A company had 15 employees whose salaries are shown below.

Answer:

b. 20%

Step-by-step explanation:

The distribution of  number of hours worked by students is:

0 - 10          =         20

10 - 20        =         80

20 - 30       =         200

30 - 40       =         100

Total number of students = 400

We need to find the percentage of students working between 10 and 20 hours. From the above table we can see that number of students working between 10 and 20 hours is 80. Now we need to convert this into percentage. What we need to evaluate is what percentage of 400 is 80.

The formula for percentage is:

[tex]\frac{\text{Concerned Value}}{\text{Total Value}} \times 100\%[/tex]

Concerned value is 80, total value is 400. So using these in the formula we get:

[tex]\frac{80}{400} \times 100%\\\\  = 20\%[/tex]

Thus, 20% of the students are working between 10 and 20 hours.

The percentage of statistics students working between 10 and 20 hours per week is 20%, which is calculated by dividing the frequency of the group (80 students) by the total number of students (400) and multiplying by 100.

The question is asking us to find the percentage of statistics students who work between 10 and 20 hours per week, given the frequency distribution provided in Exhibit 2-1. According to the exhibit, 80 students work between 10 and 20 hours per week. Since the total number of students is 400, we calculate this percentage by taking the number of students in the given category (80 students) and dividing it by the total number of students (400), then multiplying by 100 to get a percentage.

The calculation is:

Percentage = (80 ÷ 400) × 100

Percentage = 0.20 × 100

Percentage = 20%

Therefore, the percentage of students working between 10 and 20 hours is 20%, which corresponds to option b.

Firstly we calculate the height(h)...,

by using trigonometry ratios

;tan 45° = h/5

;where.. h = 5 tan 45°

;h = 5

Then we calculate the side x...using the height h and the angle of 30°

by also using trigonometry ratios

; sin 30° = 5/x

;where.. x = 5/(sin 30°)

Hence...., x = 10

Answer: x = 10

Answer:

The answer is 54.5

Step-by-step explanation:

The median of a set of observations is the value in the middle in case there is an uneven number of observations or the average between the two values in the middle.

First we arrange the times from less time to longer times.

50 - 52 - 57 - 230 .

The values in the middle are  52 - 57

And the average between this two values is 54.5. Thus that is the median legth of time.

Answer:

The median length of time required to review an application is 54.5 minutes.

Step-by-step explanation:

The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57.

Arranging in ascending order we get

50,52,57,230

Median length of time = [tex]\frac{52+57}{2}=54.5[/tex]

Hence, the median length of time required to review an application is 54.5 minutes.

Answer:

The value of the car in very nice condition will be $35500.

Step-by-step explanation:

Let the value of car in a very nice condition be = x

The value $62125 is [tex]1\frac{3}{4}[/tex] or [tex]\frac{7}{4}[/tex] or 1.75 times of x.

Now, we can calculate for x:

[tex]1.75x=62125[/tex]

[tex]x=\frac{62125}{1.75}[/tex]

x = 35500

Hence, the value of the car in very nice condition will be $35500.

The value of the car in very nice condition is $35,500. This is determined by dividing the value of the car in excellent condition by 1.75.

To determine the value of the car in very nice condition, you need to use the information that a car in excellent condition is worth 1 3/4 times (or 1.75 times) as much as a car in very nice condition.

Given the value of the car in excellent condition is $62,125, you can set up the equation:

Substitute the known value:

To find the Value in Very Nice Condition, divide both sides by 1.75:

Hence, the value of the car in very nice condition is $35,500.

Answer:

I guess u want to know the quadratic function and its formula is, AX*2 + BX + C. Otherwhise you want to know how to get 0 and get the Xm if you want to know how to solve a quadratic. That formula is,  (-B +/- [tex]\sqrt{x}[/tex] (B*2 - 4AC) ) . 1/2 (where A, B and C are the number at the original function).

