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 reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

Equations are used to solve different types of problems in mathematics and in the real world.The five types of equation are 2x = 8,2y/2 = 8/2, (1/2)x + 2 = 3,3(x+4)= 21,0.4x + 1.2 = 2.6.

What is Equations Portfolio?

Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.

One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,

3x = 15

Dividing both sides by 3

3x/3 = 15/3

x = 5

Again,

2y = 8

Dividing both sides by 2

2y/2 = 8/2

y = 4

Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:

(1/2)x + 2 = 3

Subtracting 2 from both sides

(1/2)x = 1

Multiplying both sides by 2 (LCM of 1/2)

(1/2)x × 2 = 1 × 2

x = 2

(2/3)y - 1 = 3

Adding 1 to both sides

(2/3)y = 4

Multiplying both sides by 3 (LCM of 2/3)

(2/3)y × 3 = 4 × 3

y = 6

Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,

3(x + 4) = 21

Distributing 3 to (x + 4)

3x + 12 = 21

Subtracting 12 from both sides

3x = 9

Dividing both sides by 3

x = 3

Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,

0.4x + 1.2 = 2.6

Subtracting 1.2 from both sides

0.4x = 1.4

Multiplying both sides by 10 (power of 10 for one decimal place)

0.4x × 10 = 1.4 × 10

4x = 14

Dividing both sides by 4

x = 3.5

Now let's solve a real-world problem using an equation,

Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?

Let x be the amount of money Sarah saves.

Total money = $500

Money spent on the dress = $120

Money saved = Total money - Money spent on the dress

x = 500 - 120

x = 380

Therefore, Sarah will save $380.

In conclusion, equations are used to solve different types of problems in mathematics and in the real world.

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The five types of equation are  2x = 8,2y/2 = 8/2,(1/2)x + 2 = 3,3(x + 4) = 21,0.4x + 1.2 = 2.6.

Equations are an essential part of mathematics and have various applications in real-world problems. In this portfolio, we will cover different types of equations and solve them step by step. This portfolio will cover one-step equations, equations with fractions, equations with the distributive property, and equations with decimals.

One-step equations are equations that can be solved in one step. For example, if we have the equation 2x = 8, we can solve it by dividing both sides by 2. Let's solve two one-step equations,

3x = 15

Dividing both sides by 3

3x/3 = 15/3

x = 5

Again,

2y = 8

Dividing both sides by 2

2y/2 = 8/2

y = 4

Equations with fractions are equations that contain fractions. To solve these equations, we need to clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. Let's solve two equations with fractions:

(1/2)x + 2 = 3

Subtracting 2 from both sides

(1/2)x = 1

Multiplying both sides by 2 (LCM of 1/2)

(1/2)x × 2 = 1 × 2

x = 2

(2/3)y - 1 = 3

Adding 1 to both sides

(2/3)y = 4

Multiplying both sides by 3 (LCM of 2/3)

(2/3)y × 3 = 4 × 3

y = 6

Equations with distributive property are equations that involve distributing a number or a variable to the terms inside the parentheses. Let's solve an equation with the distributive property,

3(x + 4) = 21

Distributing 3 to (x + 4)

3x + 12 = 21

Subtracting 12 from both sides

3x = 9

Dividing both sides by 3

x = 3

Equations with decimals are equations that contain decimal numbers. To solve these equations, we need to clear the decimals by multiplying both sides of the equation by a power of 10. Let's solve an equation with decimals,

0.4x + 1.2 = 2.6

Subtracting 1.2 from both sides

0.4x = 1.4

Multiplying both sides by 10 (power of 10 for one decimal place)

0.4x × 10 = 1.4 × 10

4x = 14

Dividing both sides by 4

x = 3.5

Now let's solve a real-world problem using an equation,

Sarah has $500 in her bank account. She wants to buy a dress for $120 and save the rest of the money. How much money will Sarah save?

Let x be the amount of money Sarah saves.

Total money = $500

Money spent on the dress = $120

Money saved = Total money - Money spent on the dress

x = 500 - 120

x = 380

Therefore, Sarah will save $380.

In conclusion, equations are used to solve different types of problems in mathematics and in the real world.

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The value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

The property of intersecting chords states that in a circle, if two chords intersect, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.

