Project Option 1
For this option, you will work individually.

Instructions
For this option, you will work individually.

You’ve worked hard in this module to become a pro at equations! Now, you’ll put your skills to the test. Your job is to create an equations portfolio. The format is up to you. Be creative! You may use a slideshow, document, video, etc. As long as all of the parts of the project are addressed, the delivery is up to you.

Your portfolio must include a minimum of the following five types of equations and solutions:

Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable. Once you have created each equation, you will solve it and show your work. Pretend that you are teaching the equations to a new pre-algebra student. Or you can actually teach them to a sibling or friend!

This is a total of 7 equations and solutions.

The number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

Given that

Six hundred six and four thousand, three hundred fifteen ten-thousandths

To write this number in numerical form, we need to add the values of each of its digits:

6 × 100 + 0 × 10 + 6 × 1 + 4 × 0.1 + 3 × 0.01 + 1 × 0.005 = 606.4315

Therefore, the number "Six hundred six and four thousand, three hundred fifteen ten-thousandths" is equal to 606.4315 in numerical form.

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1.  we can use the first equation to find y = 3x + 1 = 3(9) + 1 = 28 So, the larger integer is 28, (2).  The smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

An integer is a whole number ,neither a fraction or a decimal, in mathematics. Integers can be zero, positive, or negative.

Integer examples include -3, -2, -1, 0, 1, 2, 3, and so forth.

The letter "Z" stands for the set of integers.

In mathematics and allied disciplines such as computer science, physics, and finance, integers are utilized extensively.

A whole number is a non-negative integer in mathematics, which indicates that it is either a positive integer or zero.

Negative and fractional numbers are not included in whole numbers. The full integers 0, 1, 2, 3, 4, and so on are examples.

In many different branches of mathematics as well as in other disciplines, such as arithmetic, algebra, and geometry, whole numbers are used. They are also employed in daily tasks like quantity calculations and object counts.

According to question :-

Let's call the smaller integer x and the larger integer y. We know that:

y = 3x + 1 (the largest of the two integers is one more than three times the smaller)

x + y = 37 (the sum of the two integers is 37)

We can use substitution to solve for y in terms of x:

x + (3x + 1) = 37

4x + 1 = 37

4x = 36

x = 9

Now we can use the first equation to find y:

y = 3x + 1 = 3(9) + 1 = 28

So the larger integer is 28.

Let's call the smaller integer x and the larger integer y. We know that:

y = x + 1 (the integers are consecutive)

x + 2y = 29 (the sum of the smaller and twice the larger is 29)

We can substitute y = x + 1 in the second equation:

x + 2(x + 1) = 29

Simplifying and solving for x:

3x + 2 = 29

3x = 27

x = 9

So the smaller integer is 9. The larger integer is 10, which is the next consecutive integer.

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Answer:  Elaine is 135cm tall

Step-by-step explanation:

Elaine's height is 75% of her father's height.

We can calculate Elaine's height by multiplying her father's height by 75% or 0.75.

Elaine's height = 0.75 * 180 cm

                        = 135 cm

Therefore, Elaine is 135 cm tall.

Answer:

Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The sum of the interior angles of a triangle are 180.

Triangle on the left

180 - 90 - 42 = 48

Triangle on the right:

180 - 90 - 48 = 42

Since the angles measurements are the same, the triangles are similar.

Helping in the name of Jesus.

Answer: Yes, because of the Angle-Angle Theorem

Step-by-step explanation:

The two triangles have the same angles, so they are similar by the Angle-Angle Theorem.

The expression for the number of sweatshirts that were not adult sizes would be: s - 19.

What is an expression?

In mathematics, an expression is a combination of numbers, variables, operators, and/or functions, without an equals sign. It can be a single term, or a combination of terms separated by operators, such as addition, subtraction, multiplication, division, and exponentiation

Given : total number of team booster sweatshirts = s

            No. of team booster sweatshirts of adult size = 19

So,

No. of team booster sweatshirts that were not adult sizes :

= total number of team booster sweatshirts -   No. of team booster sweatshirts of adult size

= s - 19.

Hence, s - 19 expression shows how many sweatshirts were not adult sizes.

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The communication is a one-way process in which a message is conveyed from a sender to a receiver is one of the assumptions made by the linear model of communication.

The straightforward linear model of communication presents communication as a process with distinct beginnings and endings.

But this model ignores the fact that communication is frequently a more complex and involved process that needs context, feedback, and a variety of channels.

The linear model presumes that the message is clearly understood by the recipient and that it is received by the recipient free from distortion or interference.

