The type of number that is irrational is a real number that cannot be expressed as a simple fraction or ratio of two integers.
An irrational number cannot be written in the form a/b, where a and b are integers and b is not equal to zero.
These numbers have non-repeating, non-terminating decimal representations.
Some examples of irrational numbers include the square root of 2 (√2), pi (π), and Euler's number (e).
Irrational numbers are infinitely non-repeating and cannot be represented by a finite decimal or fraction.
Their decimal expansions go on forever without settling into a repeating pattern. This property makes them distinct from rational numbers, which can be expressed as fractions or decimals that repeat or terminate.
The proof of a number being irrational often involves showing that there is no rational number that can represent it.
For instance, the square root of 2 cannot be expressed as a fraction, as it is a non-repeating decimal.
Irrational numbers are crucial in various mathematical fields and have significant applications in geometry, calculus, and number theory.
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Find the length of arc
l = 8.1 ft to the nearest tenth
What is an arc of a circle?In mathematics, an arc of a circle is defined as a portion of the boundary of a circle.
It is a fraction of the total circumference of a circle.
Let point O be the center of the circle and let angle POQ be denoted by x, since the sum of angles at a point is 360°, then,
x = 360 - 150 - 65 - 73
x = 72°
The formula for the length of an arc is given by
l = (θ/360) × 2πr............. Equation 1
Where,
r = radius of the circle
θ = angle subtended by the arc at centre of circle
π = 3.14
Substitute r = 6.48 and θ = 72 into eqn. 1
l = (θ/360) × 2πr
l = (72/360) × 2 × 3.14 × 6.48
l = 0.2 × 2 × 3.14 × 6.48
l = 8.13888 ft
l = 8.1 ft to the nearest tenth
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ITS THE FOURTH QUESTION
The surface areas of the figures are 336, 82 and 836
How to calculate the surface areasFrom the question, we have the following parameters that can be used in our computation:
The figures
For the triangular prism, we have
Surface area = 2 * 1/2 * 6 * 8 + 12 * 10 + 8 * 12 + 6 * 12
Surface area = 336
For the rectangular prism, we have
Surface area = 2 * (7 * 3 + 3 * 2 + 2 * 7)
Surface area = 82
For the cylinder, we have
Surface area = 2π * 7 * (7 + 12)
Surface area = 836
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The surface area of the prisms are
1. 336 cm²
2. 82 m²
3. 836 cm²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of prism is expressed as;
SA = 2B +pH
where B is the base area , p is the perimeter and h is the height.
1. SA = 2B +ph
B = 1/2 × 6 × 8
= 24 m²
p = 6+8+10 = 24m
h = 12m
SA = 2 × 24 + 24 × 12
= 48 + 288
= 336 cm²
2. SA = 2( 3× 2) + 3× 7)+ 2 × 7)
= 2( 6+21+14)
= 2( 41)
= 82 m²
3. SA = 2πr( r +h)
= 2 × 3.14 × 7( 7 + 12)
= 44( 19)
= 836 cm²
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Which statement is true about the points shown below? The distance between them is zero because they have the same y-coordinate. The distance between them can be found by counting from -3 to 7. The distance between them cannot be calculated because the points do not have the same x-coordinate. The distance between them can be found by doubling the distance of either point from the y-axis.
The statement that is true about the points shown below is: "The distance between them is zero because they have the same y-coordinate."
The distance between two points is typically calculated using the distance formula, which involves the difference between their x-coordinates and y-coordinates. However, in this case, the statement specifies that the points have the same y-coordinate.
The y-coordinate represents the vertical position on a graph, while the x-coordinate represents the horizontal position. When two points have the same y-coordinate, it means they lie on the same horizontal line.
Since distance is measured in a straight line, and these points are already on the same horizontal line, their distance from each other is zero. This is because they are effectively occupying the same position along the horizontal axis.
In summary, when two points have the same y-coordinate, their distance from each other is zero. This is because they lie on the same horizontal line and are already as close to each other as possible in the horizontal direction.
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what value of x is in the solution set of the inequality-2(3x + 2) > -8x +6
-6
-5
5
6
Answer:
5
Step-by-step explanation:
-2（3x+2)> -8x+6
-6x-4> -8x+6
-6x+8x> 6+4
2x> 10
x> 10/2
x> 5
Simplify (2^-6)(5)(2^3*5)^2
The simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.
To simplify the expression (2^-6)(5)(2^3*5)^2, let's break it down step by step:
First, we can simplify 2^-6. A negative exponent indicates taking the reciprocal of the base raised to the positive exponent. In this case, 2^-6 can be written as 1/(2^6).
