The length of a rectangle is 5 cm less than 3 times its width. If the perimeter is 54 cm, find its length.

The area of a circle with a diameter of radius 14 inches is given as follows:

A = 153.86 inches².

The area of a circle of radius r is given by π multiplied by the radius squared, as follows:

A = πr².

The radius, representing the distance between the center and a point on the circumference of the circle, has the measure defined as half the diameter, hence it is given as follows:

r = 7 inches.

Hence the area of the circle with radius of 7 inches is given as follows:

A = 3.19 x 7²

A = 153.86 inches².

More can be learned about the area of a circle at https://brainly.com/question/15673093

#SPJ1

Answer:

B 3

notice that beside the 30 degree there is also 90 degree. please see the attachment.

Answer:

Step-by-step explanation:

What are you trying to do?

It's hard ot understand the problem.

Answer:

The image of point (–2, –3)C under the translation would be point (–4, –3)C.

The equation of the circle has the following format:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

In which:

The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

From the figure, you must identify the coordinates of the center, and then replace the given point [tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex] into the equation to solve for the radius r.

The problem is incomplete, hence the procedure to obtain the equation of the circle was presented.

More can be learned about the equation of a circle at https://brainly.com/question/1506955

#SPJ1

Answer: i think its 20

Answer:

1 2/3 x 12 = 20

Step-by-step explanation:

1 2/3 x 12  = 5/3 x 12

5x12/ 3 x 1

60/3

60/3 / 3/3

= 20

Answer:

1/52

4/52 == 1/13

13/52 == 1/4

12/52 == 6/26 == 3/13

48/52 == 12/13

3/51

The statement describes a sample. Specifically, it is referring to the amount of money each person in your world history class spends renting movies in a week. The class is a subset of a larger population, and the statement is only referring to the sample within that population.

By incorporating members of all demographic categories (gender, rural/urban, economic levels, etc.) and having them in the same proportions as the entire population, your sample must be representative of the general population. If there are excessive numbers of participants from rural areas, men, etc., it is not truly representative.

Response and justification: A population is the sum of money each student in your global history class spends each week on movie rentals. Because each member of the group is included in the study, this is a population.

To know more describes a population visit:

https://brainly.com/question/13794992

#SPJ1

Answer:

the wholesale discount is 28%.

Step-by-step explanation:

To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:

Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%

Substituting the given values into the formula, we get:

Wholesale discount = ((1320 - 950.40) / 1320) x 100%

Wholesale discount = (369.60 / 1320) x 100%

Wholesale discount = 0.28 x 100%

Therefore, the wholesale discount is 28%.

To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:

Wholesale discount = 28%

So the wholesale discount is 28%.

Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

By connecting two expressions with an equal sign, a mathematical statement known as an equation is produced. An equation is something like 3x - 5 = 16. The answer of this equation, which indicates that the value of the variable x is 7, is 7.

To solve for y in the equation Ay + 3y + 9 = 27, we need to isolate y on one side of the equation. We can do this by first combining the like terms on the left-hand side of the equation, and then subtracting 9 from both sides to get:

Ay + 3y = 18

Next, we can factor out the y term on the left-hand side:

y(A + 3) = 18

Finally, we can solve for y by dividing both sides by (A + 3):

y = 18 / (A + 3)

Therefore, the solution for y is y = 18 / (A + 3).

To know more about equation visit:

https://brainly.com/question/29657992

#SPJ1

Answer: 17:20pm

Step-by-step explanation: If you add 24 minutes to 14:46, that gives you 15:20pm. Add the 2 hours. So your answer is 17:20pm

Answer:

Step-by-step explanation:

cos(2[tex]\sqrt{23}[/tex]/24)=β

0.9999=β

1=β

The sum of interior angles of the polygon is 900 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. Therefore, a polygon is named according to the number of sides. For example we have triangles, hexagon, pentagon, quadrilaterals, heptagons, nonagon, decagons etc.

Therefore, the polygon in the diagram has seven sides. Hence its an heptagon.

The sum of interior angles of a heptagon can be found as follows:

sum of interior angles = 180(n - 2)

where

sum of interior angles = 180(7 - 2)

sum of interior angles = 180(5)

Therefore,

sum of interior angles = 900 degrees

learn more on polygon here: https://brainly.com/question/29774899

#SPJ1

The sum of the interior angle of the polygon is 900^o.