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An assumption of the linear model of communication is the belief that communication is a one-way process where a sender transmits a message to a receiver through a channel. This model assumes that communication is a linear process where the sender encodes a message, which is then sent through a channel to the receiver who decodes the message.

In the linear model, the sender encodes a message, sends it through a channel, and the receiver decodes the message. This model does not account for feedback or interaction between the sender and receiver, assuming that communication is a straightforward and direct transmission of information without any complexities or interruptions.

This model assumes that there is little to no feedback or interaction between the sender and receiver, and that the message is transmitted and received accurately without any distortion. However, this assumption is often criticized for oversimplifying the complex nature of communication and ignoring the role of context and feedback in the communication process.

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The vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.

What is vertex form?

Vertex form is a way to write a quadratic function in the form:

f(x) = a(x - h)²+ k

where "a" is the vertical stretch or compression factor, "h" and "k" are the x-coordinate and y-coordinate of the vertex of the parabola respectively. The vertex form allows you to easily identify the vertex and the direction of the parabola's opening.

To write -16x²+160x+120 in vertex form, we need to complete the square.

First, let's factor out the coefficient of x²:

-16(x² - 10x) + 120

Next, we need to add and subtract (10/2)² = 25 to the expression inside the parentheses:

-16(x² - 10x + 25 - 25) + 120

Now we can group the first three terms and factor the perfect square trinomial:

-16((x - 5)² - 25) + 120

Simplifying:

-16(x - 5)² + 520

Therefore, the vertex form of the quadratic expression -16x² +160x+120 is -16(x - 5)² + 520.

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Answer:

data given

Universal set 40people

people who can sew 14

people who can knit 12

people who can do both 5

Step-by-step explanation:

•people who can sew only

=14-5

=9

•people who can knit only

=12-9

=7

Union of people who can sew and the one who can knit

=9+7+5

=21

who do neither

=40-21

=19

: .people neither sew or knit are 19

The probability of examining the five people till first patient has athlete's foot is given by (0. 84)^4(0. 16)^1.

Percent of people have athlete foot = 16%

Let us consider the probability of success represented by p = 0.16.

Using geometric distribution,

Probability of finding first patient with athlete's foot on kth examination is given by geometric probability distribution,

P(X = k) = (1 - p)^(k - 1) × p

where X is random variable representing number of trials needed until  first success.

Probability of finding the first patient with athlete's foot on the fifth examination k = 5,

⇒ P(X = 5) = (1 - p)^(5 - 1) × p

⇒ P(X = 5) = (0.84)^4 × 0.16

Simplify it we get,

⇒ P(X = 5) = 0.0473

Therefore, the probability of a podiatrist examining five people until he finds the first patient who has athlete's foot is (0. 84)^4(0. 16)^1.

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For the given inequality substitute the coordinates of x and y to form the graph of  y ≥ 2000 (1 + 0.04)ˣ.

Interest that is calculated on both the initial principle and any accrued interest is known as compound interest. This implies that the interest for the subsequent period is computed using the new total amount after the interest for the prior month has been added to the principal. If the interest rate and the duration are both high, the interest might add up to a sizable amount over time. Savings accounts, investments, loans, and other financial instruments frequently use compound interest.

For the given inequality we have:

For x = 0, y = 2000.

For x = 1, y = 2000(1 + 0.04) = 2080.

Plot the points on the graph to determine the graph.

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In morbidity surveys of the general population, they collect data on the health status of a population group which includes the health and nutrition examination survey, that are typically uses a scientifically designed representative sample. So the answer is all of these are correct or option B.

What are Morbidity Surveys?

Morbidity surveys are research investigations designed to determine the frequency and incidence of diseases, illnesses, and injuries in a certain community. They are intended to collect data on people's health status within a certain community or population, as well as to determine the distribution and drivers of health issues in that group.

Morbidity surveys often employ structured questionnaires and physical examinations to gather data on the occurrence of certain health disorders, as well as risk factors and other variables that may be related to the development of these illnesses.

Morbidity survey data may be used to design public health policies and programs, distribute resources, and track changes in health status over time.

The answer is (b) All of these are correct.

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Health surveys provide a structured way to collect and interpret data about the health status of a population, helping researchers and policy makers understand health trends and conditions. One such survey is the Health and Nutrition Examination Survey.

Surveys, such as the Health and Nutrition Examination Survey, provide an important method for collecting data on the health status of a population group. In public health and epidemiology, these surveys typically use a scientifically designed representative sample to provide accurate data. To conduct this survey, researchers ask the same questions to all respondents, interpret the answers, and tabulate the results. A simple example could be comparing the eating habits of students eating off campus versus those in dining facilities. With the data gathered, we can identify health trends, understand the distribution of certain health conditions, and then make informed policy or healthcare decisions based on these insights.