Next, we can evaluate (2^35)^2. Inside the parentheses, we have 2^35. This can be simplified to 8*5, which equals 40. Then, we raise 40 to the power of 2, resulting in 40^2.
Now, let's put everything together:
(2^-6)(5)(2^3*5)^2 = (1/(2^6))(5)(40^2)
To simplify further, we can simplify the powers of 2 and 40:
2^6 = 64
40^2 = 1600
Substituting these values back into the expression:
(1/64)(5)(1600) = (5/64)(1600)
We can further simplify by multiplying 5 and 1600:
(5/64)(1600) = 800/64
Finally, we can simplify 800/64 by dividing both numerator and denominator by 8:
800/64 = 100/8 = 25/2
Therefore, the simplified form of the expression (2^-6)(5)(2^3*5)^2 is 25/2.
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A ship is anchored off a long straight shoreline that runs north and south. From two observation points
miles apart on shore, the bearings of the ship are
and
. What is the distance from the ship to each of the observation points? Round each answer to the nearest tenth of a mile.
The distance from the north most ship to the observation is
miles.
The distance from the south most ship to the observation is
miles.
The distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
The bearing is defined as the angle measured clockwise from the north direction. A ship is anchored off a long straight shoreline that runs north and south.
From two observation points miles apart on shore, the bearings of the ship are 52 degrees and 134 degrees respectively. To find the distance from the ship to each of the observation points, we can use trigonometry.
Let's call the distance from the north observation point to the ship x, and the distance from the south observation point to the ship y. The bearings from the north and south observation points can be drawn as follows:
[asy]
unitsize(1cm);
pair O = (0,0), N = (-2,0), S = (2,0), A = (-2,1), B = (2,-1);
draw(O--N--A,Arrow);
draw(O--S--B,Arrow);
[tex]label("$52^\circ$", N + 0.3*dir(52), NE);[/tex]
[tex]label("$134^\circ$", S + 0.3*dir(134), SE);[/tex]
draw(O--A--B--cycle,dashed);
[tex]label("$x$", (N+A)/2, W);[/tex]
[tex]label("$y$", (S+B)/2, E);[/tex]
[/asy]
We can use the tangent function to find x and y, since we have the angle and opposite side.
From the north observation point, we have:
[tex]$$\tan(52^\circ) = \frac{x}{2}$$$$x = 2\tan(52^\circ) \approx 2.95$$[/tex]
From the south observation point, we have:
[tex]$$\tan(134^\circ) = \frac{y}{2}$$$$y = 2\tan(134^\circ) \approx 9.88$$[/tex]
Therefore, the distance from the north most ship to the observation is 2.9 miles and the distance from the south most ship to the observation is 9.9 miles.
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Need answers please help
Answer:
-3, 3, 0.54545455, 8, 3.14159265..., 0, 2.44948974, 6
these are the real numbers
cool treats sold 60 ice cream cones. Single dip cones sold for $2.50 each double dip cones sold for $4.15 each. In all, $179.70 was taken in for the cones. How many of each type of cone were sold?
Answer:
Let s = number of single-dip cones
d = number of double-dip cones.
s + d = 60
2.50s + 4.15d = 179.70
2.50s + 4.15(60 - s) = 179.70
2.50s + 249 - 4.15s = 179.70
1.65s = 69.30
s = 42, d = 18
42 single-dip cones, 18 double-dip cones
A salesperson sells $3000 in merchandise and earns a commission of $540 .
Find the commission rate. Write your answer as a percentage.
Answer: Therefore, the commission rate is 18%.
Step-by-step explanation: To find the commission rate, we divide the commission earned by the total sales and then express it as a percentage.
Commission Rate = (Commission Earned / Total Sales) * 100
In this case, the commission earned is $540 and the total sales are $3000. Plugging these values into the formula, we have:
Commission Rate = (540 / 3000) * 100
Calculating this expression, we get:
Commission Rate = 0.18 * 100
There are six pizzas there are 36 players on the team. If each member has one slice and each pizza has eight slices how much pizza in fraction form will be left over.
There will be 12 slices of pizza left over, which can be expressed as 3/2 or 1 1/2 slices in fraction form.
To find out how much pizza will be left over, we need to calculate the total number of slices available and subtract the number of slices consumed by the players.
Given that there are six pizzas and each pizza has eight slices, the total number of slices available is 6 pizzas * 8 slices/pizza = 48 slices.