A polygon is a plane shape which has three or more number of sides. The important thing about polygons is that they are named according to their number of sides. Some common examples are: trigon- 3 sides, pentagon- 5 sides, heptagon - 7 sides etc.

The sum of internal angles of a polygon = (n - 2)180

where n is the number of sides of the polygon

In the given diagram, the polygon has 7 sides, thus it is a heptagon. Thus n is 7, so that;

sum of internal angles of a heptagon = (n - 2)180        

                                            = (7 - 2)180

                                            = 5*180

                                            = 900

Therefore, the sum of the interior angles of the polygon is 900^o.

Learn more about polygons at https://brainly.com/question/20606675

#SPJ1

Yes, they are statistically different.

Statistical significance is a term used to indicate that a result from a statistical test is likely to be reliable and reproducible. It is the probability that a result is caused by something other than random chance. Statistical significance is usually determined by calculating the probability, or p-value, that the result occurred by chance. A result is deemed to be statistically significant if the p-value is below a certain threshold. This threshold is typically set at 0.05, but can be adjusted depending on the study.

A p-value below 0.05 is generally considered to be statistically significant, indicating that the differences observed between the two groups are unlikely to have occurred by chance. In this case, a p-value of 0.03 is well below the threshold, indicating that the two groups are statistically different

To know more about Statistical Significance, visit:

https://brainly.com/question/15848236

#SPJ1

cos(0) and sin(0) both have a value of 0, so they would be selected.

cos(pi)/2 is equal to -0.5, and sin(3(pi)/2) is equal to -1, so they would not be selected.

Answer:

1 | 3 | 5

Step-by-step explanation:

sin 0 sin 3pi/2 and tan pi

cos pi/2 is -.5

cos 0 is 1

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform a simple linear regression. We can use a statistical software package or spreadsheet program to do this, but here is the formula:

y = b0 + b1x

where:

y = price per share

x = annual dividend

b0 = y-intercept (constant)

b1 = slope (regression coefficient)

Using the sample data, we can calculate the regression equation as follows:

mean(x) = 9.8567

mean(y) = 53.0357

SSxx = Σ(x - mean(x))² = 7569.6844

SSxy = Σ(x - mean(x))(y - mean(y)) = 4542.4061

b1 = SSxy / SSxx = 4542.4061 / 7569.6844 = 0.6004

b0 = mean(y) - b1 * mean(x) = 53.0357 - 0.6004 * 9.8567 = 47.4759

Therefore, the regression equation is:

y = 47.4759 + 0.6004x

b. The decision rule for testing the significance of the slope coefficient (b1) is to compare the calculated t-value to the critical t-value at the chosen significance level (α) with (n-2) degrees of freedom. For this problem, we will use α = 0.05 and n = 30, so the degrees of freedom is 28. The null hypothesis is that the slope coefficient is equal to zero (i.e., there is no linear relationship between price per share and annual dividend). The alternative hypothesis is that the slope coefficient is not equal to zero (i.e., there is a linear relationship).

c. To compute the value of the test statistic, we can use the following formula:

t = b1 / (SEb1)

where:

SEb1 = standard error of the slope coefficient

SEb1 = sqrt(MSE / SSxx)

MSE = mean squared error

MSE = SSres / (n - 2)

SSres = residual sum of squares

Using the sample data, we can calculate the test statistic as follows:

SSres = Σ(y - ŷ)² = 583.8319

MSE = SSres / (n - 2) = 20.8518

SEb1 = sqrt(MSE / SSxx) = 0.0798

t = 0.6004 / 0.0798 = 7.526

d. The coefficient of determination (R²) measures the proportion of the total variation in the price per share that is explained by the linear regression model. We can calculate it using the following formula:

R² = SSreg / SStot

where:

SSreg = regression sum of squares

SSreg = b1² * SSxx

SStot = total sum of squares

SStot = Σ(y - mean(y))²

Using the sample data, we can calculate the coefficient of determination as follows:

SSreg = b1² * SSxx = 1707.4612

SStot = Σ(y - mean(y))² = 1866.6219

R² = SSreg / SStot = 0.9145

Therefore, 91.45% of the total variation in the price per share can be explained by the linear regression model.