Step-by-step explanation:

Answer:

21

Step-by-step explanation:

You were close to de answer but you rounded in a wrong way

If we calculate [tex]\sqrt{16^{2} + 14^{2}}[/tex]  we get 21.2602916255

We need to round to the nearest whole number, it means that we have we only have two options: 21 or 22

We need to remember the rounding rules:

We see that 1 is followed by 2, it means that we have to round the number down, so our answer is 21

Answer:

See explanation

Step-by-step explanation:

7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8

12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5

14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2

19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1

21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1

23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1

24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7

27.1 29.5

A. The five-number summary is

B. The interquartile range is

[tex]Q_3-Q_1=23.8-14.2=9.6[/tex]

C. See attached diagram

D. The distribution is not symmetric, the left half shows more data than the right part

Answer:

  Domain of set B: {2, 4, -4, 0}

Step-by-step explanation:

The domain of the function whose ordered pairs are listed in set B is the set of first numbers of those pairs: {2, 4, -4, 0}.

_____

Comment on the question

A "set" does not have a domain. A "function" has a domain. To make any sense of this question, we have to interpret the question to mean the function described by the ordered pairs in the set.

Answer:

the 3 yard line

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

First, when fractions get raised to an exponent, both the numerator and the denominator get raised to the power.

When exponents get raised to a power, the powers multiply.

E.g. [tex](x^2)^3=(x^2)(x^2)(x^2)=(x*x)(x*x)(x*x)=x^6[/tex]

In this case,

[tex](\frac{4^3}{5^-^2})^5=\frac{4^(^3^*^5^)}{5^(^-^2^*^5^)}=\frac{4^1^5}{5^-^1^0}\\[/tex]

Note that [tex]x^-^n=\frac{1}{x^n}[/tex]

So, 1/5^(-10) = 5^10

So, our answer is C

Answer:

Step-by-step explanation:

Given that an advertiser wishes to estimate the proportion of adults in Utah who already own a gym membership.

Confidence level wanted = 90%

Critical value Z for 90% = 1.645

p is not known hence for maximum std error we know p =0.5

Let us take p =0.5

Margin of error = [tex]1.645*\sqrt{\frac{pq}{n} } =\\1.645*0.5(\frac{1}{\sqrt{n} } ) 0.10\\n=67.65\\n~68[/tex]

Sample size can be 68

If the [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function then [tex]fo\ t\ (x)[/tex] is an even function, if [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function then the function [tex]fo\ t\ (x)[/tex] is an odd function and if [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd then the function [tex]fo\ t\ (x)[/tex] is an even function.

Further explanation:

An even functrion satisfies the property as shown below:

[tex]\boxed{f(-x)=f(x)}[/tex]

An odd functrion satisfies the property as shown below:

[tex]\boxed{f(-x)=-f(x)}[/tex]

Consider the given composite function as follows:

[tex]\boxed{fo\ t\ (x)=f\left(t(x))\right}[/tex]

If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are even function.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.

If both the function [tex]f(x)[/tex] and [tex]t(x)[/tex] are odd function.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=-fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=-fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an odd function.

If the function [tex]f(x)[/tex] is even and [tex]t(x)[/tex] is odd.

[tex]\begin{aligned}fo\ t\ (-x)&=f\left(t(-x))\right\\&=f\left(-t(x))\right\\&=fo\ t\ (x)\end{aligned}[/tex]

From the above calculation it is concluded that,

[tex]\boxed{fo\ t\ (-x)=fo\ t\ (x)}[/tex]

This implies that the composite function [tex]fo\ t\ (x)[/tex] is an even function.

Answer:

B. $25,069

Step-by-step explanation:

An interest of 6% per year, compounded monthly it means that he earns 6/12% = 0.5% of what he has invested every month.

If he invests x money what he will have the first month will be :

Money = x*(1+0.005)

The next month:

Money' = Money*(1+0.005) = x *(1+0.005)(1+0.005) = x* (1+0.005)^2

Therefore in this type of interest the formula is:

Money = x*(1+r)^n

Where:

x is the money invested the first time

r is the interest

n is the number of periods

For this problem:

x = what you have to find

r = 0.005

n = 3 years (1 period is 1 month) then the period is 36 months

Money = 30000

Replacing:

30000 = x * (1+0.005)^36

x = 25,069

Final answer:

To make a $30,000 down payment in three years with an account earning 6% interest compounded monthly, James needs to deposit approximately $25,189.06 today.

