Texas Go Math

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 15.1 Answer Key Mean Absolute Deviation.

Texas Go Math Grade 8 Lesson 15.1 Answer Key Mean Absolute Deviation

Texas Go Math Grade 8 Lesson 15.1 Explore Activity Answer Key

Understanding Mean Absolute Deviation

A measure of center is a single number used to describe a data set. One measure of the center is the mean, which is the sum of the data values divided by the number of values in the data set. A measure of variability is a single number used to describe the spread of a data set. One measure of variability is the mean absolute deviation (MAD), which is the mean distance between each data value and the mean of the data set.

The data represent the height, in feet, of various buildings. Find the mean absolute deviation for each data set.
A. 60, 58, 54, 56, 63, 65, 62, 59, 56, 58
Calculate the mean. Round to the nearest whole number.
Complete the table.

Calculate the MAD by finding the mean of the values in the second row of the table. Round to the nearest whole number.
Answer:
Given that the heights of the various buildings are 60, 58, 54, 56, 63, 65, 62, 59, 56, 58.
Mean = sun of the heights of the various buildings/ number of the heights of the various buildings. = 60 + 58 + 54 + 56 + 63 + 65 + 62 + 59 + 56 + 58/10 = 526/10 = 52.6
52.6 rounded to the nearest whole number is 53. Because the decimal point is greater than 5 then remove the fraction part and 1 to the decimal.

Given that the heights of the various buildings are 60, 58, 54, 56, 63, 65, 62, 59, 56, 58.
Mean = 52.6
Distance from mean equal to
60 – 52.6 = 7.4
58 – 52.6 = 5.4
54 – 52.6 = 1.4
56 – 52.6 = 3.4
63 – 52.6 = 10.4
65 – 52.6 = 12.4
62 – 52.6 = 9.4
59 – 52.6 = 6.4
56 – 52.6 = 3.4
58 – 52.6 = 5.4
Mean absolute deviation = sum of the distances from mean/number of the distances = 7.4 + 5.4 + 1.4 + 3.4 + 10.4 + 12.4 + 9.4 + 6.4 + 3.4 + 5.4/ 10 = 6.5
6.5 rounded to the nearest whole number is 7.

B. 46, 47, 56, 48, 46, 52, 57, 52, 45
Find the mean. Round to the nearest whole number.

Complete the table.

Calculate the MAD. Round to the nearest whole number.
Answer:
Given that the heights are 46, 47, 56, 48, 46, 52, 57, 52, 45.
Mean = sum of the heights by number of the heights = 46 + 47 + 56 + 48 + 56 + 52 + 57 + 52 + 45/9 = 459/9 = 51.
51 rounded to the nearest whole number is 51.

Given that the heights are 46, 47, 56, 48, 46, 52, 57, 52, 45.
Mean = 51
Distance from mean equal to
51 – 46 = 5
51 – 47 = 4
51 – 56 = -5
51 – 48 = 3
51 – 46 = 5
51 – 52 = -1
51 – 57 = -6
51 – 52 = -1
51 – 45 = 6
Neglect the negative signs.
Mean absolute deviation = sum of the distances/ number of the distances.
= 5 + 4 + 5 + 3 + 5 + 1 + 6 + 1 + 6/9 =30/9 = 3.3
3.3 rounded to the nearest whole number is 3.

Reflect

Go Math Grade 8 Answer Key Pdf Mean Absolute Deviation Question 1.
Analyze Relationships Compare the MADs. How do the MADs describe the distribution of the heights in each group?
Answer:
Mean absolute deviation of first heights is 6.5
Mean absolute deviation of seconds heights is 3.3
The mean absolute deviation of the first heights is greater than the mean absolute deviation of the second heights.
Using the formula distance = each height – mean. We can distribute the heights in each group.

Your Turn

Question 2.
Two baristas at a coffee shop each served 10 large coffees. The amount in each large coffee is shown below. Which barista’s coffees showed less variability?

Answer:
Given that,
The Amount in the first Barista A’s large coffees = 19.1 + 20.1 + 20.9 + 19.6 + 20.9 + 19.5 + 19.2 + 19.4 + 20.3 + 20.9 = 199.9.
The Amount in the second Barista A’s large coffees = 20.1 + 19.6 + 20.0 + 20.5 + 19.8 + 20.0 + 20.1 + 19.7 + 19.9 + 20.4 = 200.1
The first coffee shop has the least variability.

Question 3.
Two aspirin-making devices are set to make tablets containing 0.35 gram of aspirin. The actual amounts in 8 tablets from each device are shown. Use a spreadsheet to determine which device has less variability.

Answer:

Given that,
The tablets contained 0.35 grams of aspirin.
The amounts of Aspirin in tablets made by device A have the least variability.

