After spending 2/5 of her money on a handbag and $20 on a belt mary had $25 left. how much money did she have at first ?

495 quadrilaterals can be formed using the given 12 points as vertices.

To answer this question, we can apply the formula to find out the number of quadrilaterals that can be formed by n points which is:  

A number of quadrilaterals that can be formed = nC4  where nC4 =  n!/(n - 4)! * 4!

Now, the number of points given is 12.

Using the formula above, we can get:

Number of quadrilaterals that can be formed

= nC4

= 12C4

= 12!/(12 - 4)! * 4!

= 495

495 quadrilaterals can be formed using the given 12 points as vertices.

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The cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

Let's call the number of miniature cycles given away "x". The number of bumper stickers given away would then be 5000 - x.

The cost of the cycles is 0.62x, and the cost of the bumper stickers is 0.52 (5000 - x).

So we can write an equation to represent the total cost:

0.62x + 0.52 (5000 - x) = 2798

Expanding the second term:

0.62x + 2600 - 0.52x = 2798

Combining like terms:

0.10x = 198

Finally, solving for x:

x = 1980

So the cycle shop gave away 1980 miniature cycles and 5000 - 1980 = 3020 bumper stickers.

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The common ratio r is 4/5, so the limit of convergence is 0. Therefore, the answer is 0.

For the sequence an = -2(5)n /(4)n, we can simplify it as follows:
an = -2(5/4)n
Since the absolute value of 5/4 is greater than 1, this sequence is divergent by the ratio test. Therefore, the answer is DIV.

For the sequence bn = (4)n/5n+1, we can write it as follows:
bn = (1/5) * (4/5)n
Since the absolute value of 4/5 is less than 1, this sequence is convergent by the geometric series test.

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Answer:

Step-by-step explanation:

To solve the given equation \(\sf x - y = 4 \\\), we can perform the following calculations:

a) To find the value of \(\sf 3(x - y) \\\):

\(\sf 3(x - y) = 3 \cdot 4 = 12 \\\)

b) To find the value of \(\sf 6x - 6y \\\):

\(\sf 6x - 6y = 6(x - y) = 6 \cdot 4 = 24 \\\)

c) To find the value of \(\sf y - x \\\):

\(\sf y - x = - (x - y) = -4 \\\)

Therefore:

a) The value of \(\sf 3(x - y) \\\) is 12.

b) The value of \(\sf 6x - 6y \\\) is 24.

c) The value of \(\sf y - x \\\) is -4.

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The estimated number of blackberry plants after 4 months is 70.86.

dN/dt = rN(1 - N/K)

where N is the number of blackberry plants, t is time, r is the monthly growth rate (0.9), and K is the carrying capacity of the yard (90 plants).

We can solve this differential equation using separation of variables:

dN/N(1 - N/K) = r dt

Integrating both sides gives:

ln|N/(K-N)| = rt + C

where C is a constant of integration. Solving for N, we get:

N = K/(1 + A e^(-rt))

where A is a constant such that A = (K/N0) - 1, where N0 is the initial number of plants.

r = 0.9 (monthly growth rate)

K = 90 (carrying capacity)

N0 = 9 (initial number of plants)

t = 4 (time in months)

We can first find A:

A = (K/N0) - 1 = (90/9) - 1 = 9 - 1 = 8

Plugging in the values, we get:

N = 90 / (1 + 8 e^(-0.9*4)) = 70.86

Therefore, the estimated number of blackberry plants after 4 months is 70.86.

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True. When performing econometric analysis on time-series data, it is a best practice to sort the data in chronological order. Econometric analysis involves using statistical methods to study and understand economic relationships, trends, and patterns.

Time-series data refers to a set of observations collected at regular intervals over time, such as stock prices, GDP growth, or unemployment rates.

Sorting the data in chronological order is essential because it allows for a proper understanding of the temporal relationship between different data points. This ordering helps researchers identify patterns, trends, and potential causal relationships within the data. Additionally, many econometric models, such as autoregressive or moving average models, rely on the assumption that the data points are arranged sequentially in time.