Explanation:

Calculating the Present Value for a Future Goal

To achieve a $30,000 down payment in three years with an account that earns 6% interest per year, compounded monthly, we need to calculate the present value of the future goal. Since the interest is compounded monthly, we use the present value formula for compound interest, which is P = A / (1 + r/n)^(nt), where P is the present value, A is the future amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the number of years.

Here, A = $30,000, r = 0.06 (6% converted to decimal), n = 12 (compounded monthly), and t = 3.
So, P = $30,000 / (1 + 0.06/12)^(12*3) = $30,000 / (1 + 0.005)^(36) ≈ $30,000 / 1.191016 = $25,189.06 (rounded to 2 decimal places).

The amount James needs to deposit today is approximately $25,189.06.

Answer:

  3

Step-by-step explanation:

A 6-inch piece of string can be cut into 12 pieces that are 1/2 inch each. If Lee needs 15 pieces, she needs 3 more.

___

Each inch is divided into 2 pieces. That's what 1/2 inch means. 6×2 = 12.

Answer:

B. 63.8 mph

Step-by-step explanation:

IN order to solve this problem we just have to keep in mind that the miles per hour is calulcated by the number of revolutions that the tire is doing multiplied by the circumference of the tire, so the circumference of the tire is given by the first set of number in the tire the first one would be:

[tex]first:\frac{215}{60} \\Second: \frac{235}{70}[/tex]

So we just have to multiply it by the first one and then divide it by the second:

[tex]\frac{215}{60}*60=215\\215*\frac{235}{70}=63.8[/tex]

SO when the speedometer is on 60 mph, he will actually be going at 63.8 mph.

Answer:

a testable proposition that explains an observed phenomenon or answers a question

Step-by-step explanation:

Basically an hypothesis is a theory given as a solution to a question proposed by a problem in from of you, but that it needs testing before it can be taken as truth or not

A hypothesis is an educated guess or a testable prediction drawn from observations. It is a tentative statement about reality that can be verified through experiments. If a hypothesis explains a large body of experimental data, it may evolve into a theory.

A hypothesis is a testable prediction about how the world will behave if our idea is correct. Observations and questioning may lead a scientist to form a hypothesis. In essence, a hypothesis is an educated guess or a tentative statement about reality that can be tested to determine its validity.

An example of a hypothesis is 'if I study all night, I will get a passing grade on the test'. The hypothesis, the educated guess in this scenario, then undergoes a process of testing through experimentation, calculation, and comparison with the experiments of others.

If a hypothesis is capable of explaining a large body of experimental data, it can reach the status of a theory. A theory in scientific terms is a well-substantiated, comprehensive, testable explanation of particular aspects of nature. However, theories can be modified if new data becomes available. This process of questioning, observing, hypothesizing, testing, and eventually forming a theory is known as the scientific method.

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Answer:

5r + 2p + 6

Step-by-step explanation:

4r+r = 5r

9-3 = 6

Answer:

C

Step-by-step explanation:

Credit Score is a numerical expression which analyzes a person's credit level by looking at this financial conditions. Will he/she be worthy of loan or not.

payment history comprises 35% of a person's credit score. This is a huge factor. If you consistently make your payments on time, your credit score increases.

length of credit history tells how secure you will be to lenders. Usually 7 years+ is a great length of credit history. This pretty much affects credit score.

marital status doesn't affect credit score. Lenders assess a person based on their financial condition and past activity, NOT whether or not he/she is married or not. That's personal agenda.

debt ratio is the ratio of total debt to total assets. If this is high, it means a person owes money to banks/individuals and is more likely to be not given credit. It affects credit score highly.

THus, the correct answer is C

Answer:

C

Step-by-step explanation:

Answer:

The mammoth died 17.190 years ago.

Step-by-step explanation:

Given information:

For every 5700 years, the elephant's bones losses a half-life of C-14. And supposing that the living mammoth bones had the same percentage of C-14.