Texas Go Math Grade 8 Lesson 15.1 Guided Practice Answer Key

Mean Absolute Deviation Part 1 Answer Key 8th Grade Go Math Question 1.
A bus route takes about 45 minutes. The company’s goal is a MAD of less than 0.5 minutes. One driver’s times for 9 runs of the route are shown. Did the bus driver meet the goal? (Explore Activity and Example 1)

a. Calculate the mean of the bus times. ______________
Answer:
Given that the time to complete the bus route is 44.2, 44.9. 46.1, 45.8, 44.7, 45.2, 45.1, 45.3, 44.6.
Mean = sum of the bus time to complete the round/number of the bus rounds to complete the round.
44.2 + 44.9 + 46.1 + 45.8 +44.7 + 45.2 + 45.1 + 45.3 + 44.6/9 = 405.9/9 = 45.1

b. Calculate the MAD to the nearest tenth. ____________
The bus driver did /did not meet the company’s goal.
Answer:
Given that the time to complete the bus route is 44.2, 44.9. 46.1, 45.8, 44.7, 45.2, 45.1, 45.3, 44.6.
Mean = 45.1
Mean absolute deviation equal to first subtracting the mean from each route.
44.2 – 45.1 = -0.9
44.9 – 45.1 = -0.2
46.1 – 45.1 = 1
45.8 – 45.1 = 0.7
44.7 – 45.1 = -0.4
45.2 – 45.1 = 0.1
45.1 – 45.1 = 0
45.3 – 45.1 = 0.2
44.6 – 45.1 = -0.5
Neglect the negative sign.
Mean absolute deviation = sum of the mean from each value/number of the mean from each value = 0.9 + 0.2 + 1 + 0.7 + 0.4 + 0.1 + 0 + 0.2 + 0.5/9 = 4/9 = 0.4 minutes.
The company’s goal is for the mean absolute deviation to be less than 0.5 minutes.
Mean absolute deviation = 0.4 minutes.
Yes, The driver did meet the company’s goal

Question 2.
Below are different driver’s times on the same route. Find the mean and the MAD using a spreadsheet. Enter the data values into row 1 using cells A to I. Enter “mean =” into cell A2 and “MAD =” into cell A3. (Example 2)

The mean is ___________ minutes, and the MAD is ____________ minutes.
This time, the bus driver did/did not meet the company’s goal.
Answer:
Given that the data of the times to complete the bus route is 44.4, 43.8. 45.6, 45.9, 44.1, 45.6, 44.0, 44.9, 45.8.
Mean = sum of the sum of the bus time to complete the round/number of the bus rounds to complete the round.
= 44.4 + 43.8 + 45.6 + 45.9 + 44.1 + 45.6 + 44.0 + 44.9 +45.8/9
=404.1/9
= 44.9
The mean absolute deviation is first to find the difference between the mean and each round.
44.4 – 44.9 = -0.5
43.8 – 44.9 = -1.1
45.6 – 44.9 = 0.7
45.9 – 44.9 = 1
44.1 – 44.9 = -0.8
45.6 – 44.9 = 0.7
44.0 – 44.9 = -0.9
44.9 – 44.9 = 0
45.8 – 44.9 = 0.9
Neglect the negative sign.
Mean absolute deviation = sum of the mean from each value/number of the mean from each value = 0.5 + 1.1 + 0.7 + 1 + 0.8 + 0.7 + 0.9 + 0 + 0.9/9 = 6.6/9 = 0.7

Essential Question Check-In

Mean Absolute Deviation 8th Grade Go Math Question 3.
What is the mean absolute deviation and what does it tell you about data sets?
Answer:
The company’s goal is for the mean absolute deviation to be less than 0.5 minutes.
Mean absolute deviation = 0.7 minutes.
The driver did not meet the company’s goal.

Texas Go Math Grade 8 Lesson 15.1 Independent Practice Answer Key

Frank wants to know how many people live in each household in his town. He conducts a random survey of 10 people and asks how many people live in their household. His results are shown in the table.

Question 4.
Calculate the mean number of people per household.
Answer:
Mean = sum of the people /number of the people
= 1 + 6 + 2 + 4 + 4 + 3 + 5 + 5 + 2 + 8/10
= 40/10 = 4
A mean number of people per household = 4.

Question 5.
Calculate the MAD of the number of people per household.
Answer:
First subtract the mean from the given number of each person.
1 – 4 = -3
6 – 4 = 2
2 – 4 = -2
4 – 4 = 0
4 – 4 = 0
3 – 4 = -1
5 – 4 = 1
5 – 4 = 1
2 – 4 = -2
8 – 4 = 4
Negate the negative sign
Mean absolute deviation = sum of the difference of mean and each person/number of the people in the household.
= 3 + 2 + 2 + 0 + 0 + 1 + 1 + 1 + 2 + 4 /10
= 16/10
Mean absolute deviation = 1.6

Question 6.
What conclusions can you draw about the “typical” number of people in each household? Explain.
Answer:
3, 2, 2, 0, 0, 1, 1, 1, 2, 4 typical numbers of people in each household.
We get these numbers by finding the difference between the mean and each number of people per household.

Teachers are being trained to standardize the scores they give to students’ essays. The same essay was scored by 10 different teachers at the beginning and at the end of their training. The results are shown in the tables.