UF × FS = VF × FT

8(10x - 1) = 9 × 16

80x - 8 = 144

80x = 144 + 8 {collect like terms}

80x = 152

x = 152/80 {divide through by 80}

x = 1.9

FS = 10(1.9) - 1 = 18

Therefore, the value of x for the intersecting chords is derived to be 1.9 and the segment FS is equal to 18

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the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

How to solve the question?

To determine whether a triangle can be formed using the given side lengths, we need to apply the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

Let's check each option:

A. XY = 11 mm, YZ = 12 mm, XZ = 18 mm

To form a triangle, we need to check whether the sum of any two sides is greater than the third side. Let's check:

XY + YZ = 11 mm + 12 mm = 23 mm > XZ = 18 mm

YZ + XZ = 12 mm + 18 mm = 30 mm > XY = 11 mm

XY + XZ = 11 mm + 18 mm = 29 mm > YZ = 12 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

B. XY = 16 mm, YZ = 12 mm, XZ = 23 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 12 mm = 28 mm > XZ = 23 mm

YZ + XZ = 12 mm + 23 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 23 mm = 39 mm > YZ = 12 mm

Again, all the combinations are greater than the third side, so a triangle can be formed with these side lengths.

C. XY = 16 mm, YZ = 17 mm, XZ = 18 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 16 mm + 17 mm = 33 mm > XZ = 18 mm

YZ + XZ = 17 mm + 18 mm = 35 mm > XY = 16 mm

XY + XZ = 16 mm + 18 mm = 34 mm > YZ = 17 mm

All the combinations are greater than the third side, so a triangle can be formed with these side lengths.

D. XY = 11 mm, YZ = 12 mm, XZ = 28 mm

Let's check whether the sum of any two sides is greater than the third side:

XY + YZ = 11 mm + 12 mm = 23 mm < XZ = 28 mm

YZ + XZ = 12 mm + 28 mm = 40 mm > XY = 11 mm

XY + XZ = 11 mm + 28 mm = 39 mm > YZ = 12 mm

The first combination is less than the third side, so a triangle cannot be formed with these side lengths.

Therefore, the answer is (D) XY = 11 mm, YZ = 12 mm, XZ = 28 mm would NOT form a triangle with vertices X, Y, and Z.

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The distance between the coordinates A and B is 2 √(10) units.

A mathematical method called the distance formula is used to determine how far apart two points in a coordinate plane are from one another. It can be used with any two points (x1, y1) and (x2, y2) and is based on the Pythagorean theorem.

d = √((x2 - x1)² + (y2 - y1)²)

where d is the separation of the two spots.

To put it another way, we may visualise a right triangle created by the two locations and the horizontal and vertical lengths separating them to get the distance between them. The triangle's hypotenuse, or the distance between its two points, is measured using the distance formula.

The distance formula is given as:

d = √((x2 - x1)² + (y2 - y1)²)

Now, for the given coordinates we have:

d = √((1 - (-5))² + (3 - 1)²)

d = √(6² + 2²)

d = √(40)

d = 2 √(10)

Hence, the distance between A and B is 2 √(10) units.

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Answer:

I cannot agree or disagree with this statement without more information.

The fact that -55 is less than -62 is correct, and it does suggest that the temperature on Mars may have been colder than the temperature on Earth (assuming that the comparison is being made between temperatures measured in the same units). However, it's important to note that comparing just two temperatures (even if they are in different units) is not enough to draw conclusions about the overall climate or temperature patterns on Mars or Earth.

In addition, it's unclear what evidence Jada is using to make this comparison. Without more context or information about the source of this statement, it's difficult to evaluate its accuracy or validity.

Answer: A. Graph D

Step-by-step explanation: Graph D shows the solution to the system of linear inequalities because it includes all the points that satisfy both inequalities. The shaded region in graph D is where the two shaded regions from the other graphs overlap, which means that it is the only region that satisfies both inequalities simultaneously.

Answer:

the outlier is 37 but for 43 are they asking for the upper and lower quartiles or the lowest and highest number

Answer:

If the mean absolute deviation of a data set is close to 0, it means that the data values in the set are very close to the mean of the set. In other words, the data points are clustered tightly around the average value, indicating that there is little variation or dispersion in the data.