In summary, when conducting econometric analysis on time-series data, it is crucial to sort the data in chronological order to accurately analyze patterns, trends, and relationships. This practice enables researchers to develop robust models that can be used for forecasting and understanding the underlying economic processes.

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A committee consists of 11 men and 12 women. In 304,920 ways can a subcommittee of 4 men and 6 women be chosen

To solve this problem, we will use the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of people (in this case, 23), r is the number of people we want to choose (4 men and 6 women), and ! means factorial (the product of all positive integers up to that number).

First, we need to find the number of ways we can choose 4 men from the 11 available. This is:

11C4 = 11! / (4! * 7!) = 330

Next, we need to find the number of ways we can choose 6 women from the 12 available. This is:

12C6 = 12! / (6! * 6!) = 924

To find the total number of ways we can choose a subcommittee of 4 men and 6 women, we need to multiply these two numbers:

330 * 924 = 304,920

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After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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Answer:

True

Explanation:

A proportion states the equality of two fractions. It is an equation that shows that two fractions are equivalent to each other.

Looking at the given statement;

10 altos for every 16 sopranos, 5 altos for every 8 sopranos.

This can be expressed as;

And we can see that the two fractions are equivalent, if we divide the numerator and denominator of the 1st fraction by 2 we'll have the 2nd fraction.

We can determine whether two lines are parallel, perpendicular, or neither using the slopes of the lines.

Two lines are parallel when both of the lines have the same slope, for example:

Two lines are perpendicular to each other when the product between the lines is equal to -1, for example:

if none of the conditions stated before the lines are neither parallel nor perpendicular.

In the given exercise:

both lines have different slopes, then they are not parallel.

Find the product between the slopes,

Answer:

The lines shown are perpendicular to each other because the product between the slopes is equal to -1.

The values of the samples are:

a.) P(y₁<=3/4, y₂<=3/4) = 7/8

b.) P(y₁<=1/2, y₂<=1/2) = 1/2

For this case we have two random variables Y1 and Y2, the joint density function is given by:

f(y₁,y₂(=2, ≤ y₁ ≤ 1, 0 ≤ y₂ ≤y₂, 0 ≤ y₁+y₂ ≤1

And 0 for other case.

We know that Y₁+Y₂≤1

Let Y1 =X and Y2 =Y we can plot the joint density function. First we need to solve the slope line equation from the condition y₁+y₂≤1

And we got that y₂≤1 - y₁ or equivalently in our notation y ≤ 1-x . And we know that the two random variables are between 0 and 1. So then the joint density plot would be given on the figure attached.

Part a

In order to find the probability that:

P(Y₁<=3/4, Y₂<=3/4) we can use the second figure attached.

We see that we have two triangles with the same Area, on this case  

A = bh/2 = 1/4×1/4/2 and then the total area for both triangles is

At = 2 ×1/4×1/4/2

Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :

Vt = 2 ×  2 ×1/4×1/4/2

And then we can find the probability like this:

P(Y₁<=3/4, Y₂<=3/4) = 1 -  2 ×  2 ×1/4×1/4/2

= 7/8

Part b

For this case w want this probability:

P(Y₁<=1/2, Y₂<=1/2)  we can use the third figure attached.

We see that we have two triangles with the same Area, on this case  

A = bh/2 = 1/2×1/2/2 and then the total area for both triangles is

At = 2 ×1/2×1/2/2

Since our density function have a height of 2 since the joint density is equal to 2 then we can find the volume for the two triangles like this :

Vt = 2 ×  2 ×1/2×1/2/2

And then we can find the probability like this:

P(Y₁<=1/2, Y₂<=1/2) = 1 -  2 ×  2 ×1/2×1/2/2

= 1/2

Hence we get the required answer.

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When interpreting the proportion of confidence intervals that capture the true mean failure time, it is crucial to assess whether the underlying assumptions of your specific analysis have been met.

In repeated sampling, the proportion of confidence intervals that capture the true mean failure time is equal to the confidence level associated with the interval.

For example, if you compute 95% confidence intervals for each sample, then approximately 95% of the confidence intervals will capture the true mean failure time in the long run.