Answer Key Mean Absolute Deviation Worksheet Answers Question 7.
Calculate the MADs for the teachers’ scores. Did the teachers make progress in standardizing their scores?
Answer:
Given that the data of the scores for the essay at the beginning of teachers’ training are 76, 81, 85, 79, 89, 86, 84, 80, 88, and 79.
Mean = sum of the scores/number of the scores.
= 76 + 81 + 85 + 79 + 89 + 86 + 84 + 80 + 88 + 79 /10
= 827/10
= 82.7
Difference = each score – mean
76 – 82.7 = -6.7
81 – 82.7 = -1.7
85 – 82.7 = 2.3
79 – 82.7 = -3.7
89 – 82.7 = 6.3
86 – 82.7 = 3.3
84 – 82.7 = 1.3
80 – 82.7 = -2.7
88 – 82.7 = 5.3
79 – 82.7 = -3.7
Negate the negative signs.
Mean absolute deviation = sum of the difference/number of the difference.
= 6.7 + 1.7 + 2.3 + 3.7 + 6.3 + 3.3 + 1.3 + 2.7 + 5.3 + 3.7 /10
= 37/10 = 3.7
The mean absolute deviation of the scores for the essay at the beginning of teachers’ training is 3.7.
Given that the data of the scores for the essay at the end of teachers training is 79, 82, 84, 81, 77, 85, 82, 80, 78, 83.
Mean = sum of the scores/number of the scores.
= 79 + 82 + 84 + 81 + 77 + 85 + 82 + 78 + 83 / 10
=731/10
Mean = 73.1
Difference = each score – mean
79 – 73.1 = 5.9
82 – 73.1 = 8.9
84 – 73.1 =10.9
81 – 73.1 = 7.9
77 – 73.1 = 3.9
85 – 73.1 = 11.9
82 – 73.1 = 8.9
80 – 73.1 =6.9
78 – 73.1 =4.9
83 – 73.1 =9.9
Mean absolute deviation = sum of the difference /number of the differences.
5.9 + 8.9 + 10. 9 + 7.9 + 3.9 + 11.9 + 8.9 + 6.9 + 4.9 + 9.9 /10
= 80/10
=8
The mean absolute deviation of the scores for the essay at the end of the teacher’s training is 8.
Yes, the teachers make progress in standardizing their scores.

Question 8.
What If? What would it mean if the teachers had a MAD of 0?
Answer: Mean absolute deviation is 0. It means that there is no deviation, so the values are the same.

The annual rainfall for Austin, Texas, and San Antonio, Texas, in each of the years from 2002 to 2011 are shown in the tables. Use the data for 9-11.

Question 9.
Use a spreadsheet to find the mean for the two cities’ annual rainfalls. In which city does it rain more in a year, on average?
Answer:

Mean of annual rainfall for Austin, Texas = sum of annual rainfall/number of years.
= 318.18/10
= 31.8

Mean of San Antonio, Texas = sum of annual rainfall/number of years = 304.59/10
Mean of San Antonio, Texas = 30.45

Mean Absolute Deviation Formula 8th Grade Go Math Question 10.
Use your spreadsheet to find the MADs. Use the MADs to compare the distribution of annual rainfall for the two cities.
Answer:

Mean of annual rainfall for Austin, Texas = sum of the deviations/number of the deviations
= 96.8/10
= 9.68

Mean absolute deviation of San Antonio, Texas = sum of the deviations/number of the deviations.
= 109.34/10
= 10.934

Question 11.
Make a Conjecture Does the information allow you to predict how the future amounts of rainfall for the two cities will compare? Explain.
Answer:
Mean of annual rainfall for Austin, Texas = 9.68
Mean absolute deviation of San Antonio, Texas = 10.93
The future rainfall in Austin, Texas is less than the Future rainfall in San Antonio, Texas.

Question 12.
Critical Thinking The life spans of 10 adult mayflies have a mean of 4 hours and a MAD of 2 hours. Fill in the table below with possible values for the life spans. You can use the same value more than once.

Can any one of the 10 mayflies in the group live for 1 full day? Justify your answer.
Answer:
Given that,
Mean = 4 hours.
Mean absolute deviation = 2 hours.
Assume that the life spans of each fisv is 4 hours
Then mean = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4/10
= 40/10
= 4hours.
No fish can live for a full day.

H.O.T. Focus on Higher Order Thinking

Question 13.
Multistep In a spreadsheet, before entering any data values, first enter “mean =” into cell A2 and the formula =AVERAGE(A1 :J1) into cell B2. Next, enter “MAD =”into cell A3 and the formula =AVEDEV(A1:J1) into cell B3.You should see #DIV/0! in cell B2 and #NUM! in cell B3 as shown. Now do the following:

a. Enter “1” into cell A1. What do you get for the mean and the MAD of the data set? Explain why this makes sense.
Answer:
Given that,
0! = 1
Enter 1 into cell A1. then mean = 1/1 = 1
Mean absolute deviation = 1.

b. Enter “2” into cell B1. What do you get for the mean and the MAD of the data set this time? Explain why this makes sense.
Answer:
Given that
Enter 2 into cell A1. then mean = 2/1 = 2
Mean absolute deviation = 2.

c. Enter the numbers 3 through 10 into cells C1 to J1 and watch the mean and the MAD change. Do they increase, decrease, or stay the same? Explain why this makes sense.
Answer:
Given that,
Enter the numbers 3 through 10 into cells C1 to J1.
The mean = 0
The mean absolute deviation increases when the number increases.

Question 14.
Make a Conjecture Each of the values in a data set is increased by 10. Does this affect the MAD of the data set? Why or why not?
Answer:
Each of the values in the data set is increased by 10 then the values of the data increase. Then the mean absolute deviation of the data will not affect.

Question 15.
What If? Suppose a data set contains all negative numbers. Would the MAD for the data set also be negative? Explain.
Answer:
The data set contains all negative numbers also the mean absolute deviation is positive. Because the negative numbers cannot be eligible.

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 15.2 Answer Key Generating Random Samples.

Texas Go Math Grade 8 Lesson 15.2 Answer Key Generating Random Samples

Texas Go Math Grade 8 Lesson 15.2 Explore Activity Answer Key

Explore Activity 1

Generating a Random Sample

When information is being gathered about a group, the entire group of objects, individuals, or events is called the population. A sample is part of the population chosen to represent the entire group.

A sample in which every person, object, or event has an equal chance of being selected is called a random sample. A random sample is more likely to be representative of the entire population than other sampling methods.