This can be useful information in analyzing the data, as it suggests that the data is relatively homogeneous and consistent. On the other hand, if the mean absolute deviation is large, it suggests that the data is widely spread out and may have significant variability, which may require further investigation or analysis.

a) Classroom:

Perimeter = 2(length + breadth) = 2(10m + 8m) = 36m

Area = length x breadth = 10m x 8m = 80m^2

Volume = length x breadth x height = 10m x 8m x 3m = 240m^3

b) Box:

Perimeter = 2(length + breadth) = 2(40cm + 25cm) = 130cm

Area = 2(length x breadth + length x height + breadth x height) = 2(40cm x 25cm + 40cm x 30cm + 25cm x 30cm) = 41500cm^2

Volume = length x breadth x height = 40cm x 25cm x 30cm = 30000cm^3

c) Cabinet:

Perimeter = 2(length + breadth) = 2(80cm + 70cm) = 300cm

Area = 2(length x breadth + length x height + breadth x height) = 2(80cm x 70cm + 80cm x 2m + 70cm x 2m) = 12640cm^2

Volume = length x breadth x height = 80cm x 70cm x 2m = 112000cm^3

Note: It's important to use consistent units in calculations. In this case, I converted the dimensions to a common unit (meters or centimeters) before performing the calculations.

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To find an expression for the width of the rectangle, we can use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we know that the area is given by the expression +7x² + 11x + 2 and the length is given by the expression (x + 2). So we can substitute these values into the formula and solve for the width:

+7x² + 11x + 2 = (x + 2) x width

Expanding the right-hand side, we get:

+7x² + 11x + 2 = xwidth + 2width

Rearranging terms, we get:

+7x² + 11x + 2 - xwidth - 2width = 0

Factoring out the width, we get:

width*(x - 2) + 2*(x - 1) = 0

Dividing both sides by (x - 2), we get:

width = -2*(x - 1)/(x - 2)

Therefore, an expression for the width of the rectangle is:

width = -2*(x - 1)/(x - 2)

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The range is the best measure of variability for this data, and it equals 8.

In statistics, the range is a measure of variability that describes the difference between the largest and smallest values in a dataset. It is the simplest measure of variability and is calculated by subtracting the smallest value in the dataset from the largest value.

The range is a measure of variability that tells us the spread of the data, i.e., how far apart the minimum and maximum values are. It is calculated by subtracting the smallest value in the dataset from the largest value.

In the given line plot, the horizontal axis represents the number of rose bouquets purchased per day, and the vertical axis represents the frequency (i.e., how many times that particular number of rose bouquets was purchased). Based on the plot, we can see that the lowest number of rose bouquets purchased in a day is 1, and the highest number is 9. Therefore, the range is 9 - 1 = 8.

In contrast, the IQR (interquartile range) is a measure of variability that gives us an idea of how spread out the middle 50% of the data is. It is calculated by subtracting the 25th percentile (Q1) from the 75th percentile (Q3). Since we do not have the values for Q1 and Q3, we cannot calculate the IQR for this dataset.

Therefore, the range is the best measure of variability for this data, and it equals 8.

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Translate the solid circle 2 units to the left and 2 units down and dilate the solid circle by a scale factor of 2. and the circles are similar

(a) To move the solid circle exactly onto the dashed circle, we need to perform the following transformations:

Therefore, the blank spaces should be filled as follows:

Translate the solid circle 2 units to the left and 2 units down.

Dilate the solid circle by a scale factor of 2.

(b) Yes, the original solid circle and the dashed circle are not similar, because they have different radii.

This is because all circles are similar

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Riley could have read any fraction between 1/2 and 4/5 of the book.

We must determine the range of potential fractions of the book that Riley may have read in order to determine what portion Riley may have read.

Riley must have read less than 4/5 of the book because we know she read less than Mariette. Riley read more than Erika, and because we also know that Riley read more, Riley must have read more than 0.5 of the book.

Therefore, the fraction of the book that Riley could have read is between 0.5 and 4/5, or:

0.5 < Riley's fraction < 4/5

To express this range as a single fraction, we can find a common denominator for 0.5 and 4/5:

0.5 = 2/4

4/5 = 4/4 * 1/5 = 5/5 × 4/25 = 20/25

So the range of possible fractions for Riley is:

2/4 < Riley's fraction < 20/25

We can simplify this range by finding the lowest common denominator of 4 and 25, which is 100:

2/4 = 25/50

20/25 = 80/100

So the range of possible fractions for Riley is:

25/50 < Riley's fraction < 80/100

We can simplify this range by dividing both sides by 50:

1/2 < Riley's fraction < 4/5

Therefore, Riley could have read any fraction between 1/2 and 4/5 of the book.