The confidence level represents the probability that the interval contains the true population parameter. It quantifies the level of uncertainty or margin of error associated with the estimation.

It's important to note that this interpretation holds true when the assumptions of the statistical method used to construct the confidence intervals are met. The most common assumption is that the sampled data follow a normal distribution or that the sample size is sufficiently large for the Central Limit Theorem to apply. Violations of these assumptions can affect the coverage properties of the confidence intervals.

Therefore, when interpreting the proportion of confidence intervals that capture the true mean failure time, it is crucial to assess whether the underlying assumptions of your specific analysis have been met.

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Answer: D

Step-by-step explanation:

D would be the line segment closest to having a 90 degree angle.

Answer:

Step-by-step explanation:

D

Adding all the sides we will get that the perimeter is 50 units.

The perimeter of the triangle will be equal to:;

P = JK + KL + LJ

We know that:

JA= 6 units.

JL = 12 units

CK = 13 units

And all the lines are tangent to the circle, that means that:

JL = JK = 12 units.

And KL = 2*CK = 2*13 = 26

Adding these we get:

P = JK + KL + LJ

P = 12 + 12  + 26

P = 24 + 26 = 50

That is the perimeter.

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Answer:

Step-by-step explanation:

I am sorry but please give detailed question

The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

To find the p-value from the t statistic on TI-84, you will need to perform a hypothesis test. Here are the steps:1. Enter your data into the calculator and choose the appropriate test.2. Calculate the t statistic by dividing the sample mean by the standard error.3. Determine the degrees of freedom. This is n-1 for a one-sample t-test or n1+n2-2 for a two-sample t-test. 4. Use the t-distribution table to find the critical value for your test.5. Calculate the p-value using the t-distribution function on the calculator.6. Compare the p-value to the significance level (usually 0.05) to determine whether to reject or fail to reject the null hypothesis.7.

Therefore, The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. If the p-value is less than the significance level, reject the null hypothesis; otherwise, fail to reject it.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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The volume of the cone, to the nearest whole number, is: 50 cm³.

The volume of a cone is defined as the amount of space it contains. The volume can be calculated using the formula:

Volume of cone = 1/3 × π × r² × h, where h is the height of the cone, and r is the radius of the cone.

Given the parameters:

Plug in the values:

Volume of the cone = 1/3 × π × 4² × 3

Volume of the cone = 1/3 × π × 16 × 3

Volume of the cone = 16π

Volume of the cone = 50 cm³

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Answer: 6/5 and -3/4

Step-by-step explanation:

(2x-3)/9=(3x-4)/6

18*(2x-3)/9=18*(3x-4)/6

2(2x-3)=3*(3x-4)

4x-6=9x-12

-5x=-6

x=6/5

(8x+2)/4=4x/3

12*(8x+2)/4=12*4x/3

3(8x+2)=4*4x

24x+6=16x

8x=-6

x=-3/4

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

We have,

a) To calculate the pressure in the production well at 12 hours of a shut-in, we can use the equation for pressure transient analysis during shut-in periods, known as the pressure buildup equation:

P(t) = Pi + (Q / (4πKh)) * log((0.14ϕμCt(t + Δt)) / (Bo(ΔP + Δt)))

Where:

P(t) = Pressure at time t

Pi = Initial reservoir pressure

Q = Flow rate

K = Permeability

h = Reservoir thickness

ϕ = Porosity

μ = Viscosity

Ct = Total compressibility

t = Shut-in time (12 hours)

Δt = Time since the start of the flow period

Bo = Oil formation volume factor

ΔP = Pressure drop during the flow period

Given:

Pi = 3100 psi

Q = 200 STB/day

K = 45 md

h = 60 ft

ϕ = 15%

μ = 1.2 cp

Ct = 15x10^-6 psi^-1

Bo = 1.3 bbl/STB

t = 12 hours

Δt = 48 hours

ΔP = Pi - P(t=Δt) = Pi - (Q / (4πKh)) * log((0.14ϕμCt(Δt + Δt)) / (Bo(ΔP + Δt)))

Substituting the given values into the equation:

ΔP = 3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15x\(10^{-6}\) * (48 + 48)) / (1.3 * (3100 - (200 / (4π * 45 * 60)) * log((0.14 * 0.15 * 1.2 * 15 x \(10^{-6}\) * (48 + 48)) / (1.3 * (0 + 48))))))

After evaluating the equation, we can find the pressure in the production well at 12 hours of shut-in.

b) Superposition in time is a principle used in pressure transient analysis to analyze and interpret pressure build-up tests.