Since there are 36 players on the team, and each player has one slice, the total number of slices consumed is 36 slices.
To determine the remaining slices, we subtract the consumed slices from the total available slices: 48 slices - 36 slices = 12 slices.
Therefore, there will be 12 slices of pizza left over.
To express this as a fraction, we can write it as 12/1, which simplifies to 12. This means there will be 12 whole slices of pizza left over.
If you would like to express it as a fraction in its simplest form, you can write it as 12/8. By dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/2. So, in fraction form, there will be 3/2 or 1 1/2 slices of pizza left over.
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A basketball team scored a total of 97 points in a basketball game. They made a total of 42 2-point and 3-point baskets. How many 2-point baskets did they make? How many 3-point baskets did they make? Let the number of 2-point baskets = and the number of 3-point baskets =
Answer:
29 2-point baskets were made
13 3-point baskets were made
Step-by-step explanation:
Given:
x=number of 2-point baskets scored
y=number of 3-point baskets scored
First set of equations:
[tex]2x+3y=97[/tex]
Second set of equations:
[tex]x+y=42[/tex]
Solve for x or y in the second equation:
[tex]x+y=42\\y=42-x[/tex]
plug in y into the first equation:
[tex]2x+3(42-x)=97[/tex]
[tex]2x+126-3x=97\\[/tex]
combine like terms
[tex]x+126=97[/tex]
[tex]x=126-97\\x=29[/tex]
So, 29 2-point baskets were made.
Now plug in 29 for x in the second equation:
[tex]29+y=42[/tex]
subtract 29 from both sides
y=13
So, 13 3-point baskets were made.
Hope this helps! :)
can you explain in detail how to solve this?
Answer:
[tex]\csc(\arctan(x))=\frac{\sqrt{1+x^2}}{x}[/tex]
Domain is [tex](-\infty,0)\cup(0,\infty)[/tex]
Step-by-step explanation:
Let [tex]\csc(\arctan(x))=\csc\theta[/tex] so that [tex]\theta=\arctan(x)[/tex] and [tex]\tan\theta=x[/tex]:
[tex]\displaystyle \tan\theta=\frac{\text{Opposite}}{\text{Adjacent}}=\frac{x}{1}\\\\\csc\theta=\frac{1}{\sin\theta}=\frac{\text{Hypotenuse}}{\text{Opposite}}=\frac{\sqrt{1+x^2}}{x}[/tex]
You can get these values by drawing a right triangle and labeling each side. Hypotenuse is easily calculated with the Pythagorean Theorem.
Now that we know [tex]\csc(\arctan(x))=\frac{\sqrt{1+x^2}}{x}[/tex], it's clear that [tex]x\neq0[/tex], so the domain of the composite trig function is [tex](-\infty,0)\cup(0,\infty)[/tex].
Prove segment AM is congruent to segment
СМ.
Using a two-column proof, we can show that segment AM is congruent to segment СМ as explained below in the given table.
How to Prove that the Segments in the Parallelogram are Congruent?The image attached below shows parallelogram ABCD having two diagonals, AC and BD. To proved that segment AM is congruent to segment CM, we would apply the two-column proof as shown below:
Statement Reason
1. Parallelogram ABCD 1. Given
2. AD║BC 2. Properties of parallelogram
3. <MAD ≅ <MCB; 3. Alternate interior angles theorem.
<ADM ≅ <CBM
4. AD ≅ CB 4. Properties of parallelogram
5. ΔADM ≅ ΔCBM 5. ASA congruence theorem
6. AM ≅ CM 6. CPCTC
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Please help me with this
Answer:
D) g(x) = -4x²
Step-by-step explanation:
From f(x) to g(x), there is a reflection about the x-axis, followed by a vertical stretch.
So, we know that g(x) needs to have a negative leading coefficient, which eliminates the first two options.
Now C can't work because that would involve a vertical compression since the absolute value of the leading coefficient is less than 1
Therefore, D is correct!
Solve for the measure of PMR
The angle PMR in the quadrilateral is 32 degrees.
How to find the angle PMR?The angle PMR can be found as follows;
The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.
∠RPM ≅ ∠WPM
Hence,
∠RPM ≅ ∠WPM = 58 degrees
Therefore,
∠WPM = 58 degrees
∠PWM = 90 degrees
Let's find ∠PMR as follows
∠PMR = 180 - 90 - 58
∠PMR = 90 - 58
∠PMR = 32 degrees
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Review the graph.