A store gets a shipment of 1000 light bulbs. Due to a manufacturing problem, 200 of the bulbs are defective, but the store’s manager is not aware of this. As she always does, however, the manager will check a sample of the bulbs to look for potential problems. How can she choose a sample of the bulbs to represent the shipment?

A. The manager will want to use a random sample to represent the entire shipment. One way to simulate a random sample is to use a graphing calculator to generate random integers.
To simulate picking out random light bulbs between 1 and 1000:

• Press MATH, scroll right and select PRB, then select 5: randlnt(.
• Enter the smallest value, comma, largest possible value.
• Hit ENTER to generate random numbers.

In this specific case, you will enter randlnt (______, __________) because there are __________ light bulbs in the shipment.

The numbers that are generated will each represent a bulb in the shipment. Because we know the numbers of defective and working bulbs, we can choose numbers to model the bulbs in the population.

Let numbers 1 to 200 represent bulbs that are ___________.
Numbers 201 to 1000 will represent bulbs that are ____________.

The manager has a calculator randomly select 4 integers to tell her which bulbs to check. To model this, generate four numbers and record them in the table below. Then tell whether each number represents a defective or a working bulb in the model.

B. If the manager’s sample matched your results, would it represent the population well? Explain.

Reflect

Question 1.
You and your classmates have generated multiple samples. Compare your results to those of your classmates. What do you notice?
Answer:

Grade 8 Math Answer Key Pdf Generating Random Samples Question 2.
Communicate Mathematical Ideas Why did you and your classmates generate different answers for the number of defective light bulbs?
Answer:

Explore Activity 2

Generating a Larger Random Sample

A. The manager wants to use a larger random sample to get better results. This time, collect a sample of 20 light bulbs.
On a separate sheet of paper copy the table from Explore Activity 1 and record your results in the table. You will need rows for 20 light bulbs.

B. Does your new sample better represent the shipment than your original sample? Explain.

Reflect

Question 3.
You and your classmates have generated multiple samples. Compare your results to those of your classmates. What do you notice?
Answer:

Explore Activity 3

Generating a Random Sample without Technology

A tree farm has a 100 acre square field arranged in a 10-by-10 array. The farmer wants to know the average number of trees on each acre. Each cell in the table below represents an acre of land. The number in each cell tells how many trees grow on that particular acre.


Because counting the trees on all of the acres is too time-consuming, the farmer decides to choose 10 acres at random and find the average number of trees.

A. To simulate the random selection, place this page on the floor. Drop 10 small objects onto the chart. Use these numbers for the 10 random acres.

B. What is the average number of trees on the 10 acres that were randomly selected?

C. Alternately, the farmer decides to choose the 10 acres in the first row. What is the average number of trees on these 10 acres?

Reflect

Question 4.
How do the averages you got with each sampling method compare?
Answer:

Lesson 15.2 Go Math Grade 8 Answer Key Pdf Question 5.
How do the averages you got with each sampling method compare to the average for the entire population, which is 48.4?
Answer:

Question 6.
Communicate Mathematical Ideas Why do you think the first method gave a closer average than the second method?
Answer:

Texas Go Math Grade 8 Lesson 15.2 Guided Practice Answer Key

Question 1.
A manufacturer gets a shipment of 600 batteries of which 50 are defective. The quality control manager tests a random sample of 30 batteries in each shipment. Simulate the test by generating random numbers between 1 and 600. How well does your sample represent the shipment? Explain. (Explore Activities 1 and 2)
Answer:

Question 2.
The farmer from Explore Activity 3 would like to have a better estimate of the number of trees per acre. This time, the farmer decides to choose 20 acres at random. Use the table to simulate the farmer’s random selection and find a new estimated average for the number of trees per acre. (Explore Activity 3)
Answer:

Essential Question Check-In

Question 3.
Why can data from a random sample be used to represent a population? What can happen if a sample is too small or not random?
Answer:

Texas Go Math Grade 8 Lesson 15.2 Independent Practice Answer Key

Maurie owns three bagel shops. Each shop sells 500 bagels per day. Maurie asks her store managers to use a random sample to see how many whole-wheat bagels are sold at each store each day. The results are shown in the table. Use the table for 4-6.

Question 4.
If you assume the samples are representative, how many whole-wheat bagels are sold at each store?
Answer:

Question 5.
Rank the samples for the shops in terms of how representative they are likely to be. Explain your rankings.
Answer:

Question 6.
Which sample or samples should Maurie use to tell her managers how many whole-wheat bagels to make each day? Explain.
Answer:

Random Math Problems for 8th Graders Lesson 15.2 Question 7.
In a shipment of 1000 T-shirts, 75 do not meet quality standards. The store manager does not know this but always tests a random sample of each shipment. The table below simulates the manager’s random sample of 20 T-shirts to inspect. For the simulation, the integers 1 to 75 represent the below-standard shirts.

In the sample, how many of the shirts are below quality standards?
If the manager assumes his sample is representative and uses it to predict how many of the 1000 shirts are below standard, what will he conclude?
Answer:

Question 8.
Multistep A 64 acre coconut farm is arranged in an 8-by-8 array. Mika wants to know the average number of coconut palms on each acre. Each cell in the table represents an acre of land. The number in each cell tells how many coconut palms grow on that particular acre.

a. The numbers in green represent Mika’s random sample of 10 acres. What is the average number of coconut palms on the randomly selected acres?
Answer:

b. Project the number of palms in the entire farm.
Answer:

H.O.T. Focus on Higher Order Thinking

Question 9.
A random sample of 15 of the 78 competitors at a middle school gymnastics competition are asked about their height. The data set lists the heights in inches: 55, 57, 57, 58, 59, 59, 59, 59, 59, 61,62, 62, 63, 64, 66. What is the mean height of the sample? Could you say this is a good estimate of the mean height of all competitors? Why or why not?
Answer:

Lesson 15.2 Go Math 8th Grade Answer Key Pdf Question 10.
Critical Thinking The six-by-six grid contains the ages of actors in a youth Shakespeare festival. Describe a method for randomly selecting 8 cells by using number cubes. Then calculate the average of the 8 values you found.

