Simplify the following expressions by combining like terms. Then, tell if the expressions are equivalent.

3r + 10 + r -8 and 8 + 2(2r) - 6

The dimensions are 12 meter by 18 meter .

perimeter of rectangle = 2(length + width)

length and width of the  Luis plot by L and W, respectively.

We know that the perimeter, is 60 meters. So we can write:

2L + 2W = 60

Simplifying this equation, we can divide both sides by 2:

L + W = 30

now , area of the plot is 216 square meters:

L x W = 216

use substitution to solve for one of the variables. Let's solve for L in the first equation:

L = 30 - W

We can substitute this expression for L into the second equation:

(30 - W) x W = 216

[tex]W^2 - 30W + 216 = 0[/tex]

We can solve this quadratic equation using the quadratic formula:

W = [30 ± [tex]\sqrt{30^2 - 4 * 1 * 216}[/tex] / 2

Simplifying:

W = [30 ± 6] / 2

So  W = 18 or W = 12.

If W = 18, then L = 30 - 18 = 12.

If W = 12, then L = 30 - 12 = 18.

Therefore, the dimensions  are 18 meters by 12 meters or 12 meters by 18 meters.

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No information is given for x and it can be fraction or real number, so option D is correct.

What is fraction ?

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Fractions represent the parts of a whole or collection of objects. A fraction has two parts. The number on the top of the line is called the numerator.

It tells how many equal parts of the whole or collection are taken.

No information is given for x and it can be fraction or real number, so option D is correct.

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Answer: There are 95 tables in the middle group

Step-by-step explanation:

There are a total number of 250 tables.

There are three groups.

We know how many tables the left and right groups have

let x be the number of tables in the middle

75+80+x=250

155+x=250

x=95

Answer:

Option 4

Step-by-step explanation:

The domain of this function is the possible values of n that are suitable for this function. Since n represents a number of vehicles, the domain of n should be a whole number (since you cannot have a negative number of vehicles or half of a vehicle).

hope this helps :)

The piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

On the graph we can see a piecewise function (piecewise means that it has different equations defined for different intervals in the domain).

On the left side, we can see a linear equation that comes from negative infinity and ends at x = 2 with an open circle (so the domain does not contain that value).

That line passes through (-1, 0) and (0, 1), then the slope is:

a = (1 - 0)/(0 -(-1)) = 1

And the y-intercept is y = 1, then the equation of the line is:

y = x + 1

The other line starts at x = 5 (again, open circle) and keeps going, it passes through the points (5, 7) and (6, 0)

The slope is:

a = (0 - 7)/(6 -5) = -7

Then the line is something like:

y = -7*x + b

To find b, we use the point (6, 0)

0 = -7*6 + b

7*6 = 42 = b

Then this line is:

y = -7x + 42

Concluding, the piecewise function is:

f(x) = x + 1             if x < 2

f(x) = -7x + 42       if x > 5

The complete question is : Help please!! Express the function graphed on the axes below as a piecewise function.

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Answer:

pls rate as brainliest it will go a long way

Step-by-step explanation:

(x–1)(x+2)

STEP 1

using the first bracket to expand the other

= x(x + 2) –1(x + 2)

= x² + 2x –x –2

= x² + x – 2

Step 2

or by using the other bracket to expand the other

(x – 1)(x + 2)

x(x – 1) + 2(x – 1)

= x² – x + 2x – 2

= x² + x – 2

The measure of the other angle is 73°.

What are complementary angles?

Complementary angles are those whose combined angle is exactly 90 degrees. 30 degrees and 60 degrees, for instance, are complimentary angles.

How do you find a complementary angle?

Two angles are said to be complimentary if their sum is 90 degrees. So, to find the complement of an angle, subtract it from 90.

Here, we have

Given

Two angles are complementary. If one measures 17 degrees.

Complementary angles are two angles that add up to exactly 90 °.

∠A + ∠B = 90°

17 + ∠B = 90°

∠B = 90 - 17

∠B = 73°

Hence, the measure of the other angle is 73°.

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The side of the equilateral triangle is 2 ³/4 feet, having perimeter 8 ¹/₄  feet.

If all three of a triangle's sides are the same length, the triangle is said to be equilateral. Congruent sides refer to sides that have the same length, and they characterize an equilateral triangle.

Given that,

The perimeter of equilateral triangle = 8 ¹/₄  feet.

Simplify the rational term.

8 ¹/₄ = (32 + 1) / 4 = 33 /4.

Let each side of an equilateral triangle is a feet.