On a coordinate plane, a circle has center (4, 0) and radius 4. Another circle has center (2, negative 3) and radius 6. The area inside of the first circle and outside of the second circle between the 2 circles is shaded.
Which system of inequalities is shown in the graph?
36 > (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 > (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
36 < (x + 3)2 + (y – 2)2 and 16 > (x – 4)2 + y2
36 < (x – 2)2 + (y + 3)2 and 16 > (x – 4)2 + y2
Answer:
36 < (x - 2)² + (y + 3)² and 16 > (x - 4)² + y²
Step-by-step explanation:
This is because the shaded area is inside the first circle (centered at (4, 0) with a radius of 4) but outside the second circle (centered at (2, -3) with a radius of 6). The inequalities reflect these conditions by setting the inequality signs accordingly. The inequality with "<" for the first circle ensures that the shaded area is within the circle, and the inequality with ">" for the second circle ensures that the shaded area is outside the circle.
what is the answer to
-5x+y=-210
Answer:
y=−210+5x
Step-by-step explanation: easy
ab-c/d has a value of 24. write the values if :-
1- a, b, c, d are all positive.
2- a, b, c, d are all negative.
3- a, b, c, d are mixed of negative and positive.
WRITE ANSWERS FOR 1, 2 AND 3
The values of ab, b - c, and c/d are 6, -1, and 4 respectively when a = 2, b = 3, c = 4 and d = 1.Using BODMAS rule, we can simplify the given expression.ab - c/d = 24
Given ab-c/d has a value of 24.Now, we have to find the value ofab, b - c, and c/d.Multiplying d on both sides, we getd(ab - c/d) = 24dab - c = 24d...(1)Now, we can find the value of ab, b - c, and c/d by substituting different values of a, b, c and d.Value of ab when a = 2, b = 3, c = 4 and d = 1ab = a * b = 2 * 3 = 6.
Value of b - c when a = 2, b = 3, c = 4 and d = 1b - c = 3 - 4 = -1Value of c/d when a = 2, b = 3, c = 4 and d = 1c/d = 4/1 = 4Putting these values in equation (1), we get6d - 4 = 24dSimplifying, we get-18d = -4d = 2/9
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the absolute value of the quantity one fifth times x plus 2 end quantity plus 4 is greater than or equal to 6
Answer: x <= -70 or x >= 22.
Step-by-step explanation:
The solution to the inequality is x <= -70 or x >= 22. To solve the inequality, we can begin by isolating the absolute value term. |1/5x + 2| + 4 >= 6 |1/5x + 2| >= 2 Next, we can split the inequality into two cases: 1/5x + 2 >= 2 or 1/5x + 2 <= -2 Solving for the first case: 1/5x + 2 >= 2 1/5x >= 0 x >= 0 Solving for the second case: 1/5x + 2 <= -2 1/5x <= -4 x <= -20 Therefore, the solution is x <= -70 or x >= 22.
7, 11, 2, 18, -7 select the next number continuing the pattern
Answer:
29
Step-by-step explanation:
7 + 4 = 11 --> 4 = 2²
11 - 9 = 2 --> 9 = 3²
2 + 16 = 18 --> 16 = 4²
18 - 25 = -7 --> 25 = 5²
Notice that the pattern is adding and then subtracting the next square number up. Therefore, the next number in the sequence would be -7 + 36 = 29 since 6²=36.
Compare the values of the following numbers, using the symbols > (greater than), < (less than), and = (equal to).
0.5 _____0.500
Answer:
0.5 = 0.500
Step-by-step explanation:
Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.
0.5 = 0.500
see photo please thank you
The area of the garden in this problem is given as follows:
201.07 ft².
How to obtain the area of the garden?For the rectangular part of the garden, the area is given by the multiplication of the dimensions as follows:
22 x 31 = 682 ft².
For the semi-circle, the radius is given as follows:
r = 0.5 x 22
r = 11 ft.
Hence the area is given as follows:
A = 0.5 x π x 11²
A = 190.07 ft.
Hence the total area is given as follows:
190.07 + 11 = 201.07 ft².
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WILL GIVE BRAINLIEST IF CORRECT ANSWER ASAP
What is the equation of the graphed function?