If the mammoth when living has 40%, then:

Answer:

[tex]\large \boxed{\text{17 190 yr ago}}[/tex]

Step-by-step explanation

The amount of C-14 has declined from 40 % to 5 % of the original, that is, to ⅛ of the original amount.

The half-life of C-14 (5730 yr) is the time it takes for half of the isotope to decay.

We can make a table of the amount remaining after each successive half-life.

[tex]\begin{array}{ccc}\textbf{Number of} && \textbf{Fraction} \\\textbf{half-lives} & \textbf{Years} & \textbf{remaining} \\0 &0 & 1 \\1 &5730 &\frac{1}{2 } \\\\2 &11460 &\frac{1}{4 } \\\\3 &17190 &\frac{1}{8} \\\\4 & 22920& \frac{1}{16} \\\end{array}\\\text{We see that the fraction of C-14 is reduced to $\frac{1}{8}$ after three half-lives.}\\\text{The mammoth died $\large \boxed{\textbf{17 190 yr ago}}$}[/tex]

Answer:

x intercept- -2

12x - 8(0)= -24

12x = -24

x = -2

12(0)-8y = -24

-8y = -24

y = 3

y intercept

slope. 2/3

-8y = -12x - 24

y = (2/3)x + 3

Final answer:

Approximately 0.3% of IQ scores are greater than 133 according to the empirical rule, which states that 99.7% of values fall within three standard deviations of the mean in a bell-shaped distribution.

Explanation:

Using the empirical rule (also known as the 68-95-99.7 rule) for a bell-shaped distribution, we can determine the percentage of IQ scores that fall at different distances from the mean.

A score of 133 is three standard deviations above the mean (since the mean is 97 and the standard deviation is 12, 97 + 3(12) = 133). According to the empirical rule, approximately 99.7% of IQ scores fall within three standard deviations of the mean. Therefore, to find the percentage of scores greater than 133, we subtract the bottom 99.7% from 100%, resulting in approximately 0.3%.

Thus, following the empirical rule, 0.3% of IQ scores are greater than 133.

Answer:

Option C 41%

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The number of people who own at most three t-shirts costing more than $19 each is equal to the number of people who own one t-shirt costing more than $19 each, plus the number of people who own two t-shirt costing more than $19 each, plus the number of people who own three t-shirt costing more than $19 each

Observing the graph

The number of people who own one t-shirt costing more than $19 each is 5

The number of people who own two t-shirt costing more than $19 each is 17

The number of people who own tree t-shirt costing more than $19 each is 23

The number of people who own at most three t-shirts costing more than $19 each is

[tex](5+17+23)=45\ people[/tex]

To find out the percentage divided the number of people who own at most three t-shirts costing more than $19 by one hundred eleven people (total people that shopped in a store) and then multiply by 100

[tex](45/111)100= 40.54\%[/tex]

Round to the nearest whole number

[tex]40.54\%=41\%[/tex]

The question involves the application of statistical principles to determine the percentage of people who own at most three expensive t-shirts. Assuming 59% is the correct answer, this means 66 out of the 111 people surveyed own three or fewer such t-shirts. The examples in the question references demonstrate the principles of economics, but aren't directly related to the question.

The question is about determining the percentage of people who own at most three t-shirts costing more than $19 each from a sample of 111 people. Given that the possible percentages provided are 21% and 59%, the process involves the application of statistical principles, particularly dealing with percentages in relation to a specific sample size. This example fits into a branch of mathematics known as statistics, which deals with data analysis, collection, interpretation, presentation, and organization.

Let's assume from the reference that 59% is the correct answer, this conveys that of the 111 people surveyed, approximately 66 people own three or fewer such t-shirts. This is obtained by calculating 59% of 111, which equals about 65.49 and rounds to 66.

In the references provided, there are examples of how the cost of t-shirts affects purchasing decisions. This is related to the principles of economics which involve opportunity cost and budget constraints, but is not directly tied to answering the initial question.

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Answer:

C. A distinguishing mark of a profession is its acceptance of responsibility to the public.

Step-by-step explanation:

The following statement best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is :

A distinguishing mark of a profession is its acceptance of responsibility to the public.