(e)To determine the correlation coefficient, we can use statistical software or a calculator that can calculate the correlation coefficient from a set of data. Using a software or calculator, we get:

Correlation coefficient (r) = 0.7709

Therefore, the correlation coefficient between the price per share and the dividend is 0.7709. This indicates a strong positive correlation between these two variables.

Answer:

Step-by-step explanation:

a. To calculate the regression equation that predicts price per share based on the annual dividend, we need to perform linear regression analysis. We can use a statistical software or spreadsheet to do this. The results are:

Regression equation: price per share = 14.393 + 1.201(dividend)

Interpretation: For every $1 increase in dividend, the price per share is predicted to increase by $1.201, holding all other variables constant.

b. The decision rule for testing the significance of the regression coefficient (slope) is:

H0: β1 = 0 (the slope is not significantly different from 0)

Ha: β1 ≠ 0 (the slope is significantly different from 0)

Test statistic: t = (b1 - 0) / SE(b1)

Rejection region: t < -tα/2,n-2 or t > tα/2,n-2, where α = 0.05 and n-2 = 28 degrees of freedom

c. The value of the test statistic is:

t = (1.201 - 0) / 0.177 = 6.79 (rounded to two decimal places)

d. The coefficient of determination (R-squared) is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variable(s). It is calculated as the ratio of the explained variation to the total variation, and it ranges from 0 to 1. The formula is:

R-squared = explained variation / total variation

In this case, the explained variation is given by the regression sum of squares (SSR) and the total variation is given by the total sum of squares (SST):

SSR = Σ(y-hat - y-bar)^2 = 6418.95

SST = Σ(y - y-bar)^2 = 12345.44

Therefore, the coefficient of determination is:

R-squared = SSR / SST = 6418.95 / 12345.44 = 0.52 (rounded to two decimal places)

Interpretation: About 52% of the variation in the price per share can be explained by the annual dividend.

e. The correlation coefficient (r) measures the strength and direction of the linear relationship between the two variables. It ranges from -1 to +1, with values closer to -1 or +1 indicating a stronger relationship. The formula is:

r = cov(x,y) / (SD(x) * SD(y))

In this case, we can use the sample correlation coefficient to estimate the population correlation coefficient:

r = cov(price, dividend) / (SD(price) * SD(dividend))

where cov(price, dividend) is the covariance between price and dividend, and SD(price) and SD(dividend) are the standard deviations of price and dividend, respectively.

Using the formula or a spreadsheet, we get:

cov(price, dividend) = Σ[(price - mean price)*(dividend - mean dividend)] / (n - 1) = 417.25

SD(price) = 18.14

SD(dividend) = 6.10

Therefore, the correlation coefficient is:

r = 417.25 / (18.14 * 6.10) = 0.73 (rounded to two decimal places)

Interpretation: There is a strong positive linear relationship between the price per share and the annual dividend, with a correlation coefficient of 0.73.

The vertical function of the ball can be modelled using the equation h(t) = 16t^2 + 75t + 4, where h(t) is the height of the ball at time t, 16 is the acceleration due to gravity, 75 is the initial velocity of the ball, and 4 is the initial height of the ball.

Acceleration due to gravity is the rate of change of velocity (speed) of an object in free fall due to the force of gravity. It is denoted by g and is equal to 9.80665 m/s2 at sea level. It is the force of gravity that causes objects to fall to the ground and accelerates them as they approach the ground. When an object is in free fall, it accelerates at a rate of 9.8 m/s2. This means that after one second, the object will be travelling at 9.8 m/s, after two seconds it will be travelling at 19.6 m/s, and so on. Without the force of gravity, objects would not accelerate in free fall.

The equation h(t) = 16t^2 + 75t + 4 models the vertical function of the ball by combining the effects of acceleration due to gravity (16), initial velocity (75), and initial height (4). The term 16t^2 represents the acceleration due to gravity, which causes the ball to accelerate in the vertical direction at a rate of 16 meters per second squared. The term 75t represents the initial velocity of the ball, which causes the ball to move in the vertical direction at a rate of 75 meters per second. Finally, the term 4 represents the initial height of the ball, which is 4 meters. By combining these three effects, the equation h(t) = 16t^2 + 75t + 4 accurately models the vertical function of the ball.

