A college entrance exam had a mean of 80 with a standard deviation of 12 find the actual test score that coincides with a z-score of -1.25

The type of statistical study in which the population is influenced by researchers is known as an experimental study.

In an experimental study, researchers manipulate one or more variables to observe the effect on another variable. The population in an experimental study is usually a sample that is randomly selected to represent the larger population.

The researchers intentionally intervene in the study, which can impact the behavior or responses of the participants. This can be seen as a form of bias since the researchers are influencing the population. However, in some cases, this is necessary to determine causality or to test a hypothesis.

To minimize bias, experimental studies often use control groups. The control group is used to provide a baseline for comparison with the group that is exposed to the manipulated variable. This helps to determine if any observed effects are due to the intervention or if they are due to other factors.

In summary, an experimental study is the type of statistical study in which the population is influenced by researchers. While this can introduce bias, the use of control groups and other measures can help to minimize the impact of this bias on the results.

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After about 15.7 months, the apartment complex will have 800 occupied units.

Logistic growth is a type of growth in which the growth rate of a population decreases as the population size approaches its maximum value. In this case, the apartment complex has a maximum capacity of 1500 units.

Starting with 15 occupied units and growing at a rate of 10% per month, the number of occupied units can be modeled by a logistic function.

To find the number of months it takes to reach 800 occupied units, we need to solve for the time when the logistic function equals 800.

Let P(t) be the number of occupied units at time t (in months), then we have:

P(t) = 1500 / (1 + 1485[tex]e^{(-0.1t)}[/tex])

We want to find t such that P(t) = 800. Solving for t, we get:

t = -10 ln(1 - 4/37) ≈ 15.7 months

This means that after about 15.7 months, the apartment complex will have 800 occupied units.

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The table of values in a graph for fabian's income in expenses is

n            E(n)

0           825

1            828.25

2           831.5

4          838

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

The expenses E to make n cakes per month is given by the equation

E = 825 + 3.25n

Next, we assume values for n and calculate E

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

E = 825 + 3.25(0) = 825

E = 825 + 3.25(1) = 828.25

E = 825 + 3.25(2) = 831.5

E = 825 + 3.25(4) = 838

So, we have

n            E(n)

0           825

1            828.25

2           831.5

4          838

This represents the table of values

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For the first problem, we can interpret the confidence interval as follows:

We are 95% confident that the true mean commuting time for workers who drive to work is between 27.74 and 30.06 minutes.

This means that if we were to repeat the sampling process many times and construct a 95% confidence interval each time, about 95% of those intervals would contain the true mean commuting time.

For the second problem, we can use the following formula to find a 95% confidence interval for the true mean length of long distance telephone calls:

[tex]CI = X ± t*(s/sqrt(n))[/tex]

Where X is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-value from the t-distribution with n-1 degrees of freedom for a 95% confidence interval.

Plugging in the values given, we get:

[tex]CI = 1.68 ± t*(5.2/sqrt(45))[/tex]

To find the value of t, we can look it up in a t-distribution table or use a calculator. For a 95% confidence interval with 44 degrees of freedom, we get t = 2.015.

Plugging this value in, we get:

[tex]CI = 1.68 ± 2.015*(5.2/sqrt(45)) = (0.86, 2.50)[/tex]

So we can interpret the interval as follows:

We are 95% confident that the true mean length of long distance telephone calls made by customers of this company is between 0.86 and 2.50 minutes longer or shorter than the sample mean of 1.68 minutes.

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The correct symbol to compare the expressions is < (less than).

7 × (2/10) is equivalent to 1.4, which is less than 7. Therefore, 7 is greater than 1.4, and we can write 7 × (2/10) < 7 as the comparison between the expressions.

To compare the two expressions, we can analyze their values without actually multiplying them. The expressions are:

1. 7 × (2/10)
2. 7

Now let's simplify the first expression without multiplying:

7 × (2/10) = 7 × (1/5) (since 2 and 10 have a common factor of 2)

Now let's compare:

7 × (1/5) ? 7

Since we're multiplying 7 by a fraction that is less than 1 (1/5), the result will be smaller than 7. Therefore, the correct comparison symbol is "<":

7 × (1/5) < 7

The correct expression so formed is 7 × (2/10) < 7.

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The class will use 20 yards of the 50-yard spool, leaving 30 yards of string leftover.

This leftover string could be used for future projects or saved for another occasion.

Lacey's class will use a total of 720 inches (30 inches per student x 24 students) of string for the candy necklaces.