The perimeter of the equilateral triangle = 3a

Since, 3a = 33/4

a = 11/4

a = 2 ³/4

The required side of the equilateral triangle is 2 ³/4.

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The required, team 3, tower garden donation shows the proportional relationship between weeks and donation,

Proportionality is described as the relationship between two or more sets of values, and whether these values are directly proportional or inversely proportionate to one other.

here,
From the table,
The ratio of a week to the donation of the individual team must be the same as the ratio of the preceding week and the donation of the respective team,
So,
Team 1,
1 / 1 =  2 / 3[1/4], false

Similarly, team 2 and team 4's relationship is also not proportional,
Now, team 3
1 / [2 1 / 3] = 2 / [4 2/3 ]
3 / 7 = 3/7

Thus, The necessary, team 3, tower garden gift illustrates the proportional relationship between weeks and donation.

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Answer:

x=-2

y = 3× -2 + 4

y= -6 + 4

y = -2

Answer:

The circumference of a corcle is double the perimeter of square having area 484 m^2. what is the area of the circle. Ans:2464 cm^2.

Answer:

Hence the area of a circle is 2466[tex]m^{2}[/tex]

Step-by-step explanation:

Review of the question

[tex]Given,[/tex]

Area of the circle

,

Area of square =[tex]sideXside[/tex]

[tex]484[/tex]=[tex]side^{2}[/tex]

[tex]\sqrt{484}=side^{2}[/tex]

[tex]22 = side[/tex]

Perimeter of square = [tex]4Xside[/tex]

[tex]4X22[/tex]

[tex]88[/tex]

Circumference of the circle = Perimeter of square  x 2

Circumference of the circle = 88x2

Circumference of the circle = 176

Now we need to find the radius of the circle

[tex]2\pi r=176[/tex]

[tex]2X3.14Xr=176\\6.28Xr=176\\r=\frac{176}{6.28} \\r=28.025477707[/tex]

Area of the circle=[tex]\pi r^{2}[/tex]

[tex]3.14X[/tex][tex](28.025477707)^{2}[/tex]

[tex]2466[/tex]

Hence the area of a circle is 2466[tex]m^{2}[/tex]

Answer:

meter - yard

kilogram - 2 pounds

liter - quart

Answer:  12 row plans

The first seat has 2 possible options, the 2 directors. The second seat has another 2 options. With each director comes 2 options for the second seat, so 2 x 2=4 possible options for the 1st and 2nd seats. The third seat has 3 options. That means for each combination of the 1st and 2nd seat, there are 3 possible options. 4x3=12 combinations.

Step-by-step explanation:

The required number of new boys in a sports team is 62.

As mentioned in the question,  A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
Given that the number of men is now 60% of the total members, how many of the 50 new members were women is to be determined,
Percentage of women, in the team = 100 - 60 = 40%
40% of total members are women = 35 + 50

Total members = 85 / 40%
Total member = 212
Number of new member that are boys = 212 - 85 - 65 = 62 boys

Thus, the required number of new boys in a sports team is 62.

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Answer:

g(x) = 4x - 3

Step-by-step explanation:

f(x) = 2x − 3

g(x) = f(2x)

g(x) = 2(2x) - 3  ==> plugin 2x for x in f(x) in order to get f(2x)

g(x) = 4x - 3

The equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

What is equation?

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation

3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Consider the given equation

5/6 x + 2/3 = -9

Subtract 2/3 from both sides,

5/6x + 2/3 - 2/3 = -9 - 2/3

5/6x = -29/3

[tex]x = -\frac{29}{3}*\frac{6}{5}\\ x = -11.6[/tex]

The value of x is -11.6.

Hence, the equations have the same value of x are,

A) 5x + 4 = -54

B) 6(5/6x + 2/3) = -9(6)

C) 5x = -58

After solving above these equations we get the same value of x which is -11.6.

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Complete question:

Which equations have the same value of x as 5/6x + 2/3 = -9? Select three options. 6(5/6x + 2/3) = -9

6(5/6x + 2/3) = -9(6)

5 x + 4 = -54 5 x + 4 = -9

5 x = -13

5 x = negative 58

The distance between  the tent pole to the rope along the ground is 15 feet.

What is a cone?

A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.

Given that length of the tent pole is 8 feet.

The angle between the tent pole and the ground is 90°.

Thus the tent pole, the rope and the ground form a right angle triangle.

According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.

Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.

Assume that the distance the tent pole to the rope along the ground be x.

The length of the rope is 17 feet which is hypotenuse of the right angle triangle.