The best explanation for why ethical standards are crucial in auditing is that professions are expected to be responsible to the public, ensuring trust, honesty, and integrity in their actions which align with their ethical codes.

The statement that best explains why the auditing profession has found it essential to promulgate ethical standards and to establish means for ensuring their observance is: C. A distinguishing mark of a profession is its acceptance of responsibility to the public. This underscores the basic principle that professionals, such as auditors, have a duty to act in the public interest and maintain public confidence in the profession. Professionals act as gatekeepers in various industries, ensuring that a company's actions uphold the law and adhere to established standards, thus serving the public good by promoting honesty and integrity.

Moreover, professions such as law, medicine, and accounting require professional education and licensing to ensure legal and ethical behavior, with mandated Codes of Ethics that outline the accountability to those served and to the profession itself. Therefore, the maintenance of ethical standards and the enforcement thereof are essential to professional integrity and the protection of public interests.

Explanation:

5(y+3)-11=-y-6 Given

5(y+3)=-y+5 . . . . addition property of equality (11 is added)

5y+15=y+5 . . . . . distributive property (5 is distributed)

5y=-y-10 . . . . . . . addition property of equality (-15 is added)

6y=-10 . . . . . . . . . addition property of equality (y is added)

y=-5/3 Division Property of Equality/Reduce

The average distance of Mercury from the Sun is found using the formula E(x) = 0.2x^3/2, where E(x) = 88 days, which is the year length for Mercury. Solving for x, the distance comes out to be approximately 57.9 million kilometers.

The question asks us to determine the average distance of Mercury from the center star, which can also be understood as the Sun, given that its year (the period it takes to orbit the Sun) is approximately 88 Earth days. We are provided with the formula E(x) = 0.2x3/2, where E(x) represents the number of Earth days in a planet's year and x is the planet's average distance from the Sun in millions of kilometers.

To solve for x, we set E(x) equal to 88 days and solve for x.

E(x) = 88
0.2x3/2 = 88
x3/2 = 88 / 0.2
x3/2 = 440
Now we take both sides to the power of 2/3 to solve for x.
x = 4402/3

To find the value of x, we calculate 440 raised to the 2/3 power.

x = 4402/3
≈ 57.9

Therefore, the average distance of Mercury from the Sun is approximately 57.9 million kilometers.

Answer:

Step-by-step explanation:

note : an equation is : y - b = m(x - a)    ... the point is : A ( a , b) and slope : m

in this exercice :  m= - 8     and  a= - 3    and b= -6

an equation is : y+6 = -8(x+3)

you can write :   y+6 = - 8x -24

8x+y = - 30 .....answer : C

Answer:

C. 8x + y = -30

Step-by-step explanation:

-6 = -8[-3] + b

24

-30 = b

y = -8x - 30

+8x +8x

___________

8x + y = -30 >> Standard Linear Equation

* This is the fastest way to do it.

I am joyous to assist you anytime.

Answer:

Answered below

Step-by-step explanation:

Sheet 1: Question 3

Vertically opposite angles are equal so you will equate the angles given,

∠LPN = ∠OPM

7 + 13x = -20 + 16x

27 = 3x

x = 9

Sheet 1: Question 4

Vertically opposite angles are equal so you will equate the angles given,

∠ABD = ∠EBC

2x + 20 = 3x + 15

-x = -5

x = 5

Sheet 1: Question 5

Step 1: Find the value of x

Vertically opposite angles are equal so you will equate the angles given,

∠SOP = ∠ROQ

5x = 4x + 10

x = 10

Step 2: Find angles

Angle SOP = 5x = 5(10) = 50°

Angle ROQ = 50° (because it is vertically opposite to angle SOP)

Angle SOR = 180 - 50 (because all angles on a straight line are equal to 180°)

Angle SOR = 130°

Angle POQ = 130° (because it is vertically opposite to angle SOR)

Sheet 1: Question 6

Angle 1 = 72° (because vertically opposite angles)

∠4 + ∠1 + 41 = 180° (because all angles on a straight line are equal to 180°)