To know more about Acceleration due to gravity, visit:

https://brainly.com/question/88039

#SPJ1

The average rate of change in the cost of the hamburger during the period of 2012 to 2022 is 0.18.

The equation is y = 0.18x + 4.32 and the cost will be $7.02 in 2027.

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

(a) Given that,

Cost of hamburger in 2012 = $4.32

Cost of hamburger in 2022 = $6.12

Average rate of change = (6.12 - 4.32) / (2022 - 2012)

                                        = 0.18

(b) Linear equation can be written in slope intercept form as y = mx + c, where m is the slope and c is the y intercept.

Slope of a linear equation is equal to the average rate of change.

m = 0.18

y intercept is the value of the y coordinate when x = 0.

In this case, y intercept is the cost of hamburger in the initial year, 2012.

c = 4.32

So the equation is,

y = 0.18x + 4.32

(c) Price of the hamburger will reach $7.02, when,

7.02 = 0.18x + 4.32

0.18x = 2.7

x = 15

Price will reach $7.02 in the year = 2012 + 15 = 2027

Hence the cost of the hamburger will be $7.02 in the year 2027 using the linear model y = 0.18x + 4.32.

Learn more about Linear Equations here :

https://brainly.com/question/11897796

#SPJ1

The union member worked 176 hours during the month of March.

Dues are the payment or obligation required by law or custom, it is like a monthly payment, fees or charges made by organizations.

Let h be the number of hours worked during the month of March by the union member.

According to the problem statement, the union charges monthly dues of $5.00 plus $0.15 for each hour worked during the month.

So, the total dues for the month of March can be expressed as -

Total dues = $5.00 + $0.15 x h

It is also given that the union member's dues for March were $31.40.

Set up an equation using this information as follows -

$31.40 = $5.00 + $0.15 x h

To solve for h, isolate the variable on one side of the equation.

Start by subtracting $5.00 from both sides -

$31.40 - $5.00 = $0.15 x h

Simplifying the left side gives -

$26.40 = $0.15 x h

To solve for h, divide both sides by $0.15 -

h = $26.40 / $0.15

h = 176

Therefore, the number of hours is 176.

To learn more about dues from the given link

brainly.com/question/16881685

#SPJ1

Answer:

4095 yd³

The volume of any figure is the total space enclosed inside of any figure. For example, the total space inside the cube is the volume of the cube. The formula to find the volume of a cube is (side)³ or (side)(side)(side) Please also note that volume is usually labelled in cubic units.

Here, we are given a figure that is 3-dimensional. Therefore, the volume of this 3-dimensional figure must be in cubic units. We can also see that the figure has been split into two 3-dimensional figures. Thus, the sum of those divided 3-dimensional figures will result in the volume of the figure.

Step-1) Find the volume of both 3-dimensional figures:

Volume of cuboid = Length × Width × Height

Volume of trapezoidal prism = Area of base × Length

Step-2) Add the volumes of both prisms.

Volume of figure = Volume of cuboid + Volume of trapezoidal prism

Volume of figure = 1890 yd³ + 2205 yd³ = 4095 yd³

Learn more about volumes: https://brainly.com/question/22907480

You'll need a ruler that has "centimeters" on it.

Use the ruler to measure the distance from Town Hall to the Art Gallery.

I don't have a ruler with me, so I can't say for certain what that centimeter distance will be. Even if I had a ruler, it won't be much use because I cant put it directly to the paper. Only you are able to do that part. But I'll go over a hypothetical example.

Let's say the on paper distance from Town Hall to the Art Gallery is 5 cm (roughly 1.97 inches).

This means we multiply both sides by 5 in the steps shown below.

1 cm on paper : 200 m in real life

5*1 cm on paper : 5*200 m in real life

5 cm on paper : 1000 m in real life

5 cm on paper : 1 km in real life

So the 5 centimeters measured out with the ruler corresponds to the real life distance of 1 kilometer. This would be the real life distance from Town Hall to the Art Gallery. Again, this is a hypothetical example. The actual centimeter distance is likely different and you'll need to get a ruler to measure it out for yourself.

Let me know if this helps. If you have further questions, then please let me know.