Therefore,

x² + 8² = 17²

x² + 64 = 289

x²  = 225

x = 15

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Answer: 15 feet

Step-by-step explanation:

first we grab 17 feet a square it

17^2 = 289

then we square 8 feet

8^2 = 64

subtract

289-64= 225

what squared equals 225?

15 does

By using the formula for area of parallelogram, it can be calculated that

Felix needs to buy 80 [tex]cm^2[/tex] of tiles

What is area of parallelogram?

Area of parallelogram is the total space taken by the parallelogram.

If b is the base of the parallelogram and h is the height of the parallelogram, then area of the parallelogram is calculated by the formula

Here,

Base of each parallelogram = 4cm

Height of each parallelogram = 2cm

Area of  each parallelogram = 4 [tex]\times[/tex] 2 = 8 [tex]cm^2[/tex]

Area of 10 parallelograms = 8 [tex]\times[/tex] 10 =  80 [tex]cm^2[/tex]

Felix needs to buy 80 [tex]cm^2[/tex] of tiles

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Complete Question

The full diagram has been attached.

A polygon is a plane shape with a minimum of three straight sides. Thus the appropriate answer are:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Polygons are majorly plane shapes which have straight sides. They are named with respect to the number of their sides, and the minimum sides is three. Some common examples are: trigon (3 sides), octagon (8 sides), hexagon (6 sides), pentagon (5 sides) , etc.

Two or more shapes are said to be similar if and only if they have some common properties with respect to their sides or internal angles.

Considering the ratios of the sides of the given polygons, it can be deduced that:

i. A and B Not Similar

ii. B and C Not Similar

iii. A and C Not Similar

Thus none of the polygons are similar.

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Answer:

23328

Step-by-step explanation:

since it is a geometrics sequence we will use the formula

[tex] {ar}^{n - 1} [/tex]

The first term(a) = 3

The second term = ar = 18

divide the first term and second term to find the common ratio

[tex] \frac{t2}{t1} = \frac{ar}{a} = \frac{18}{3} [/tex]

r = 6

Now lets find the sixth term

[tex]t6 = {ar}^{6 - 1} [/tex]

[tex]t6 = {ar}^{5} [/tex]

by substituting for the values

[tex]t6 = 3 \times {6}^{5} [/tex]

= 3 × 7776

= 23328

i hope this helped

Answer:

[tex]a_{6} = 23,328[/tex]

Step-by-step explanation:

⭐ Geometric Progression formula: [tex]a_{n} = a_1(b)^{n-1}[/tex]

We are given that [tex]a_{1}[/tex] = 3. Now, we need to find b.

b is the quotient of [tex]\frac{a__3}{a__2}[/tex].

Let's substitute the first term and common ratio into the formula.

[tex]a_n = 3(6)^{n-1}[/tex]

The problem wants us to solve for the 6th term, so we have to substitute 6 for n and solve.

[tex]a_6 = 3(6)^{6-1}\\a_6 = 3(6)^5\\a_6 = 3(7,776)\\a_6 = 23,328[/tex]

Answer:

The empirical rule states that for a bell-shaped distribution, approximately 68% of the data values will fall within one standard deviation of the mean, 95% of the data values will fall within two standard deviations of the mean, and 99.7% of the data values will fall within three standard deviations of the mean.

Using this information, we can calculate the range of values that fall within two standard deviations of the mean for the given data set:

Mean: $1200

Standard deviation: $100

Two standard deviations: $200

Therefore, the range of values that fall within two standard deviations of the mean is $1200 - $200 = $1000 to $1200 + $200 = $1400.

With this information, we can determine which of the given data values are unusual (more than two standard deviations from the mean):

$1064 is within two standard deviations of the mean.

$1417 is outside of two standard deviations of the mean.

$1373 is within two standard deviations of the mean.

$856 is outside of two standard deviations of the mean.

$1250 is within two standard deviations of the mean.

$1102 is within two standard deviations of the mean.

Therefore, the data values $1417 and $856 are unusual (more than two standard deviations from the mean).

We can also determine which of the given data values are very unusual (more than three standard deviations from the mean) using the same process. The range of values that fall within three standard deviations of the mean is $1000 to $1600. With this information, we can see that none of the given data values are very unusual (more than three standard deviations from the mean).

Answer: 4 i think

Step-by-step explanation:

65=15y+5

65 - 5 = 15y +5 -5

60 = 15y

60/15 = 15y/15

4 = y

Kurt will eat 1/6 cups more than Danielle if Kurt ate 1/3 of a cup of nuts and Danielle ate 1/6 of a cup of nuts by using ratio and proportion concept.