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The area of the garden which is same as the shape of an octagon would be = 101.2in².

To calculate the area of an octagon the formula that can be used is given below;

Area of an octagon = (number of sides × length of one side × apothem)/2

For an octagon = 8 sides

apothem = 5.5in

Length of one side = 4.6in

Area = 8×4.6×5.5/2

= 202.4/2

= 101.2in²

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Answer:

135.07 mm2

Step-by-step explanation:

height = 10.39 mm

area = 135.07 mm2

Answer:

Peter opens an account with a $600 deposit that earns 8% simple interest annually. He makes no other deposits or withdrawals.

Complete the sentences:

This situation can be modeled by a linear function that grows in interest.

Peter will earn $48 in interest each year.

Explanation:

Simple interest is calculated as a percentage of the principal amount and does not compound over time. Therefore, the amount of interest earned each year is constant, and the growth of the account is linear.

To calculate the amount of interest earned each year, we multiply the initial deposit by the interest rate:

$600 x 0.08 = $48

Therefore, Peter will earn $48 in interest each year. After four years, he will have earned:

4 x $48 = $192

So his total balance will be:

$600 + $192 = $792

Since the growth of the account is linear, we can model it with a linear function of the form:

y = mx + b

Where y is the total balance, x is the number of years, m is the slope (or rate of growth), and b is the initial balance.

In this case, the slope is the amount of interest earned each year, which is $48, and the initial balance is $600. So the linear function that models this situation is:

y = 48x + 600

Answer:

Answer is 20

Step-by-step explanation:

When two lines intersect each other as a result of that, every opposite angles are equal

so,

6x+20 = 140

6x = 120

x = 120/6

x = 20

Answer:

x = 20

Step-by-step explanation:

Vertically opposite are equal

therefore

6x + 20 = 140

6x = 140-20

6x = 120

6x/6 = 120/6

x = 20

Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.

Explain average

The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.

According to the given information

Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:

Y = (X1 + X2 + X3 + X4 + X5) / 5

Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:

E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)

Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:

E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4

Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:

E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)

Thus, we can simplify the expression as:

E(Y|X1=150) = (4E(X) / 4) = E(X) = 100

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Answer:

The comparison that is not correct is:

C. -8 > -6

This is not correct because -8 is actually less than -6. Therefore, the correct comparison would be -8 < -6.

The other comparisons are correct:

A. 1 > -9 (true, because 1 is greater than -9)

B. 3 < 6 (true, because 3 is less than 6)

D. -3 < 4 (true, because -3 is less than 4)

To subtract (c-3d-e) from the sum of (4c+d-e) and (2c-3d+2e), we can first find the sum of the two polynomials, which is (4c+d-e) + (2c-3d+2e) = 6c - 2d + e. Then, we can subtract (c-3d-e) from this sum by changing the signs of the terms in (c-3d-e) and adding the resulting polynomial to 6c - 2d + e. This gives us:

(4c+d-e) + (2c-3d+2e) - (c-3d-e) = 5c + d + 4e

Therefore, the answer is 5c + d + 4e.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman.

Numbers are mathematical units of measurement and labelling. It is a sign or collection of symbols that are used to represent a quantity, usually a real or integer number.

Out of a group of ten men & eight women, there are 1320 possible ways to form a committee of two men and one woman. The idea of combination can be used to arrive to this number.

Calculating the number of possible combinations of a given number of things is done mathematically using the concept of combination. C(n,r) = n! / (r! (n - r)!), where n is the total number of items and r is the number of things to be picked at a time, is the formula used to compute it. In this instance, r is the number of persons to be picked, which is 3, and n is the total number of people to be chosen from the group, which is 18, consisting of 10 males and 8 women.

As a result, there are a total of 10 ways for men and 8 ways for women to form a committee of two men and one woman C(18,3) = 18! / (3! (18 - 3)!) = 18! / (3! 15!) = 1320.

Thus, there are 1320 different methods to create a committee of two men and one woman out of a group of ten men and eight women.

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The Correct Answer Is:  High-strength sports.

explanation:

Because for wrestling you have to use, you're strength. (And I just did the exam and I got it wrong for choosing the wrong answer, so I believe it's my answer. !!so, it's not high-power sports)

I hope it helps you!

:)

From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)

b, c, d, and f are true

The opposite angles of a parallelogram are congruent (b)

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)

Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)

Transitive property, like c (f)

Answer: This triangle is isoscele

Step-by-step explanation: