table 1:  From this table, we can see that when x = 2, f(x) = 5. If we subtract 5 from this value, we get 0, which is the correct value of g(2). Similarly, when x = 3, f(x) = 7. If we subtract 5 from this value, we get 2, which is the correct value of g(3). Therefore, this table represents the function g(x) obtained by shifting f(x) 5 units down.

Table 2: From this table, we can see that when x = 0, f(x) = 1. If we subtract 5 from this value, we get -4, which is not the correct value of g(0). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.

Table 3: From this table, we can see that when x = -2, f(x) = -3. If we subtract 5 from this value, we get -8, which is not the correct value of g(-2). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.

Table 4: From this table, we can see that when x = 5, f(x) = 0. If we subtract 5 from this value, we get -5, which is not the correct value of g(5). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.In conclusion,

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A  graph that represents a Functional relationship between x and y on the given grid.

To draw a graph that represents a functional relationship between x and y on the given grid below, you need to follow the steps mentioned below:

First, draw a horizontal line called the x-axis. The x-axis represents the independent variable, and the values of x are plotted along this axis. Second, draw a vertical line called the y-axis.

The y-axis represents the dependent variable, and the values of y are plotted along this axis. Third, select some values of x, and substitute each value of x into the function to obtain the corresponding values of y. For each (x, y) pair, plot a point on the graph.

Finally, connect the points with a line to obtain the graph that represents the functional relationship between x and y.

Example: Let's say we have a functional relationship given as y = 2x + 3

Now, we can use this equation to calculate the values of y for different values of x. For example, when x = 0, y = 2(0) + 3 = 3.

When x = 1, y = 2(1) + 3 = 5. When x = 2, y = 2(2) + 3 = 7. When x = 3, y = 2(3) + 3 = 9. When x = 4, y = 2(4) + 3 = 11.Now we can plot these points (0, 3), (1, 5), (2, 7), (3, 9), and (4, 11) on the grid, and connect them with a line to obtain the graph as shown below:

Therefore, this is how you can draw a graph that represents a functional relationship between x and y on the given grid.

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The calculated value of X in the circle is 6

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

The circle

The value of X can be calculated using the following intersecting secants equation

5 * (5 + 7) = x * (x + 4)

using the above as a guide, we have the following:

x * (x + 4) = 60

When solved for x, we have

x = 6

Hence, the value of X is 6

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The solution to the inequality |1/4x - 3| - 5 ≥ 4 is x ≥ 48 or x ≤ -28. The graph of the solution is a number line with the regions to the right of 48 and to the left of -28 shaded, indicating the values of x that make the inequality true.

Part A: To solve the inequality |1/4x - 3| - 5 ≥ 4, we can follow these steps:

Step 1: Remove the absolute value brackets and rewrite the inequality as two separate inequalities:

1/4x - 3 - 5 ≥ 4   or   -(1/4x - 3) - 5 ≥ 4

Step 2: Simplify each inequality:

1/4x - 8 ≥ 4   or   -1/4x + 2 - 5 ≥ 4

Step 3: Solve each inequality separately:

1/4x ≥ 12   or   -1/4x - 3 ≥ 4

Step 4: Continue solving each inequality:

x ≥ 48   or   -1/4x ≥ 7

Step 5: Multiply both sides of the second inequality by -4, remembering to reverse the inequality sign when multiplying by a negative number:

x ≤ -28

Part B: The graph of the solution would be a number line with shaded regions. The region to the right of 48 (including 48) would be shaded to represent x ≥ 48. The region to the left of -28 (including -28) would also be shaded to represent x ≤ -28. These shaded regions represent the values of x that satisfy the inequality. The rest of the number line, between -28 and 48, would remain unshaded, indicating that those values of x do not satisfy the inequality.

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The area that was removed from the shape was 3.9 square inches, and the remaining area is 50.1 square inches. (None of the options given)

The area of the parallelogram is given by the formula A_p = b * h, where b is the base and h is the height. In this case, the base is 2 feet or 24 inches, and the height is 2.25 inches. Therefore, the area of the parallelogram is:

A_p = b * h = 24 inches * 2.25 inches = 54 square inches

Next, we compute the area of the cut-out rectangle. The area of a rectangle is given by the formula A_r = L * W, where L is the length and W is the width. In this case, L = 3 inches and W = 1-5/8 inches.

A_r = L * W = 3 inches * 1-5/8 inches

A_r = 3 inches * 13/8 inches

A_r = 3.9 square inches

Therefore, the area that was removed from the parallelogram is 3.9 square inches.

To find the remaining area of the parallelogram that was not cut-out, we simply subtract the area of the cut-out rectangle from the area of the parallelogram:

Remaining area = Area of parallelogram - Area of cut-out rectangle

Remaining area = 54 square inches - 3.9 square inches

Remaining area = 50.1 square inches

None of the answer options provided matches with the correct calculation above.

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In terms of measures of spread, Group B has a wider IQR than Group A

The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.

For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.

For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.

This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.

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Answer:

Please help me important question in image

Step-by-step explanation:Please help me important question in image

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Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities.

If Mofor only has time to do two homework assignments out of the five subjects, he will need to choose which subjects to prioritize. The specific subjects he chooses to work on will depend on various factors such as his strengths, weaknesses, upcoming deadlines, and personal preferences. Here are a few strategies he could consider:

1. Prioritize based on importance: Mofor can prioritize the homework assignments that carry more weight in terms of grades or have upcoming deadlines. This way, he ensures that he completes the assignments that have a higher impact on his overall academic performance.

2. Focus on challenging subjects: If Mofor finds certain subjects more difficult or time-consuming, he can prioritize those assignments to allocate more time and effort to them. This approach allows him to concentrate on improving his understanding and performance in subjects that require extra attention.

3. Balance workload: Mofor can choose to distribute his efforts evenly across subjects, selecting two assignments from different subjects. This strategy ensures that he maintains a balanced workload and avoids neglecting any particular subject.

The decision of which two homework assignments to complete depends on Mofor's individual circumstances and priorities. It is essential for him to consider his academic goals, time constraints, and personal strengths to make an informed decision.

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