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The MAD of the hourly wages given would be $ 0.48. The range would be $ 2.00. Q1 would be $8.25. Q3 would then be $9.25. The IQR would be $1.00

Calculate the MAD:

First, find the mean of the data set:

mean = (sum of all values) / (number of values)

mean = (8.25 + 8.50 + 9.25 + 8.00 + 10.00 + 8.75 + 8.25 + 9.50 + 8.50 + 9.00) / 10

mean = 88.00 / 10 = 8.80

Then, find the mean of these absolute deviations:

MAD = (sum of absolute deviations) / (number of values)

MAD = (0.55 + 0.30 + 0.45 + 0.80 + 1.20 + 0.05 + 0.55 + 0.70 + 0.30 + 0.20) / 10

MAD = 4.10 / 10 = 0.41

Calculate the range:

range = maximum value - minimum value

range = 10.00 - 8.00 = 2.00

Find Q1 and Q3:

{8.00, 8.25, 8.25, 8.50, 8.50, 8.75, 9.00, 9.25, 9.50, 10.00}

Q1 is the median of the lower half, and Q3 is the median of the upper half.

Lower half: {8.00, 8.25, 8.25, 8.50, 8.50}

Upper half: {8.75, 9.00, 9.25, 9.50, 10.00}

Q1 = median of lower half = 8.25

Q3 = median of upper half = 9.25

Calculate the IQR:

IQR = Q3 - Q1

IQR = 9.25 - 8.25 = 1.00

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The resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

Expressions in writing are made using mathematical operators such as addition, subtraction, multiplication, and division.

For instance, "4 added to 2" will have the mathematical formula 2+4.

So, we have the expression:

= x² + 10x + 24

Now, solve when x = 3 as follows:

= x² + 10x + 24

= 3² + 10(3) + 24

= 9 + 30 + 24

= 63

Therefore, the resultant value of the given expression x² + 10x + 24 when x = 3 is (C) 63.

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Correct question:

Evaluate the expression when x = 3.

x² + 10x + 24

a. 81

b. 86

c. 63

d. 60

I gotchu <3

Since the vertex is (0, -3), the quadratic function can be written in vertex form as:

f(x) = a(x - 0)^2 - 3

Where 'a' is a constant that determines the shape of the parabola. Since the end behavior of the function is y --> - Infinite as x --> - infinite and y --> - Infinite as x --> + infinite, the leading coefficient 'a' must be negative.

So, f(x) = -a(x^2 - 0x) - 3

Now, using the given point (1, -7) on the parabola, we can substitute the coordinates into the function and solve for 'a'.

-7 = -a(1^2 - 0(1)) - 3

-7 = -a - 3

a = 10

Therefore, the quadratic function that satisfies the given characteristics is:

f(x) = -10x^2 - 3

Hope this helps :)

Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the Domain range of g.

Determine the values of the independent variable x for which the function is specified in order to find the domain and range of the equation y = f(x). Simply write the equation as x = g(y), and then determine the domain of g(y) to determine the function's range.

Since g has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45, we can eliminate options B and D as they fall outside the range of g.

Since -13 is outside of the range of g, we are unable to verify whether g(-13) = 20 for option A.

For option C, we are given that g(0) = -2, so option C cannot be true.

Therefore, the correct answer is A. We cannot determine whether g(-13) = 20 or not as -13 is outside the domain of g, but it is a possibility within the range of g.

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The slope of the given line is 1/3 for the line passes through (0, 2) and (3, 3).

The slope of a line represents the rate at which it rises or falls as it moves horizontally from left to right.

It is calculated by taking the difference in the y-coordinates (vertical change) and dividing it by the difference in the x-coordinates (horizontal change) of two points on the line.

The slope can also be thought of as the tangent of the angle formed by the line and the positive x-axis.

In this problem, we are given that the slope of the line is 1/3.

We can use this information to find the slope between any two points on the line.

Let's consider the points (0, 2) and (3, 3) that lie on the line.

The change in y-coordinates is 3 - 2 = 1, and the change in x-coordinates is 3 - 0 = 3.

Therefore, the slope between these two points is 1/3.

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The question is -

What is the slope of the line?

Derive Linear Equations-Quiz-Level H

Answer: See Bellow

Step-by-step explanation:

Juliet's sample may not be valid for several reasons. Firstly, her sample size of 20 students may not represent the entire student population at her school. If her class is not a random sample of the whole student population, her results may not generalize to the entire school. Additionally, the model may suffer from selection bias if she only surveyed students she knew liked short stories or if she conducted the survey in a way that only sure students responded. Therefore, it is essential to have a large and representative sample to ensure the validity of the conclusions drawn from the survey results.