It involves adding or superimposing the responses of multiple transient tests to simulate the pressure behavior of a reservoir.

The principle of superposition states that the response of a reservoir to a series of pressure changes is the sum of the individual responses to each change.

Superposition allows us to combine the information obtained from multiple tests and obtain a more comprehensive understanding of the reservoir's behavior and properties.

It is a powerful technique used in reservoir engineering to optimize production strategies and make informed decisions regarding reservoir management.

Thus,

a) To calculate the pressure at 12 hours of shut-in:

substitute the given values into the pressure buildup equation and solve for P(t=12).

b) Superposition in time is used in pressure buildup analysis by adding or summing the responses of multiple transient tests to analyze and interpret reservoir behavior and properties.

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Change management is a significant challenge for many organizations during enterprise system implementation due to various factors such as resistance to change, organizational culture, lack of employee engagement, and inadequate communication and training.

During enterprise system implementation, organizations typically undergo significant changes in processes, roles, and technologies. This can lead to resistance from employees who may be accustomed to existing ways of working. Resistance to change can hinder the adoption and utilization of the new system, affecting its success.

Organizational culture also plays a role. If the organization has a rigid or hierarchical culture that is resistant to change or lacks a culture of innovation and learning, it becomes difficult to implement and integrate the new system effectively.

Lack of employee engagement and involvement in the implementation process can further impede change. Employees need to understand the reasons behind the change, how it will benefit them and the organization, and be provided opportunities for input and feedback.

Inadequate communication and training can be a major obstacle. Employees must be informed about the changes, their roles and responsibilities, and be provided with sufficient training to effectively use the new system. Insufficient communication and training can lead to confusion, frustration, and resistance.

Overall, change management is crucial during enterprise system implementation to address these challenges and ensure a smooth transition, user acceptance, and successful adoption of the new system.

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The exact values for each trigonometric function are:

(a) cos(θ) = -√7/4

(b) tan(θ) = 3√7 / 7

(c) sec(θ) = -4√7 / 7

(d) csc(θ) = -4/3

(e) cot(θ) = √7 / 3.

Given that sin(θ) = -3/4 and θ is in quadrant III, we can determine the values of the trigonometric functions as follows:

(a) cos(θ):

In quadrant III, cosine is negative. We can use the Pythagorean identity to find the value of cos(θ):

cos(θ) = -√(1 - sin²(θ)) = -√(1 - (-3/4)²) = -√(1 - 9/16) = -√(7/16) = -√7/4.

(b) tan(θ):

To find tan(θ), we can use the identity: tan(θ) = sin(θ) / cos(θ):

tan(θ) = (-3/4) / (-√7/4) = 3√7 / 7.

(c) sec(θ):

sec(θ) is the reciprocal of cos(θ):

sec(θ) = 1 / cos(θ) = 1 / (-√7/4) = -4 / √7 = -4√7 / 7.

(d) csc(θ):

csc(θ) is the reciprocal of sin(θ):

csc(θ) = 1 / sin(θ) = 1 / (-3/4) = -4/3.

(e) cot(θ):

cot(θ) is the reciprocal of tan(θ):

cot(θ) = 1 / tan(θ) = 1 / (3√7 / 7) = 7 / (3√7) = 7√7 / 21 = √7 / 3.

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Answer:

p = 6.95 + (0.95 × t)

Step-by-step explanation:

A function rule explains how to convert an input value (x) into an output value (y) for any given function.

To get the total price (p) we need to add the cost of the pizza itself, and add each topping. The part of the equation (0.95 × t) can solve for the price of each topping, so we add that on.