To convert this to yards, we divide by 36 (since there are 36 inches in a yard). 720 inches ÷ 36 = 20 yards

It's important to note that when working with different units of measurement, it's necessary to convert them to the same unit before performing calculations.

In this case, we converted inches to yards in order to determine the amount of string used by the class. By doing so, we were able to determine how much string was leftover in yards, which is a more appropriate unit of measurement for a spool of string.

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Answer:

1.6×10^-12..............

From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵).  The value of  fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:

fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]

Simplifying and applying the power rule of differentiation, we get:

fx = -10x³y⁵ / (-2x⁴ + 3y⁵)

Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:

fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

Applying the power rule of differentiation and simplifying, we get:

fy = 15y⁴ ln(-2x⁴ + 3y⁵)

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The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.

We are given that the radius is increasing at a rate of 5 mm per second. This means that the rate of change of the radius with respect to time is dr/dt = 5 mm/s.

To find the rate at which the area is changing, we need to find dA/dt, the derivative of the area with respect to time. We can use the chain rule to find this derivative:

dA/dt = dA/dr * dr/dt

We can find dA/dr by taking the derivative of the area formula with respect to r:

dA/dr = 2πr

Now we can substitute the values we know into the chain rule formula:

dA/dt = dA/dr * dr/dt = 2πr * 5

When the radius is 28 mm, the rate of change of the area is:

dA/dt = 2π(28) * 5 = 280π ≈ 879.64 mm^2/s

Therefore, the area is changing at a rate of approximately 879.64 mm^2/s when the radius is 28 mm.

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Answer:

-----------------------

Given:

(i) We know 60 out of 110 can speak both languages, so as 60 out of 85. The number 60 is counted twice if we add them together.

Find the number of those speak either language:

(ii) Find the number of thise who can talk neither of these languages:

Let's break down the information given in the problem:

- Jane became a real estate agent in 1990.

- She sold a house 8 years later (in 1998) for $144,000.

- She sold the same house 11 years after that sale (in 2009), which is 19 years after she became an agent, for $245,000.

To write an equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent, we can use the information from the two sales to find the rate of change in the value of the house over time. We can use this rate of change to write an equation in point-slope form:

V - V1 = m(t - t1)

where V1 is the value of the house at time t1, m is the rate of change in the value of the house, and t is the time since Jane became a real estate agent.

Using the two sales, we can find the rate of change in the value of the house as follows:

m = (V2 - V1) / (t2 - t1)

where V2 is the value of the house at the second sale, t2 is the time of the second sale (19 years after Jane became an agent), V1 is the value of the house at the first sale, and t1 is the time of the first sale (8 years after Jane became an agent).

Substituting the given values, we get:

m = ($245,000 - $144,000) / (19 - 8) = $10,100 per year

Now we can use the point-slope form equation to find the value of the house at any time t since Jane became a real estate agent. Let's choose 1990 as our initial time (t1), so V1 = $0:

V - 0 = $10,100 (t - 0)

Simplifying, we get:

V = $10,100t

Therefore, the equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent is V = $10,100t. Note that this equation assumes a constant rate of change in the value of the house over time, which may not be accurate in real life.

The optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

To solve the optimization problem and maximize P = xy with the constraint x + 2y = 26, follow these steps:

1. Express one variable in terms of the other using the constraint: x = 26 - 2y

2. Substitute the expression for x into the objective function P: P = (26 - 2y)y

3. Differentiate P with respect to y to find the critical points: dP/dy = 26 - 4y

4. Set the derivative equal to zero and solve for y: 26 - 4y = 0 => y = 6.5

5. Plug the value of y back into the expression for x: x = 26 - 2(6.5) => x = 13

6. Check the second derivative to confirm it's a maximum: d²P/dy² = -4 (since it's a constant negative, this confirms it's a maximum)

Thus, the optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

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Answer:

the diameter is 14 and the perimeter is 43.97

Answer:

The length of one leg of this right triangle is 4/√2 = 2√2 cm.

Answer:

Of course, I can assist you with your question. The volume of a sphere with a radius of 2.5 can be calculated using the formula (4/3)*pi*(2.5^3). This results in an answer of approximately 65.45 cubic units in terms of pi.

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EDIT: The volume of a sphere with a radius of 2.5 can be calculated using the formula V = (4/3)πr^3. Plugging in the value of r as 2.5, we get V = (4/3)π(2.5)^3. Simplifying this expression, we get V = 65.45π/3. Thus, the answer in terms of π is 65.45/3π or approximately 21.82π. None of the given options matches the calculated answer.