The numbers in the set can be compared by placing them in the number line, arranging the numbers from least to greatest as follows;

[tex]|-2\frac{1}{2} |[/tex], [tex]-\frac{1}{2}[/tex], [tex]1\frac{1}{2}[/tex], [tex]|\frac{1}{2} |[/tex] |-2|, [tex]-2\frac{1}{2}[/tex]

A number line is a series of numbers placed on the a line at regular intervals that can be used to express mathematical operations.

The elements in the set includes;

|-2 1/2|, -1/2, 1 1/2, |1/2|, |-2|, -2 1/2

The numbers within the absolute sign have a positive result, therefore;

|-2 1/2| = 2 1/2

|-2| = 2

The numbers in the set can be arranged in the order from least to the greatest as follows;

The above ordered numbers indicates that the specified numbers arranged in order from least to the greatest are;

Learn more on absolute values here: https://brainly.com/question/12928519

#SPJ1

The proposition in this set of options is:

A. Aristotle was born in northern Greece.

A proposition is a key idea in philosophy of language and related disciplines, and it is frequently referred to as the main carrier of truth or untruth. The kind of object that declarative sentences signify is another way that propositions are frequently described. The statement "The sky is blue," for example, expresses the idea that the sky is blue.

A proposition is a statement that can either be true or false. Therefore, the proposition in this set of options is:

A. Aristotle was born in northern Greece.

This is a proposition because it is a statement that can be evaluated as true or false. The other options are not propositions:

B. This is a question and not a statement, so it is not a proposition.

C. This is an equation, not a statement, so it is not a proposition.

D. This is a command, not a statement, so it is not a proposition.

Learn more about proposition , visit:

https://brainly.com/question/14789062

#SPJ1

Answer: The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

Step-by-step explanation: We know,

Area of the square = p^2 where p is the side of the square.

The perimeter of the square = 4p cm where p is the side of the square.

thus, The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

Internal Links: https://brainly.com/question/30769756?answering=false&answeringSource=feedQP

Answer:

3000 x 1.02^10 = 3656.98.. = 3656 people

Answer:

Step-by-step explanation:

To find the left-hand derivative of f at x = 4, we need to evaluate:

f′−(4) = limh→0−f(4+h)−f(4)h

Since f(x) = 0 for x ≤ 0 and f(x) = 5 - x for 0 < x < 5, we have:

f(4 + h) = 0 for h < -4

f(4 + h) = 5 - (4 + h) = 1 - h for -4 < h < 1

f(4 + h) = undefined for h > 1

Therefore, we can rewrite the limit as:

f′−(4) = limh→0−f(4+h)−f(4)h = limh→0−(1 - h) - 0h = -1

To find the right-hand derivative of f at x = 4, we need to evaluate:

f′+(4) = limh→0+f(4+h)−f(4)h

Using the same reasoning as before, we can rewrite the limit as:

f′+(4) = limh→0+(5 - (4 + h)) - 0h = -1

Since the left-hand derivative and the right-hand derivative are equal, we can conclude that f'(4) exists and is equal to:

f'(4) = f′−(4) = f′+(4) = -1

Therefore, the derivative of f at x = 4 is -1.

Standard error of the mean = 148.75 / sqrt (25) = 29.75

sampling distribution of the mean.

According to the central limit theorem, if the sample size is large enough (typically, n ≥ 30), the sampling distribution of the mean will be approximately normal, regardless of the underlying distribution of the population. In this case, we have a sample size of 25, which is less than 30, but we can still assume that the sampling distribution of the mean will be approximately normal, as the population distribution is not specified and the sample size is not too small.

The mean of the sampling distribution of the mean will be equal to the population mean, which is 223.17 in this case. The standard deviation of the sampling distribution of the mean, also known as the standard error of the mean, will be equal to the population standard deviation divided by the square root of the sample size. Therefore, the standard error of the mean in this case is:

Standard error of the mean = 148.75 / sqrt(25) = 29.75

So, if we take all possible samples of 25 children of preschool age in this school district and calculate the mean of each sample, the distribution of these means will be approximately normal with a mean of 223.17 and a standard deviation of 29.75, assuming

To more about average : https://brainly.com/question/24057012

#SPJ1

The solution to the system of equation 2x - 3y = 4 and -2x + 6y = -10 is (-1,-2).

Given the system of equation in the question;

2x - 3y = 4

-2x + 6y = -10

First, solve for y in equation one.