Answer:

Question 11.
Communicating Mathematical Ideas Describe how the size of a random sample affects how well it represents a population as a whole.
Answer:

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 15 Answer Key Sampling.

Texas Go Math Grade 8 Module 15 Answer Key Sampling

Texas Go Math Grade 8 Module 15 Are You Ready? Answer Key

Find the percent.

Question 1.
20% of 50 ___________
Answer:
20% = 20/100
\(\frac{20}{100}\) × 50
2 × 5 = 10
So, 20% of 50 is 10

Texas Go Math Grade 8 Pdf Module 15 Answer Key Question 2.
8.5% of 300 ____________
Answer:
8.5% = 8.5/100
\(\frac{8.5}{100}\) × 300
= 8.5 × 3
= 25.5
Therefore 8.5% of 300 is 25.5

Question 3.
175% of 16.8 ____________
Answer:
175% = 175/100
\(\frac{175}{100}\) × 16.8
= 1.75 × 16.8
= 29.4
Therefore 175% of 16.8 is 29.4

Solve for x.

Question 4.
\(\frac{x}{12}\) = \(\frac{24}{36}\) ____________
Answer:
Given,
\(\frac{x}{12}\) = \(\frac{24}{36}\)
x = \(\frac{24}{36}\) × 12
x = 8

Question 5.
\(\frac{8}{x}\) = \(\frac{16}{7}\) ____________
Answer:
Given,
\(\frac{8}{x}\) = \(\frac{16}{7}\)
8 × \(\frac{7}{16}\) = x
x = 7/2
x = 3.5

Go Math Grade 8 Pdf Module 15 Answer Key Pdf Question 6.
\(\frac{5}{6}\) = \(\frac{x}{18}\) ____________
Answer:
Given,
\(\frac{5}{6}\) = \(\frac{x}{18}\)
x = \(\frac{5}{6}\) × 18
x = 5 × 3
x = 15

Question 7.
\(\frac{14}{15}\) = \(\frac{x}{75}\) ____________
Answer:
Given,
\(\frac{14}{15}\) = \(\frac{x}{75}\)
x = \(\frac{14}{15}\) × 75
x = 14 × 5
x = 70

Find the mean of the data.

Question 8.
55, 44, 53, 62, 51: ____________
Answer:
Given data 55, 44, 53, 62, 51
mean = sum of observations/number of observations
mean = (55 + 44 + 53 + 62 + 51)/5
mean = 265/5
mean = 53
Thus the mean of the data is 53.

Module 15 Go Math 8th Grade Answer Key Pdf Question 9.
3, 5, 3, 5, 2, 2, 5, 7: _____________
Answer:
Given data 3, 5, 3, 5, 2, 2, 5, 7
mean = sum of observations/number of observations
mean = (3 + 5 + 3 + 5 + 2 + 2 + 5 + 7)/8
mean = 32/8
mean = 4
Thus the mean of the data is 4.

Texas Go Math Grade 8 Module 15 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the right column of the chart.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
The entire group of objects, individuals, or events is the ____________.
Answer: The entire group of objects, individuals, or events is the population.

Go Math Grade 8 Answer Key Module 15 Question 2.
A sample in which every person, object, or event has an equal chance at being selected is a ___________.
Answer: A sample in which every person, object, or event has an equal chance of being selected is a simple random sample.

Active Reading
Layered Book Before beginning the module, create a layered book to help you learn the concepts in this module. Label each flap with lesson titles from this module. As you study each lesson, write important ideas, such as vocabulary and formulas, under the appropriate flap. Refer to your finished layered book as you work on exercises from this module.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 2.3 Answer Key Proportional Relationships and Graphs.

Texas Go Math Grade 7 Lesson 2.3 Answer Key Proportional Relationships and Graphs

Your Turn

Question 1.
Jared rents bowling shoes for $6 and pays $5 per bowling game. Graph the data. Is the relationship a proportional relationship? Explain.

Answer:
The relationship isn’t proportional, because the points form a line that does not go through the origin.

Example
The graph shows the relationship between time in minutes and the number of miles Damon runs. Write an equation for this relationship.

STEP 1: Choose a point on the graph and tell what the point represents.
The point (25, 2.5) represents the distance (2.5 miles) that Damon runs in 25 minutes.
STEP 2: What ¡s the constant of proportionality?
Because distance \(\frac{\text { distance }}{\text { time }}=\frac{2.5 \mathrm{mi}}{25 \mathrm{~min}}=\frac{1}{10}\), the constant of proportionality is \(\frac{1}{10}\).
STEP 3: Write an equation in the form y = kx.
y = \(\frac{1}{10}\)x

Reflect

Question 2.
Communicate Mathematical Ideas What does the point (0, 0) on the graph represent?
Answer:
The point (0, 0) represents a start on the graph, origin.