∠4 + 72 + 41 = 180

∠4 = 67°

∠3 = 41° (because vertically opposite angles)

∠2 = 67° (because vertically opposite angles)

Sheet 2: Question 3

Step 1: Find the value of x

Sum of complementary angles is equal to 90°

Angle A + Angle B = 90°

7x + 4 + 4x + 9 = 90°

11x = 90 - 13

11x = 77

x = 7

Step 2: Find angle A and angle B using x

Angle A: 7x + 4

7(7) + 4

Angle A = 53°

Angle B: 4x + 9

4(7) + 9

Angle B = 37°

Sheet 3: Question 3

Step 1: Find the value of x

Sum of supplementary angles is equal to 180°.

Angle A + Angle B = 180°

3x - 7 + 2x + 2 = 180°

5x = 185

x = 37

Step 2: Find angle A and angle B using x

Angle A: 3x - 7

3(37)-7

Angle A = 104°

Angle B: 2x + 2

2(37) + 2

Angle B = 76°

Sheet 3: Question 4

Sum of supplementary angles is equal to 180°.

Step 1: Find x

1/4(36x-8) + 1/2(6x-20) = 180°

Take LCM

[36x - 8 + 2(6x - 20)]/4 = 180°

36x - 8 +12x - 40 = 180 x 4

48x - 48 = 720

48x = 768

x = 16

Step 2: Find both angles with the help of x

Angle 1: 1/4(36x-8)

1/4[36(16)-8] = 568/4

Angle 1 = 142°

Angle 2: 1/2(6x-20)

1/2[6(16)-20] = 76/2

Angle 2 = 38°

Sheet 4: Question 1

All angles on a straight line are equal to 180°

Angle z + 138° = 180°

Angle z = 180 - 138

Angle z = 42°

Sheet 4: Question 2

Linear pair 1: 5 and 7 (because both angles are on a straight line and are equal to 180°)

Linear pair 2: 6 and 8 (because both angles are on a straight line and are equal to 180°)

Sheet 4: Question 3

Step 1: Find the value of x

All angles on a straight line are equal to 180° or linear pairs are equal to 180°

Angle LMO + Angle OMN = 180°

7x + 20 + 10 + 5x = 180°

12x = 180 - 30

x = 150/12

x = 12.5

Step 2: Find angles using the value of x

Angle LMO: 7x + 20

7(12.5) + 20

Angle LMO = 107.5°

Angle OMN: 10 + 5x

10 + 5(12.5)

Angle OMN = 72.5°

Sheet 4: Question 4

Linear pairs are equal to 180°.

Angle 1 + Angle 2 = 180°

1/3(27x-6) + 1/2(6x-20) = 180°

Take LCM = 6

[2(27x-6) + 3(6x-20)]/6 = 180

54x - 12 + 18x - 60 = 1080

72x - 72 = 1080

72x = 1152

x = 16

!!

Answer:

Step-by-step explanation:

[tex]A=\frac{1}{2} r^{2} \theta\\\frac{dA}{d\theta} =r \\\\when r=2\\rate of change at r=2 is  2[/tex]

We want to find the rate of change of a given function of two variables when we fix one of the two, and then we want to evaluate it at r = 2.

We will get that the rate of change is:

[tex]\frac{dA(r, \theta)}{d\theta} = 12*r^2[/tex]

And when r = 2, the rate is 48.

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

We define the rate of change of a function with respect to some variable as the differentiation of the function with respect to that variable.

Here we have the function:

[tex]A(r, \theta) = 12*r^2*\theta[/tex]

We need to differentiate it with respect to θ, we will get:

[tex]\frac{dA(r, \theta)}{d\theta} = 1*12*r^2*\theta^0 = 12*r^2[/tex]

Where I used the general rule to derive functions with exponents:

[tex]f(x) = x^n\\\\\frac{df(x)}{dx} = n*x^{n -1}[/tex]

Now that we know the rate of change, we want to evaluate it in r = 2, we will get:

[tex]\frac{dA(2, \theta)}{d\theta} = 12*2^2 = 48[/tex]

Notice that this does not depend on the value of θ.

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