## Envision Math Grade 8 Volume 1 Chapter 4 Investigate Bivariate Data

**Page 243 Exercise 1 Answer**

The video mentioned above shown some images that predict the height and the length of various humans and things.

The reason is for knowing the average height each of them follows and how much it will grow in their lifetime.

You may frequently utilize visual cues to figure out what’s in the shot and what the remainder of the thing could appear like.

The first question that comes to my mind after watching this video is “What is my height and is that normal for my age?”

“What is my height and is that normal for my age?”

This is the question that made up my mind after watching this video.

**Page 243 Exercise 2 Answer**

The video mentioned above shown some images that predict the height and the length of various humans and things.

The reason is for knowing the average height each of them follows and how much it will grow in their lifetime.

You may frequently utilize visual cues to figure out what’s in the shot and what the remainder of the thing could appear like.

The main question that comes to my mind after watching this video is “Is that height normal for my age?”.

The main question that I will answer that I saw in the video is “Is that height normal for my age?”.

**Page 243 Exercise 3 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The first question that comes to my mind after watching this video is “What is my height and is that normal for my age?”.

An answer that I was predicted to this main question is 158 cm and it is below average for my age.

An answer that I was predicted to this main question is 158 cm and it is below average for my age. I found my answer by measuring myself using a tape and the people of my age are far taller than me this means that I’m shorter than them.

**Page 243 Exercise 4 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

A number that I know which is too small to be the answer is 50 cm since infants grow 50 cm within the age of three.

A number that is too large to be the answer is 214 cm since the percentage of 7 footers is only 0.000038%.

On the number line below, we have written a number that is too small to be the answer. Also, we have written a number that is too large.

**Page 243 Exercise 5 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

A number that I know which is too small to be the answer is 50 cm since infants grow 50 cm within the age of three.

A number that is too large to be the answer is 214 cm since the percentage of 7 footers is only 0.000038%.

My height is 158 cm.

Plotting my prediction on the same number line, I get,

**Page 244 Exercise 6 Answer**

Informally, a conjecture is simply making judgments over something based on what you understand and monitor.

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

In this situation, information regarding the average height of a normal healthy person of my age would be more helpful to know.

This is because I can use that information to know that my height is normal or not.

In this situation, information regarding the average height of a normal healthy person of my age would be more helpful to know.

I can use that information to know that my height is normal or not.

**Page 244 Exercise 7 Answer**

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

To get the information I need regarding the height, I have to use a measuring tape.

This will determine the height of every person accurately.

A measuring tape can be used to get the information I need. My height is 158 cm.

**Page 244 Exercise 8 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The following steps are used to refine my conjecture:

Measure your height several times.

Recognize each one of the conjecture’s circumstances – The situations of a conjecture are the requirements that must be met already when we acknowledge the conjecture’s findings.

Create both examples and non-examples – Find items that meet the criteria and verify to see if they also fulfill the conjecture’s inference. Start by removing each situation one at a time and build non-examples that gratify the other circumstances but not the inference.

Seek out counterexamples – A counterexample meets all of the circumstances of a statement except the conclusion.

Try comparing yours with others.

From this way, I have found out that my height is 158 cm and it is below average.

**Page 244 Exercise 9 Answer**

A conjecture is a declaration that is thought to be accurate based on data.

In general, a conjecture is your view or an informed guess over something you recognize.

You can’t indicate any of it; you simply observed a pattern and conclude.

I have found out that my height is 158 cm.

The average height of a person of my age is 175 cm.

This is far greater than my prediction.

The answer to the Main Question is that the average height of a person of my age is 175 cm. It is far greater than my prediction.

**Page 245 Exercise 10 Answer**

A conjecture is a result or statement in math that is thought to be valid based on basic evidence to back it up but for which no evidence or falsifiability has ever been produced.

A conjecture is nothing but a conclusion we made up where it doesn’t have any proof to make it false.

The first question that comes to my mind after watching this video is “What is my height and is that normal for my age?”.

The answer that I was predicted to this main question is 158 cm.

The answer that I saw in the video is “175 cm”.

The answer that I saw in the video is 175 cm as the average height for my age.

**Page 245 Exercise 11 Answer**

The first question that comes to my mind after watching this video is “What is my height and is that normal for my age?”.

The answer that I was predicted to this main question is 158 cm.

The answer that I saw in the video is “175 cm”.

My answer doesn’t match the answer in the video. This is because my genetic factors and lack of physical work are some of the reasons for my shorter height.

My answer doesn’t match the answer in the video. This is because genetic factors play a vital role in deciding one’s height.

**Page 245 Exercise 12 Answer**

The answer that I was predicted to this main question is 158 cm.

The answer that I saw in the video is “175 cm”.

My answer doesn’t match the answer in the video. This is because my genetic factors and lack of physical work are some of the reasons for my shorter height.

I am going to do some physical exercises, stretching, and yoga to increase my height in order to change my model.

Yes, I would change my model now that I know the answer.

**Page 246 Exercise 13 Answer**

The following steps are used to refine my conjecture:

Measure your height several times.

Recognize each one of the conjecture’s circumstances – The situations of a conjecture are the requirements that must be met already when we acknowledge the conjecture’s findings.