Enter your answer in the box.
f(x)=
Answer:
[tex]f(x) = {(x + 3)}^{2} = {x}^{2} + 6x + 9[/tex]
Step-by-step explanation:
move 3 units to the left
[tex] {x}^{2} [/tex]
hence
[tex] {(x + 3)}^{2} [/tex]
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age. Round your answer to the nearest a needed 54, 68, 68, 54, 59, 58, 68, 57, 57
A. 59.7
B. 58.0
C. 59.0
D. 60.3
Answer:
D. 60.3
Step-by-step explanation:
Finding the mean,
M = (sum of values of data)/(number of data)
now, number of data = 9,
calculating the mean,
M = (54 + 68 + 68 + 54 + 59 + 58 + 68 + 57 + 57)/9
M = 543/9
M = 60.333
M = 60.3
The diagram shows a particle P of mass M kg suspended from two strings
The angle made by one of the tensions suspending particle P is 50⁰.
What is the angle made by the two tensions?The angle θ made by one of the tensions is calculated by applying trig identities as follows;
the force opposite the angle = weight of the block = mg
W = 7.75 kg x 9.8 m/s²
W = 75.95 N
The angle θ made by one of the tensions is calculated as follows;
cos θ = (38 N ) / ( 59 N)
cos θ = 0.6441
θ = arc cos (0.6441)
θ = 50⁰
Thus, the angle θ made by one of the tensions is determined as 50 degrees.
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The missing part of the question is in the image attached.
Assume that by contributing your education you increase your yearly earning potential from 21,484 to 39,746 if the additional education cost $36,000 in about many years, will a it pay for itself
Yes, the additional education costing $36,000 will pay for itself in less than 2 years based on the increased earning potential.
To determine whether the additional education costing $36,000 will pay for itself, we need to consider the time it takes to recover the investment through the increased earning potential.
The additional yearly earning potential is the difference between the post-education income ($39,746) and the pre-education income ($21,484), which is $18,262.
To calculate the payback period, we divide the cost of education ($36,000) by the annual increase in earning potential ($18,262).
Payback Period = Cost of Education / Annual Increase in Earning Potential
Payback Period = $36,000 / $18,262
The payback period is approximately 1.97 years, meaning that it would take approximately 1.97 years to recover the cost of education through the increased earning potential.
If the time required to recover the cost is less than the time in which the increased earning potential will be realized, then the additional education would be considered to have paid for itself.
In this case, since the payback period is less than 2 years and the increased earning potential will continue for subsequent years, it can be concluded that the additional education costing $36,000 will pay for itself over time.
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Sarah predicted that she could text 80 words
per minute on her phone. However, she only
texted 52 words per minute. What was Sarah's
percent error?
Prediction Actual |
| Actual |
Round to the nearest percent.
Hint: Percent error =
-
x 100
Answer:
20
Step-by-step explanation:
percentage error = predictions - actual ÷actual × 100
error
[tex] \frac{82 - 52 \\ }{52} \times 100[/tex]
=
20
The area of the U.S. is about 3.751 million square miles. Approximately 580000 square miles are worked for food production. What percent of the U.S. is worked for food production?
Round your answer to the nearest tenth of a percent
The percentage of US used for food production is 15.5%.
How to find percentage area used for food production?The area of the U.S. is about 3.751 million square miles. Approximately 580000 square miles are worked for food production.
Therefore, the percentage of the US area that is used for food production can be calculated as follows:
percentage use for food production = 580,000 / 3,751,000 × 100
percentage use for food production = 58,000,000 / 3,751,000
percentage use for food production = 15.4625433218
percentage use for food production = 15.5%
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A straight line l has gradient 2 and passes through the point (0,3) write the equation for l
Answer:
The equation for a straight line in slope-intercept form is y = mx + b, where m is the gradient (slope) of the line and b is the y-intercept (the point where the line crosses the y-axis).
We are given that the gradient of the line is 2, so we can substitute m = 2 into the equation:
y = 2x + b
We are also given that the line passes through the point (0,3), which means that when x = 0, y = 3. We can substitute these values into the equation and solve for b:
3 = 2(0) + b
b = 3
Now we know that the y-intercept is 3, so we can write the equation of the line:
y = 2x + 3
As we know that a straight line is represented by its equation, which is in the form of y = mx + c where m is the gradient and c is the y-intercept of the line.
Here, the gradient of the line l is given as 2 and the point (0,3) lies on the line l. We can use the point-slope form of a line to write the equation of line l.
The point-slope form of a line is given by:
y - y1 = m(x - x1)
where (x1,y1) is a point on the line and m is the gradient of the line.
Using the given information, we can substitute the values of m, x1 and y1 in the equation:
y - 3 = 2(x - 0)
Simplifying the equation:
y - 3 = 2x
Adding 3 to both sides of the equation:
y = 2x + 3
Therefore, the equation for line l is y = 2x + 3.
The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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