Go Math Lesson 2.3 7th Grade Proportional Relationships Question 3.
What If? Esther runs faster than Damon. Suppose you drew a graph representing the relationship between time in minutes and distance run for Esther. How would the graph compare to the one for Damon?
Answer:
Esther’s Line would be steeper than Damon’s

Your Turn

Question 4.
The graph shows the relationship between the distance a bicyclist travels and the time in hours.

a. What does the point (4, 60) represent?
Answer:
The point (4,60) represents the distance (60 miles) that the bicyclist travels in 4 hours

b. What is the constant of proportionality?
Answer:
The constant is equal to 15 because \(\frac{\text { distance }}{\text { time }}=\frac{60}{4}\) = 15. Only one point is enough since the relationship is proportional.

c. Write an equation in the form y = kx for this relationship.
Answer:
The equation is equal to y = 15x.

Texas Go Math Grade 7 Lesson 2.3 Guided Practice Answer Key

Complete each table. Tell whether the relationship is a proportional relationship. Explain why or why not. xpIore Activity)

Question 1.
A student reads 65 pages per hour.

Answer:

3 × 65 = 195
5 × 65 = 325
585 ÷ 65 = 9
10 × 65 = 650
The relationship is proportional because we made sure with our calculations that all constants are equal to 65.

Lesson 2.3 Proportional Relationships Answer Key Grade 7 Question 2.
A babysitter makes $7.50 per hour.

Answer:

2 × 7.51 = 15
22.50 ÷ 7.50 = 3
5 × 7.50 = 37.5()
60 ÷ 7.50 = 8
The relationship is proportional because we made sure with our calculations that all constants are equal to 7.50.

Tell whether the relationship is a proportional relationship. Explain why or why not. (Explore Activity and Example 1)

Question 3.

Answer:
The relationship is not proportional because the line does not go through the origin.

Question 4.

Answer:
The relationship is proportional, the constant is equal to 2 because \(\frac{2}{1}\) = \(\frac{4}{2}\) = \(\frac{10}{5}\) = \(\frac{16}{8}\) = 2. The equation is equal to y = 2x.

Write an equation of the form y = kx for the relationship shown in each graph.

Question 5.

Answer:
The relationship is proportional because points form a line through the origin.
Thus, we need only one point to determine the constant
7 ÷ 2 = 3.5
y = Balloon height(ft)
x = Time(s)
Equation: y = 3.5x

Graphing Proportional Relationships 7th Grade Answer Key Question 6.

Answer:
The relationship is proportional because points form a line through the origin.
Thus, we need only one point to determine the constant
2 ÷ 8 = 025
y = Cost ($)
x = Number of items
Equation: y = 0.5x

Essential Question Check-In

Question 7.
How does a graph show a proportional relationship?
Answer:
The graph forms a line that passes through the origin.

Texas Go Math Grade 7 Lesson 2.3 Independent Practice Answer Key

For Exercises 8-12, the graph shows the relationship between time and distance run by two horses.

Question 8.
Explain the meaning of the point (0, 0).
Answer:
The point (0,0) represents the start, position of horses right before they started to run.

Question 9.
How long does it take each horse to run a mile?
Answer:
We can see from the graph that horse A takes 4 minutes to run a mile, while horse B takes 2.5 minutes to run a mile.

Lesson 2.3 Reteach Answer Key Go Math Grade 7 Question 10.
Multiple Representations Write an equation for the relationship between time and distance for each horse.
Answer:
Horse A runs 1 mile in 4 minutes. That means he runs \(\frac{1}{4}\) miles per minute.
Horse B runs 1 mile in 2.5 minutes That means he runs \(\frac{1 \times 2}{2.5 \times 2}\) = \(\frac{2}{5}\) miles per minute.
x = Time (min)
y = Distance(miles)
Horse A: y = \(\frac{1}{4}\) x
Horse B: y = \(\frac{2}{5}\) x

Question 11.
Draw Conclusions At the given rates, how far would each horse run in 12 minutes?
Answer:
Use the equations from 11:
Horse A:
y = \(\frac{1}{4}\) x
y = \(\frac{1}{4}\)(12)³
y = 3

Horse B:
y = \(\frac{2}{5}\) x
y = \(\frac{2}{5}\) (12)
y = \(\frac{25}{4}\)
y = 4\(\frac{4}{5}\)
Horse A passes 3 miles in 12 minutes.
Horse B passes 4\(\frac{4}{5}\) in 12 minutes.

Question 12.
Analyze Relationships Draw a line on the graph representing a horse than runs faster than horses A and B.
Answer:

Go Math Grade 7 Lesson 2.3 Constant of Proportionality Question 13.
A bullet train can travel at 170 miles per hour. Will a graph representing the distance in miles compared to the time in hours show a proportional relationship? Explain.
Answer:
The graph will show a proportional relationship because of the constant unit rate, 170 miles per hour.

Question 14.
Critical Thinking When would it be more useful to represent a proportional relationship with a graph rather than an equation?
Answer:
It would be easier to draw graphs when we have whole numbers
It would not be easy to draw a graph if a constant is a long decimal number or a fraction with big numbers. Thus, we rather use the equation in this case.

Question 15.
Multiple Representations Bargain DVDs cost $5 each at Mega Movie.
a. Graph the proportional relationship that gives the cost y in dollars of buying x bargain DVDs.

Answer:
Graph

b. Give an ordered pair on the graph and explain its meaning in the real world context.
Answer:
The point (4, 20) represents $20 you have to pay for renting 4 DVDs.

The graph shows the relationship between distance and time as Glenda swims.

7th Grade Constant of Proportionality Answer Key Go Math Question 16.
How far did Glenda swim in 4 seconds?
Answer:
Glenda swam 8 feet in 4 seconds.