When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. Two ratios are set to be equal in an equation called a proportion. For instance, if there is 1 boy and 3 girls, the ratio would be written as 1: 3 (there are 3 girls for every boy), meaning that there are 1 in 4 boys and 3 in 4 girls.

A: b a/b is the ratio formula, which may be used to calculate any two values. A:b::c:da:b::c:da, on the other hand, is how the percentage formula is written. A ratio in mathematics displays the multiplicative relationship between two numbers.

Given,

A cup of nuts ate by Kurt=1/3

A cup of nuts ate by Danielle=1/6

(1/3)-(1/6)

=1/6

Therefore, Kurt will eat 1/6 cups more than Danielle.

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22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.

Given that,

When the other two sides of a triangle are measured at 7 km and 29 km.

We have to determine the range for the third side's measurement.

We know that,

Take the measured sides.

7 km and 29 km

So, we can write as

The two sides added together are greater than the third side.

So, take one side as x

We get,

7+x>29

Taking 7 to the right side we get negative 7
x>29-7

x>22

Now taking 29 to left side and x to sides

7+29>x

36>x

Therefore, 22>x>36 is the range for the third side's measurement when two sides of a triangle are measured at 7 km and 29 km.

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Step-by-step explanation:

The firm should manufacture 50 units of product I, 100 units of product II, and 100 units of product III each week to meet all contractual obligations and maximize its total profit.

To set up the mathematical model for this problem, we can use variables to represent the number of units of each product that the firm manufactures each week. Let x1 be the number of units of product I, x2 be the number of units of product II, x3 be the number of units of product III, and x4 be the number of units of product IV.

The first constraint is that the firm has a contract to provide 50 units of product I and 100 units of any combination of products II and III each week. This can be represented as:

x1 = 50

x2 + x3 = 100

The second constraint is that the firm has a maximum of 480 hours of machining time, 400 hours of polishing time, and 400 hours of assembling time each week. The time required for each product can be represented as:

x16 + x28 + x34 + x410 <= 480 (machining time)

x14 + x26 + x32 + x48 <= 400 (polishing time)

x14 + x24 + x34 + x46 <= 400 (assembling time)

The third constraint is that the firm can sell as many units of products I, II, and III as it can produce, but only a maximum of 25 units of product IV. This can be represented as:

x1 >= 0

x2 >= 0

x3 >= 0

x4 <= 25

The objective is to maximize the firm's total profit, which is the sum of the profits for each product. The unit profits for each product are Birr 360, Birr 240, Birr 360, and Birr 480, respectively. The total profit can be represented as:

360x1 + 240x2 + 360x3 + 480x4

The complete mathematical model for this problem is:

Maximize: 360x1 + 240x2 + 360x3 + 480x4

Subject to:

x1 = 50

x2 + x3 = 100

x16 + x28 + x34 + x410 <= 480

x14 + x26 + x32 + x48 <= 400

x14 + x24 + x34 + x46 <= 400

x1 >= 0

x2 >= 0

x3 >= 0

x4 <= 25

This model can be solved using linear programming techniques to find the values of x1, x2, x3, and x4 that maximize the total profit while satisfying all of the constraints. In this case, the optimal solution is x1 = 50, x2 = 100, x3 = 100, and x4 = 0, which corresponds to manufacturing 50 units of product I, 100 units of product II, and 100 units of product III each week. This meets all of the contractual obligations and maximizes the total profit.

The objective is to maximize total profit, which is given as

P = 360 [tex]x_1[/tex]+ 240[tex]x_2[/tex]+ 360[tex]x_3[/tex] + 480[tex]x_4[/tex]

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation.

Let[tex]x_1[/tex] , [tex]x_2[/tex],  [tex]x_3[/tex] and  [tex]x_4[/tex] be the number of units of product I, II, III and IV to be produced, respectively.

The constraints are that the time requirements for each product should not exceed the available time, the firm is contractually obligated to produce 50 units of product I and 100 units of products II and III, and the firm can sell at most 25 units of product IV.