Answer:

Step-by-step explanation:

You will first need to remember when solving equations or inequalities that have a variable you will need to make sure that the variable is on one side alone.

So, b-2>-1 you will add 2 to both sides . Whatever you do to one side of the equal sign or inequality you do to the other side.

b-2>-1

  +2  +2

b > 1  

Also, because it has a line under the greater than or equal to sign you will graph it on a number line as a closed circle with the closed circle on the 1 and the arrow pointing to the right. The symbol in the inequality is the way the arrow should be pointing . ≤ ≥ closed circle < > open circle.

closed circle and arrow pointing to the right →

The second selection is the right one.

The graduated measuring cups are made from something glass or something transparent to markings on the side with different measurements are visible. Option (d) is the correct answer.

The kind of cups for measuring that are sometimes made from glass or something transparent so the markings on the side with different measurements are visible are called graduated measuring cups. These cups are designed to make measuring precise amounts of liquid or dry ingredients easy, and the transparent material allows you to see the measurement markings clearly. Graduated measuring cups are commonly used in baking and cooking, as well as in scientific research and other applications where accurate measurements are essential.

Therefore, Graduated measuring cups is the answer.

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The dress was sold at a profit of 20%.

Profit percent is the percentage of profit earned on a product or investment, calculated as the profit divided by the cost price multiplied by 100%.

The profit or loss percent can be calculated using the following formula:

Profit/Loss percent = (Profit or Loss / Cost Price) x 100%

Here, the Cost Price (CP) of the dress is Rs. 2500, and the Selling Price (SP) is Rs. 3000.

Profit = SP - CP = Rs. 3000 - Rs. 2500 = Rs. 500

Therefore, the profit percent is

Profit percent = (Profit / CP) x 100%

Substitute the values in the equation

= (500 / 2500) x 100%

= 20%

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I have solved the question in general, as the given question is incomplete.

The complete question is:

A dress was bought for Rs. 2500 and sold for Rs. 3000. Find the profit or loss percent

In the ANOVA test, degrees of freedom within (dfw) is equal to the total number of observations minus the total number of groups if we have N total observations and k groups, then dfw = N - k.

The ANOVA (Analysis of Variance) test is a statistical method used to compare the means of three or more groups.

Degrees of freedom within (dfw) are determined by the total number of observations minus the total number of groups, and degrees of freedom between (dfb) is simply the number of groups minus one.

On the other hand, degrees of freedom between (dfb) is equal to the number of groups minus 1, which is simply k - 1.

So, the final answer is:

dfw = N - k

dfb = k - 1

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Data collected from several entities over a period of time (minutes, hours, days, etc.) are called time series data.

Time series data is a type of data that is collected over a period of time, with measurements taken at regular intervals. The data is often used to track changes in a particular variable over time and to analyze patterns or trends in the data.

Examples of time series data include stock prices, temperature readings, and daily sales figures. Time series data can be used to make forecasts or predictions about future trends based on past data, and it is often analyzed using statistical methods such as trend analysis, seasonality analysis, and autocorrelation analysis.

Time series data can be represented graphically using a line chart or a scatterplot, with time on the x-axis and the variable of interest on the y-axis. Time series data can be univariate, meaning that there is only one variable being measured, or multivariate, meaning that there are multiple variables being measured at the same time.

Statistical methods are a set of techniques and procedures used to analyze and interpret data in order to draw meaningful conclusions from it. These methods involve the collection, analysis, and interpretation of data in order to identify patterns, trends, and relationships between variables.

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Joshua started his own lawn care business. He donates 10% of his income to a local charity, which is recognized by the IRS as a qualified charitable organization. Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income.

The first blank should be filled with "tax reductions" and the second blank should be filled with "amount of taxable income."

Hence, the correct statement would be: "Joshua can claim expenses from his business and charitable donations as tax reductions, and they will reduce the amount of taxable income."

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According to the investment, after 15 years, the balance in the account would be $1185.

To calculate the final balance after 15 years, we can use the formula for simple interest:

Simple Interest = Principal x Interest Rate x Time

In this case, the principal is $600, the interest rate is 6.5%, and the time is 15 years.

Simple Interest = $600 x 0.065 x 15

Simple Interest = $585

So the investment of $600 earns $585 in simple interest over 15 years. To find the final balance, we add the interest earned to the initial investment:

Final Balance = Principal + Simple Interest

Final Balance = $600 + $585

Final Balance = $1185

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When solving an oblique triangle given three sides, use the inverse cosine form of the Law of cosines to solve for an angle.