Question 17.
Communicate Mathematical Ideas Is this a proportional relationship? Explain your reasoning.
Answer:
This is a proportional relationship because points form a line through the origin.

Texas Go Math Grade 7 Answer Key Lesson 2.3 Question 18.
Multiple Representations Write an equation that shows the relationship between time and distance. ________________________________
Answer:
Because the relationship is proportional we can calculate the constant k. From point (2, 4) we conclude the constant is equal to 2.
x = Time(s)
y = Distance(ft)
Thus, the equation is y = 2x.

H.O.T.S Focus On Higher Order Thinking

Question 19.
Make a Conjecture If you know that a relationship is proportional and are given one ordered pair other than (0, 0), how can you find another pair?
Answer:
From the point that is given to us, we can draw a line on the graph through that point and (0, 0). Then we can find whichever point we need.

The tables show the distance traveled by three cars.

Proportional Relationships 7th Grade Answer Key Question 20.
Communicate Mathematical Ideas Which car is not traveling at a constant speed? Explain your reasoning.
Answer:
Car 3 is not traveling at a constant speed because \(\frac{65}{1}\) ≠ \(\frac{85}{2}\).

Question 21.
Make a Conjecture Car 4 is traveling at twice the rate of speed of car 2. How will the table values for car 4 compare to the table values for car 2?
Answer:
The time column will stay the same but the distance column will double its values because the constant doubles.

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 14 Quiz Answer Key.

Texas Go Math Grade 8 Module 14 Quiz Answer Key

Texas Go Math Grade 8 Module 14 Ready to Go On? Answer Key

14.1 Scatter Plots arid Association

An auto store is having a sale on motor oil. The chart shows the price per quart as the number of quarts purchased increases. Use the data for 1-2.

Question 1.
Use the given data to make a scatter plot.

Answer:
Plot the points: (1, 2), (2, 1.50), (3. 1.25), (4, 1.10), (5, 1), (6, 0.95)

Scatter Plot Quiz Module 14 Test Answers 8th Grade Go Math Question 2.
Describe the association you see between the number of quarts purchased and the price per quart. Explain.
Answer:
The association seen between the number of quarts purchased and the price per quart is negative and nonlinear. As the number of quarts rises, the price per quart decreases but there is a data curve.

14.2 Trend Lines and Predictions

The scatter plot below shows data comparing wind speed and wind chill for an air temperature of 20 °F. Use the scatter plot for 3-5.

Question 3.
Draw a trend line for the scatter plot.
Answer:
Draw a trend line for the scatter plot.

Question 4.
Write an equation for your trend line.
Answer:
Find the slope of the trend line The line passes through points (10, 8.75) and (35, 0).
Use the slope formula: m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
m = \(\frac{0-8.75}{35-10}\)
m = \(\frac{-8.75}{25}\)
m = -0.35
Find the y-intercept of the trend line.
Slope-intercept form : y = mx + b
0 = -0.35.0 + b
0 = -12.25 + b
b = 12.25
Use your slope and y-intercept values to write the equation.
y = mx + b
y = -0.35x + 12.25
The equation for the trend line is y = -0.35x + 12.25

Module 14 Scatter Plots Module Quiz D Answer Key Question 5.
Use your equation to predict the wind chill to the nearest degree for a wind speed of 60 mi/h.
Answer:
Use the equation for the trend line.
y = mx+b
y = -0.35(60) + 12.25
y = -21 + 12.25
y = -8.75
y ≈ -9
The wind chill to the nearest degree for a wind speed of 60 mi/h is 9°F.

Essential Question

Question 6.
How can you use scatter plots to solve real-world problems?
Answer:
Using a scatter plot, you can see positive and negative trends such as prices over time. You can also make predictions such as height at a certain age.

Texas Go Math Grade 8 Module 14 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Which scatter plot could have a trend line whose equation is y = 3x + 10?

Answer:
(C)

Explanation:
Equation for the trend Line is y = 3x + 10
y = mx + b
The slope of the trend line is m = 3.
The slope is positive, m > 0, which means that a trend line is increasing.
If the line is increasing, options A and C are not solutions because in these options trend line decreasing.
The y-intercept of the trend line is b = 10.
That is the y-coordinate where the line intersects the y-axis.
(0, 10) where the trend line intersects the y-axis is in scatter plot in option B.

Question 2.
What type of association would you expect between a person’s age and hair length?
(A) linear
(B) negative
(C) none
(D) positive
Answer:
(B) negative

Explanation:
The length of their hair reduces. This is because the length of hair changes with the growth phase of the hair follicles. When one is young, the cells of the papilla divide more rapidly, and hence the length of the hair to be long before reaching the transitional phase and then shed off in the telogen phase. The older one gets, the papilla cells do not divide as rapidly and the length of the hair shortens with age.
The older persons tended to have shorter hair.

Question 3.
Which is not shown on the scatter plot?

(A) cluster
(B) negative association
(C) outlier
(D) positive association
Answer:
(D) positive association

Explanation:
Cluster, negative association and outlier are shown on the scatter plot.
Cluster is visible between points (12, 21) and (5, 43).
Outlier is visible at point (10, 59)
If we draw the trend line, line would decrease. Because of that, on the scatter plot is shown negative association.
If the trend line decreases, on the scatter plot is not shown positive association.