Create both examples and non-examples – Find items that meet the criteria and verify to see if they also fulfill the conjecture’s inference. Start by removing each situation one at a time and build non-examples that gratify the other circumstances but not the inference.

Seek out counterexamples – A counterexample meets all of the circumstances of a statement except the conclusion.

Try comparing yours with others.

The model helps me answer the Main Question by making accurate measurements of my height and to know whether my height is normal or not for my age.

**Page 246 Exercise 14 Answer**

The first question that comes to my mind after watching this video is “What is my height and is that normal for my age?”

The answer that I was predicted to this main question is 158 cm.

The answer that I saw in the video is “175 cm”.

My answer doesn’t match the answer in the video. This is because my genetic factors and lack of physical work are some of the reasons for my shorter height.

The height which I notice in my classmate’s model is that he is 185 cm tall.

This helps me to know under which conditions people’s height is increasing.

The calculations differ based on the genetic factors and physical conditions I am in. This helps me to know under which conditions people’s height is increasing.

**Page 246 Exercise 15 Answer**

The length of my classmate’s wingspan is 185 cm.

I have also calculated his height which is also 185 cm.

This means that both his wingspan or arm span and his height are equal.

My classmate’s wingspan is 185 cm. This is equal to my classmate’s height. My model predicts my classmate’s actual height well.

**Page 247 Exercise 1 Answer**

The number of visits, age, months, and time are examples of measurement data.

Colors, gender, and nationality are examples of categorical data.

If 7out of 20 people prefer reading a book to watching a movie, then saying that 35 of the people polled prefer reading a book is the relative frequency.

The number of visits, age, months, and time are examples of measurement data.

Colors, gender, and nationality are examples of categorical data.

If 7 out of 20 people prefer reading a book to watching a movie, then saying that 35 of the people polled prefer reading a book is the relative frequency.

**Page 247 Exercise 1 Answer**

This scatter plot shows a positive association between vacation and hours of employees at ABC Corporation.

Some of the points are far from the trend line. This shows a weak association.

This scatter plot shows a weak, positive linear association between experience and vacation of employees at ABC Corporation.

**Page 249 Exercise 1 Answer**

Since we can see that in the given graph as the x-coordinate increases than the y-coordinate is decreasing

This means there is a negative association.

We can draw a trend line to see whether the association is weak or strong.

Place the pencil in the middle of all points and draw a line.

As we can see the points are not really close to the trend line which means there is a weak negative association.

There is a weak negative association.

**Page 249 Exercise 2 Answer**

If we look at the graph we can already see that the data are not linear when the points shape as than the association is no longer linear.

Hence, the data is not linear.

**Page 249 Exercise 1 Answer**

Given

y = 6x + 120

y = $570

To find – expected number of copiers sold

Therefore, the expected number of copies sold is 75

**Page 249 Exercise 2 Answer**

Given

y = 6x + 120

x = 100

Substitute 100 for x and simplify

Therefore, the expected wage for given employee is 720.

**Page 251 Exercise 1 Answer**

Given:

A) (6,−0.5y + 20−0.5y = 13)

−y + 20 = 13

−y = 13 − 20

−y = −7

y = 7

(6,7)

B) (4−3x + 7x = −8,7)

4 + 4x = −8

4x = −8 −4

4x = −12

x = \(-\frac{12}{4}\)

(−3,7)

C) (2x + 4 − 6x = 24,5)

4 − 4x = 24

−4x = 24 − 4

−4x = 20

x = −5

(−5,5)

D) (5x + 6 − 10x = 31,1)

−5x + 6 = 31

−5x = 31 − 6

−5x = 25

x = −5

(−5,1)

E) (7x − 3 − 3x = 13,−2)

4x − 3 = 13

4x = 13 + 3

x = 4

(4,−2)

F) (4,− 12y + 8y − 21 = −5)

−4y − 21 = −5

−4y = −5 + 21

−4y = 16

y = −4

(4,−4)

G) (44 = 6x − 1 + 9x,−5)

44 = 15x − 1

45 = 15x

x = 3

(3,−5)

H) (−5, 4y + 14 − 2y = 4)

2y + 14 = 4

2y = 4 − 14

2y = −10

y = −5

(−5,−5)

I) (−5, 15 + y + 6 + 2y = 0)

21 + 3y = 0

3y = −21

y = −7

(−5,−7)

J) (4,3y + 32 − y = 18)

2y + 32 = 18

2y = 18 − 32

2y = −14

y = −7

(4,−7)

K) (6, 5y + 20 + 3y = −20)

8y + 20 = −20

8y = −20 − 20

8y = −40

y = −5

(6,−5)

L) (9x − 14 − 8x = −8,−1)

x − 14 = −8

x = −8 + 14

x = 6

(6,−1)

M) (−3,−5y + 10 − y = −2)

−6y + 10 = −2

−6y = −2 −10

−6y = −12

y = 2

(−3,2)

N) (−3,− 5y + 10 − y = −2)

−6y + 10 = −2

−6y = −2 −10

−6y = −12

y = 2

(−3,2)

If we simply look at the graph, than we know that we simply have to remove letter’s’ from the word seven, and we are left with ‘even’.