The equation y=−4(5)x y = − 4 ( 5 ) x can be simplified to y = -20x. This equation is a linear function with a slope of -20. As x increases, y decreases at a rate of 20 units for every one unit increase in x. Therefore, the value of y will decrease rapidly as x increases.

a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.

b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars

c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour

d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.

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Answer:

In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =

Answer:

52 degrees

Step-by-step explanation: because i looked and they looked the same so i put 52 and it was right

The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:

[tex]z = 9 - (r^2)[/tex]

The limits of integration are:

0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 9 - (r^2)

The triple integral becomes:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]

Simplifying, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]

Evaluating the innermost integral, we get:

∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]

Substituting this back into the triple integral, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]

Evaluating the remaining integrals, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]

= 2π [243/5]

= 486π/5

Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

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The given equation is 4h(x) = x - 4.

To find the domain of h(x), we need to determine the set of all possible input values for x that will result in a valid output value for h(x).

Since there are no restrictions on the input values for x in the given equation, the domain of h(x) is all real numbers.

Your answer: The domain of h(x) is all real numbers.

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The domain of the function 4h(x) = x - 4 is all real numbers, because there's no value of x that can make the equation undefined. It's represented as (-∞, ∞).

In the function 4h(x) = x - 4, the variable x is an independent variable and it can take any real number as value. Therefore, the domain of this function refers to the set of all possible x-values. In other words, the domain of this function is all real numbers.

A function's domain is essentially the set of all values that can be plugged into the function without causing problems such as division by zero or taking the square root of a negative number. In the given equation, there's nothing that would limit the possible values of x.

Therefore, the domain of h(x) in this case is all real numbers, symbolically represented as (-∞, ∞).

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You bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

Let's assume you bought x stamps that cost 45 cents each and y stamps that cost 30 cents each.

From the given information, we can create two equations:

The total number of stamps is 10: x + y = 10.

The total cost is $4.20: 45x + 30y = 420 (since the cost is given in cents).

Now we can solve this system of equations to find the values of x and y.

We can multiply the first equation by 30 to eliminate y:

30x + 30y = 300.

Now we have a system of equations:

30x + 30y = 300,

45x + 30y = 420.

Subtracting the first equation from the second equation, we get:

45x + 30y - (30x + 30y) = 420 - 300,

15x = 120,

x = 120/15,

x = 8.

Substituting the value of x back into the first equation:

8 + y = 10,

y = 10 - 8,

y = 2.

Therefore, you bought 8 stamps that cost 45 cents each and 2 stamps that cost 30 cents each.

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The given expression is a trinomial because it consists of three terms: 4x²-y+oz⁴

A trinomial is a polynomial with three terms. It is a type of algebraic expression that consists of three monomials connected by addition or subtraction. The general form of a trinomial is:

ax^2 + bx + c

A monomial is an algebraic expression that consists of a single term. It is a polynomial with only one term. A term is a combination of a coefficient and one or more variables raised to non-negative integer exponents.  The general form of a monomial is:c * xᵃ,  yᵇ, zⁿ....

where 'c' represents the coefficient (a constant), and 'x', 'y', 'z', etc., represent variables, each raised to a non-negative exponent (a, b, n, etc.).

example of monomials:  5x² - This monomial has a coefficient of 5 and a single variable 'x' raised to the power of 2.

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Answer:

Step-by-step explanation:

To solve the triangle, we can use the law of sines and the fact that the sum of the angles in a triangle is 180 degrees.

First, we can find angle A by using the fact that the sum of the angles in a triangle is 180 degrees:

A = 180 - B - C

A = 180 - 92 - 16

A = 72 degrees

Next, we can use the law of sines to find side a:

a/sin(A) = c/sin(C)

a/sin(72) = 32/sin(16)

a = (32*sin(72))/sin(16)

a ≈ 89.4

Finally, we can use the fact that the sum of the angles in a triangle is 180 degrees to find angle B:

B = 180 - A - C

B = 180 - 72 - 16

B = 92 degrees

Therefore, the triangle has angle B = 92 degrees, angle A = 72 degrees, and side a ≈ 89.4.

This is the inequality that represents all possible widths, w, in feet of the garden is W^2 + 2W - 120 ≥ 0

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. In this problem, we are given that the garden is rectangular and that the length is 2 feet longer than the width, so we can write L = W + 2.

We are also told that the area of the garden is at least 120 square feet, so we can write:
A = L x W ≥ 120
Substituting L = W + 2, we get:
(W + 2) x W ≥ 120

expanding the left side, we get:
W^2 + 2W ≥ 120
Rearranging, we get:
W^2 + 2W - 120 ≥ 0

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Answer:

B, A, C

Step-by-step explanation:

The rate is the another name for the slope.

A:

Change in y over the change in x.  You find the change by subtracting

[tex]\frac{7-3}{5-3}[/tex] = [tex]\frac{4}{2}[/tex] = 2

The rate is 2.

B:

Change in y over the change in x. You find the change by subtracting.

[tex]\frac{0-3}{-5-0}[/tex] = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

The rate is [tex]\frac{3}{5}[/tex].

C:

The rate is the number before the x in the equation.

The rate is 3.

Helping in the name of Jesus.

The area of the wheel is approximately 7.07 square feet.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this case, the diameter of the wheel is given as 3 feet, so the radius is half of that, which is 1.5 feet.

Substituting the value of the radius into the formula, we get A = π(1.5)^2. Simplifying this expression gives us approximately 7.07 square feet. Therefore, the closest answer to the area of the wheel is 7.07 square feet.

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Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

Let's assign variables to represent Angela and Walker's salaries 25 years ago. Let A be Angela's salary 25 years ago and W be Walker's salary 25 years ago.

Using the information given in the problem, we can set up two equations:

A + W = 550 (their total salary 25 years ago)
4A + 3W = 2000 (their total current salary)

To solve for A and W, we can use substitution or elimination. Let's use substitution.

From the first equation, we can rearrange to solve for A:

A = 550 - W

Substitute this into the second equation:

4(550 - W) + 3W = 2000

Distribute the 4:

2200 - 4W + 3W = 2000

Simplify:

W = 800

Now that we know Walker's salary 25 years ago was $800, we can plug that into the first equation to solve for Angela's salary:

A + 800 = 550

A = -250

Uh oh, a negative salary doesn't make sense in this context. We made a mistake somewhere.

Let's go back to our original equations and try elimination instead:

A + W = 550
4A + 3W = 2000

Multiplying the first equation by 4, we get:

4A + 4W = 2200

Subtracting the second equation from this, we get:

W = 200

Now we can plug this into either equation to solve for A:

A + 200 = 550

A = 350

So Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

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The inverse for each relation:

1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)} - {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. {(4,2),(5,1),(6,0),(7,‐1)} - {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. Inverse equation: y=(-1/8)x+3/8

4. Inverse equation: y=3/2x+15/2

5. Inverse equation: y=2x-20

6. Inverse equation: y=[tex]x^{(1/2)}+3[/tex]

7. Since fog(x) = gof(x) = x, f and g are inverse functions.

8. Since fog(x) = gof(x) = x, f and g are inverse functions.

1. To find the inverse of the relation, we need to swap the positions of x and y for each point and then solve for y.

{(1, -2), (2, 3), (3, -3), (4, 2)}

Inverse: {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. Again, we swap x and y and solve for y.

{(4, 2), (5, 1), (6, 0), (7, -1)}

Inverse: {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. To find the inverse equation for y=-8x+3, we swap x and y and solve for y.

x=-8y+3

x-3=-8y

y=(x-3)/-8

Inverse equation: y=(-1/8)x+3/8

4. To find the inverse equation for y=2/3x-5, we swap x and y and solve for y.

x=2/3y-5

x+5=2/3y

y=3/2(x+5)

Inverse equation: y=3/2x+15/2

5. To find the inverse equation for y=1/2x+10, we swap x and y and solve for y.

x=1/2y+10

x-10=1/2y

y=2(x-10)

Inverse equation: y=2x-20

6. To find the inverse equation for y=(x-3)², we swap x and y and solve for y.

x=(y-3)²

[tex]x^{(1/2)}=y-3[/tex]

[tex]y=x^{(1/2)}+3[/tex]

Inverse equation: [tex]y=x^{(1/2)}+3[/tex]

7. To verify that f(x)=5x+2 and g(x)=(x-2)/5 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x

gof(x) = g(f(x)) = g(5x+2) = ((5x+2)-2)/5 = x/5

Since fog(x) = gof(x) = x, f and g are inverse functions.

8. To verify that f(x)=1/2x-7 and g(x)=2x+14 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f(2x+14) = 1/2(2x+14) - 7 = x

gof(x) = g(f(x)) = g(1/2x-7) = 2(1/2x-7) + 14 = x

Since fog(x) = gof(x) = x, f and g are inverse functions.

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