In general, given a function f(x), a horizontal translation by b units is expressed by the transformation below

The graph of the function is

1. The contrapositive of the statement "If a graph G has an Euler circuit, then G is not a tree" is: "If a graph G is a tree, then G does not have an Euler circuit."

2. The formal negation of the statement "VIED, 2€ E" is: "There exists an x such that x is not an element of E."

3. The probability of ending up with 4 green balls is 1/14.

1. The contrapositive of a conditional statement swaps the hypothesis and the conclusion, and negates both. In the original statement, the hypothesis is "G has an Euler circuit" and the conclusion is "G is not a tree." In the contrapositive, the hypothesis becomes "G is a tree" (negating the original conclusion) and the conclusion becomes "G does not have an Euler circuit" (negating the original hypothesis).

2. The statement "VIED, 2€ E" can be translated as "For all x, x is an element of E." The negation of a universal quantifier (∀) is an existential quantifier (∃), and the negation of "x is an element of E" is "x is not an element of E." Therefore, the formal negation is "There exists an x such that x is not an element of E."

3. To calculate the probability of ending up with 4 green balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of possible outcomes = Total number of ways to pick 4 balls from the 8 available balls = C(8, 4) = 70.

Number of favorable outcomes = Number of ways to pick 4 green balls from the 5 available green balls = C(5, 4) = 5.

Probability = Number of favorable outcomes / Total number of possible outcomes = 5/70 = 1/14.

Therefore, the probability of ending up with 4 green balls is 1/14.

In this scenario, there are 8 balls in total, with 3 red balls and 5 green balls. We need to pick 4 balls without replacement. The total number of possible outcomes is given by the combination formula C(n, k), which calculates the number of ways to choose k items from a set of n items. In this case, we want to pick 4 balls out of the 8 available balls.

To determine the number of favorable outcomes, we only consider the green balls since we want to end up with 4 green balls. We calculate the number of ways to choose 4 green balls out of the 5 available green balls.

Finally, we divide the number of favorable outcomes by the total number of possible outcomes to obtain the probability. In this case, the probability is 1/14.

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The Linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

The point-slope equation for a line is of the form y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope of the line. Given the point-slope equation y - 5 = 3(x - 2),

we can see that the slope of the line is 3 and it passes through the point (2, 5).

To find the linear function for the line, we need to write the equation in slope-intercept form, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line intersects the y-axis).

To get the equation in slope-intercept form, we need to isolate y on one side of the equation.

We can do this by distributing the 3 to the x term:y - 5 = 3(x - 2)  y - 5 = 3x - 6  y = 3x - 6 + 5  y = 3x - 1

Therefore, the linear function for the line represented by the point-slope equation y - 5 = 3(x - 2) is y = 3x - 1.

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The induction principle can be proven from the well-ordering principle through a contradiction.

The well-ordering principle states that every non-empty set of positive integers has a least element. We can prove the induction principle by assuming its negation and arriving at a contradiction.

Assume that there exists a set A of positive integers for which the induction principle does not hold. This means there must be a smallest positive integer, n, for which the statement is false. Let B be the set of positive integers for which the statement is true.

Since n is the smallest positive integer for which the statement fails, we know that n-1 must be in B. If it were not, then the statement would hold for n-1, contradicting the assumption that n is the smallest counterexample.

However, if n-1 is in B, then by the induction principle, the statement must also hold for n. This contradicts our assumption that n is a counterexample, leading to a contradiction.

Therefore, our assumption that a counterexample exists is false, proving the induction principle.

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A real-world example of how piecewise functions can be used is in:

Modeling electricity pricing, where different rates are said to be used for different usage tiers.

Calculating income tax based on different types of income brackets.

Here, we have,

Piecewise functions are tools that are often used for representing ways where the connection between variables alters under varying intervals or conditions.

To demonstrate the application of piecewise functions, consider the following example such as  calculating taxes on income. where a different nations implement an income tax system that make use of a segmented function to determine tax rates based on various income brackets.

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complete question;

What’s a real world example of how piece wise functions can be used?