These constraints can be written mathematically as:

3[tex]x_1[/tex]  + 2 [tex]x_2[/tex]+ 2 [tex]x_3[/tex]   + 4[tex]x_4[/tex] ≤ 480  (Machining)

[tex]x_1[/tex] +  [tex]x_2[/tex] +  [tex]x_3[/tex]   + 3[tex]x_4[/tex] ≤ 400  (Polishing)

2[tex]x_1[/tex]  +  [tex]x_2[/tex]+ 2 [tex]x_3[/tex]  + [tex]x_4[/tex] ≤ 400 (Assembling)

and, [tex]x_1[/tex]  ≥ 50 (Product I)

[tex]x_2[/tex] +  [tex]x_3[/tex]  ≥ 100 (Products II and III)

[tex]x_4[/tex] ≤ 25 (Product IV)

[tex]x_1[/tex] , [tex]x_2[/tex],  [tex]x_3[/tex]  , [tex]x_4[/tex] ≥ 0

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Answer:

< 1 = 64°

Step-by-step explanation:

First at all the sum of 2 angles should be 180°

< 3 + 116° = 180°

< 3 = 180 - 116

< 3 = 64°

Then, the sum of intern angles of a triangle must sum 180°, so:

< 1 + 52° + < 3 = 180°

< 1 +52 + 64 = 180

< 1 = 180 - 64 -52

< 1 = 64°

[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

[tex]3/4x + 2/3y - 3/8x + 1/2y[/tex]

a) First, start by operating with the terms that contain the "x" variable.

[tex]3/4x- 3/8x\\ \\\frac{3}{4}x-\frac{3}{8}x\\ \\ \frac{3*2}{4*2}x-\frac{3}{8}x\\ \\\frac{6}{8}x-\frac{3}{8}x\\ \\x(\frac{6}{8} -\frac{3}{8} )\\ \\x(\frac{6-3}{8} )\\ \\x(\frac{3}{8} )\\ \\\frac{3}{8}x[/tex]

b) Start with terms containing "y".

[tex]2/3y+1/2y\\ \\\frac{2}{3}y +\frac{1}{2} y\\ \\\frac{2*2}{3*2}y +\frac{1*3}{2*3} y\\ \\\frac{4}{6}y +\frac{3}{6} y\\ \\y(\frac{4+3}{6})\\ \\y(\frac{7}{6})\\ \\\frac{7}{6} y[/tex]

[tex]\frac{3}{8} x+\frac{7}{6} y[/tex].

The correct answer is Option C. The proper decision, in this case, is  "Fail to reject H0. There is not enough evidence at the 1% level of significance to reject the claim."

The alternative hypothesis, in this case, is "μ1 ≠ μ2", as the claim being tested is that the two population means are equal.

To calculate the standardized test statistic, we can use the following formula:

Substituting in the values given in the problem, we get:

z = (18 - 20) / sqrt(((3.6^2) / 27) + ((1.4^2) / 26))

z = (-2) / sqrt((12.96 / 27) + (1.96 / 26))

z = (-2) / sqrt(0.481 + 0.075)

z = (-2) / sqrt(0.556)

z = (-2) / 0.746

z = -2.67

To calculate the P-value, we can use the standard normal table to look up the probability of getting a value of -2.67 or lower if the null hypothesis were true. The P-value in this case would be the probability of getting a value equal to -2.67 or lower, plus the probability of getting a value equal to 2.67 or higher.

Using the standard normal table, we find that the probability of getting a value equal to -2.67 or lower is 0.0039, and the probability of getting a value equal to 2.67 or higher is 0.9961. Therefore, the P-value is 0.0039 + 0.9961 = 1.0000.

Since the P-value is equal to 1.0000, which is greater than the level of significance α = 0.01, we fail to reject the null hypothesis.

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Answer:

  x = 7.2

Step-by-step explanation:

You want the value of x that makes ∠BCE = 45° = (5x +9)°.

Divide by ° and subtract 9 to get ...

  36 = 5x

Divide by 5, and you have the value of x:

  7.2 = x

The value of x is 7.2.

__

Additional comment

You know that the corner angles of a square are 90°, and that the diagonals bisect the corner angles. Each half is 45°.

To calculate the total amount of interest that Edgar will owe on his credit card debt after 2 years of quarterly compounding at a 20% annual interest rate, we need to use the formula A = P(1 + r/n)^nt, where A is the total amount of money owed after t years, P is the initial principal (or amount borrowed), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years. In this case, the initial principal is $9,000, the annual interest rate is 20%, the number of times the interest is compounded per year is 4 (since the interest is compounded quarterly), and the number of years is 2. Plugging these values into the formula, we get A = $9,000(1 + 0.20/4)^4 * 2 = $9,000(1.05)^8 = $9,000 * 1.4064 = $12,658.40. Thus, after 2 years of quarterly compounding at a 20% annual interest rate, Edgar will owe approximately $12,658.40 on his credit card debt. This result should be rounded to the nearest cent, giving us $12,658.40.