When solving an "oblique-triangle" given three sides, we would use the inverse cosine, form of the Law of Cosines to solve for an angle.

The "Inverse-Cosine" function allows us to find the measure of an angle when given the ratio of the lengths of the triangle's sides.

The "Law-of-Cosines" relates the lengths of the sides of a triangle to the cosine of one of its angles.

The "Law-of-Cosines" states that for any triangle with sides of lengths a, b, and c, and opposite angles A, B, and C, respectively:

⇒ c² = a² + b² - 2ab × cos(C),

To solve for an angle, we would rearrange the equation to find the cosine of the angle,

⇒ Cos(C) = (a² + b² - c²)/(2ab),

Then, we will take the inverse cosine of both sides of the equation to find the value of the angle,

⇒ C = cos⁻¹((a² + b² - c²)/(2ab)),

This helps us to find the measure of angle C, depending on the units used in the original triangle sides.

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The given question is incomplete, the complete question is

When solving an oblique triangle given three sides, use the _____ form of the Law of cosines to solve for an angle.

Number of red counters in the original bag is 3, and the number of green counters is 7.

Let's use algebra to solve the problem. Let U be the number of red counters and G be the number of green counters originally in the bag.

From the first part of the problem, we know that

Probability (selecting a green counter) = G / (U + G) = 3/7

Solving for U in terms of G, we get

U = (7G - 3G) / 3 = 4G/3

So we know that there were 4G/3 red counters and G green counters in the bag originally. But since the number of counters must be a whole number, we can assume that there were 4R red counters and 3G green counters originally, where R and G are both integers and R + G is the total number of counters.

After adding 2 red and 3 green counters, the number of counters in the bag is now R + 2 + G + 3 = R + G + 5.

From the second part of the problem, we know that

P(selecting a green counter) = (G + 3) / (R + G + 5) = 6/13

Solving for R in terms of G, we get

R = (13G - 9G - 15) / 7 = 4G/7 - 15/7

Since R must be an integer, we can try different values of G to see if R is an integer. For example, if G = 7, then R = 3 and the total number of counters is 10.

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The given question is incomplete, the complete question is:

There are only U red counters and G green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is 3/7. The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is 6/13. Find the number of red counters and the number of green counters that were in the bag originally

SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.

The process you are referring to is called Statistical Process Control (SPC), which involves monitoring and analyzing a process to ensure it is within the acceptable range of variation. This is done by comparing the current amount of outcome variation against the established outcome specifications, allowing for corrective action to be taken if necessary. SPC is widely used in manufacturing, healthcare, and other industries to improve quality and efficiency.

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Process control is based on comparing the current amount of outcome variation against outcome specifications.

Process control is a management approach that involves monitoring and adjusting a process to ensure that it meets its intended outcome specifications.

The goal of process control is to maintain consistent outcomes over time, despite natural variation in the inputs or other factors that may affect the process.

In order to achieve this goal, process control typically involves monitoring the process using statistical methods and comparing the current level of variation in the process outcomes against the desired outcome specifications.

If the variation is within acceptable limits, the process is considered to be under control.

If the variation is outside of acceptable limits, the process may require adjustment or other corrective action to bring it back into control.

Overall, process control is an important tool in quality management, manufacturing, and other fields where consistent outcomes are critical to success.

By monitoring and adjusting processes over time, organizations can ensure that their products and services meet the needs and expectations of their customers, while minimizing waste, errors, and other sources of variation.

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The sampling method used by the principal in this scenario is stratified sampling.

Stratified sampling involves dividing the population into distinct subgroups, or strata, based on certain characteristics (in this case, grade level), and then randomly sampling from each stratum to ensure that each subgroup is represented in the sample.

By organizing the school's population by grade level and sampling from each grade level (freshman, sophomore, junior, and senior), the principal is using stratified sampling to gather data on preferred elective courses.

Therefore, This method helps ensure that the sample is representative of the entire population and can provide more accurate results compared to other sampling methods, such as convenience sampling, systematic sampling, or volunteer sampling, which may introduce biases or limitations in the sample.

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See text below



3. A principal wants to know what electives should be added to the school schedule. He organizes the school's population by grade level and then randomly samples fifty students in the freshman, sophomore, junior, and senior classes about their preferred elective course. What sampling method did the principal use?

convenience sampling

stratified sampling

systematic sampling

volunteer sampling

The Area of square is 64 square unit.

We have the coordinates (-3, -3) and (5, -3).

Using distance formula

d = √ (5 + 3)² + (-3 + 3)²

d= √8² + 0

d= 8 units

So, the Area of square

= d x d

= 8 x 8

= 64 square unit

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