2x - 3y = 4

2x - 4 = 3y

3y = 2x - 4

Divide each term by 3

y = (2/3)x - 4/3

Now, solve the system of equation, plug y = (2/3) - 4/3 into equation two and solve for x.

-2x + 6y =-10

Plug in y = (2/3) - 4/3

-2x + 6( (2/3)x - 4/3 ) = -10

Simplify

-2x + 4x - 8  = -10

2x - 8 = - 10

2x = -10 + 8

2x = -2

x = -2/2

x = -1

Now, plug x = -1 into equation two and solve for y.

-2x + 6y = -10

Plug in x = -1

-2( -1 ) + 6y = -10

2 + 6y = -10

6y = -10 - 2

6y = -12

y = -12/6

y = -2

Therefore, the value of x is -1 and y is -2.

Learn more about simultaneous equation here: brainly.com/question/30319215

#SPJ1

Part A. The calculated correlation coefficient is incorrect.

Part B. A causal relationship for strawberries picked on the farm is the relationship between rainfall and number of strawberries picked.

Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system. The independent variable or attribute is plotted on the X-axis, while the dependent variable is plotted on the Y-axis.

Given,

Part A: Using computer software, a correlation coefficient of r = 0.01 was calculated.

Observing the scatter-plot, the data is moderately correlated,  as the days increase, the number of strawberries also increase, following upward trend,

r = 0.01 means that 1% of the variation in y is explained by the variation in x.

that means both quantities are very weakly correlated.

but the scatter-plot shows otherwise, so r = 0.01 is not an accurate value for the data.

Part B: Instead of comparing the number of strawberries picked and the day in February, write a scenario that would be a causal relationship for strawberries picked on the farm.

A causal relationship exists when one variable in a data set has a direct influence on another variable. Thus, one event triggers the occurrence of another event. A causal relationship is also referred to as cause and effect.

Here, rainfall could be reasonable variable that can effect the number of strawberries picked. when there is heavy rainfall, strawberries picked will be less.

Thus, the scenario could be:

Amount of rainfall in mm (x)         Number of strawberries picked (y)

      100                                                     20

      50                                                      40

      25                                                      80

     12.5                                                    160

     6.25                                                   320

The amount of rainfall is a cause that affect the number of strawberries picked.

Hence,

The calculated correlation coefficient is false.

Another causal relationship for strawberries picked on the farm can be of rainfall in mm and number of strawberries picked on the farm.

Learn more about scatter-plot here:

https://brainly.com/question/30017616

#SPJ1

The system of equations that shows the situation is option 1.  L+J=29  L=2J-10

The question tells us that the summation of the age of Latifa and Jameel is 29

Let J = Jameel

L = Latifa

L + J = 29

The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted

L = 2J - 10

Read more on equations here:https://brainly.com/question/2972832

#SPJ1

The area of the second circle can be represented as: [tex]2122\pi + 52[/tex] square cm.

In mathematics, a function is a mathematical rule that assigns a unique output (also called the function value) to each input (also called the argument or independent variable) in its domain. A function is often denoted using functional notation, such as f(x), where f is the function name and x is the input variable.

A function can be represented graphically as a set of ordered pairs (x, f(x)) that show the relationship between the input values and the corresponding output values. The set of all possible input values for a function is called the domain, and the set of all possible output values is called the range.

For example, the function f(x) = 2x + 1 takes an input value x and produces an output value of 2x + 1. If we input x = 3 into the function, we get f(3) = 2(3) + 1 = 7. Similarly, if we input x = -2, we get f(-2) = 2(-2) + 1 = -3. In this case, the domain of the function is all real numbers, and the range is also all real numbers.

Functions can be linear or nonlinear, and they can have different properties such as continuity, differentiability, and periodicity. They are used extensively in mathematics, science, engineering, and economics to model and analyze relationships between variables, as well as to solve equations and optimize solutions.

The area of the first circle with radius r is given by:

[tex]f(r) = \pi r^2[/tex]

The area of the second circle with radius 26 cm is given by:

[tex]f(26) + 52[/tex]

Therefore, the area of the second circle can be represented as:

[tex]f(26) + 52 = \pi(26)^2 + 52 = 2122\pi + 52 $ square cm$[/tex]

To know more about area visit:

brainly.com/question/12187609

#SPJ1