Module 14 Scatter Plots Quiz Ready To Go On 8th Grade Math Question 4.
A restaurant claims to have served 352,000,000 hamburgers. What is this number in scientific notation?
(A) 3.52 × 10⁶
(B) 3.52 × 10⁸
(C) 35.2 × 10⁷
(D) 352 × 10⁶
Answer:
(B) 3.52 × 10⁸

Explanation:
100,000,000 is 10⁸
352,000,000 = 352 × 10⁶ = 3.52 × 10⁸

Question 5.
Which equation describes the relationship between x and yin the table?

(A) y = -4x
(B) y = \(\frac{-1}{4}\)x
(C) y = 4x
(D) y = \(\frac{1}{4}\)x
Answer:
(B) y = \(\frac{-1}{4}\)x

Explanation:
In order to find out the relationship between x and y, we have use the values in the question and substitute them into the solution options.
So, we will use point (- 8, 2) and substitute x with -8 and y with 2 in every option.

(a)
y = -4x
2 = -4(-8)
2 = 32
False

(b)
y = \(\frac{-1}{4}\)x
2 = \(\frac{-1}{4}\) (-8)
2 = 2
True

(c)
y = 4x
2 = 4(-8)
2 = -32
False

(d)
y = \(\frac{1}{4}\)x
2 = \(\frac{1}{4}\)(-8)
2 = -2
False

Gridded Response

8th Grade Math Problems Scatter Plot Quiz Answer Key Question 6.
Predict the number of visitors when the temperature is 102°F.

Answer:
a)

b)
An outlier is points (92, 135).

c)
Based on the number of visitors on a day with a temperature of 100° F, I would expect that on a day with a temperature of 102°, the pool would have between 350 and 400 visitors.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 1.6 Answer Key Dividing Rational Numbers.

Texas Go Math Grade 7 Lesson 1.6 Answer Key Dividing Rational Numbers

Texas Go Math Grade 7 Lesson 1.6 Explore Activity 1 Answer Key 

A diver needs to descend to a depth of 100 feet below sea level. She wants to do it in 5 equal descents. How far should she travel in each descent?

A. To solve this problem, you can set up a division problem: \(\frac{-100}{}\) =?
B. Rewrite the division problem as a multiplication problem. Think: Some number multiplied by 5 equals -100.
_______ × ? = -100
C. Remember the rules for integer multiplication. If the product is negative, one of the factors must be negative. Since ________ ¡s positive, the unknown factor must be [Positive/negative.]
D. You know that 5 × _________ = 100. So, using the rules for integer multiplication you can say that 5 × ____ 100.
The diver should descend ________ feet in each descent.

Reflect

Question 1.
What do you notice about the quotient of two rational numbers with different signs?
Answer:
The quotient of two rational numbers with different signs will have a negative sign.

Texas Go Math Grade 7 Pdf Lesson 1.6 Answer Key Question 2.
What do you notice about the quotient of two rational numbers with the same sign? Does it matter if both signs are positive or both are negative?
Answer:
The quotient of two rational numbers with the same sign will have a positive sign. It does not matter if both signs are positive or both signs are negative.

Write two equivalent expressions for each quotient.

Question 3.
\(\frac{14}{-7}\) __________, __________
Answer:
\(\frac{-14}{7}\), – (\(\frac{14}{7}\))

Question 4.
\(\frac{-32}{-8}\) __________, ___________
Answer:
\(\frac{32}{8}\), -(\(\frac{-32}{8}\))

Your Turn

Find each quotient.

Question 5.
\(\frac{2.8}{-4}\) = ____________
Answer:
The quotient will be negative because signs are different.
Write a decimal as fraction: \(\frac{\frac{28}{10}}{-4}\)
Write complex fraction as division: \(\frac{28}{10}\) ÷ (-4)
Rewrite using multiplication:
\(\frac{28}{10} \times \frac{-1}{4}=\frac{-28}{40}\)
= \(\frac{-7}{10}\)

Question 6.
\(\frac{-\frac{5}{8}}{-\frac{6}{7}}\) = ____________
Answer:
The quotient will be positive because the signs are the same.
Write complex fractions as division:
–\(\frac{5}{8}\) ÷ (-\(\frac{6}{7}\))
Rewrite using multiplication:
–\(\frac{5}{8}\) × (-\(\frac{7}{6}\)) = \(\frac{35}{48}\)

Texas Go Math Grade 7 Pdf Dividing Rational Numbers Question 7.
– \(\frac{5.5}{0.5}\) = ___________
Answer:
The quotient will be negative because signs are different.
Write decimal numbers as fractions:
\(-\frac{\frac{55}{10}}{\frac{5}{10}}\)
Write complex fractions as division:
–\(\frac{55}{10}\) ÷ \(\frac{5}{10}\)
Rewrite using multiplication:
–\(\frac{55}{10}\) × \(\frac{10}{5}\) = -11

Texas Go Math Grade 7 Lesson 1.6 Guided Practice Answer Key 

Find each quotient. (Explore Activity 1 and 2, Example 1)

Question 1.
\(\frac{0.72}{-0.9}\) = ____________
Answer:
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(\frac{\frac{72}{100}}{\frac{-9}{10}}\)
Write complex fraction as division:
\(\frac{72}{100}\) ÷ \(\frac{-9}{10}\)
Rewrite using multiplication:
\(\frac{72}{100}\) × \(\frac{10}{-9}\) = \(\frac{8}{-10}\)
= –\(\frac{4}{5}\)

Question 2.
\(\left(-\frac{\frac{1}{5}}{\frac{7}{5}}\right)\) = ____________
Answer:
The quotient will be negative because signs are different.
Write complex fraction as division:
–\(\frac{1}{5}\) ÷ \(\frac{7}{5}\)
Rewrite using multiplication:
–\(\frac{1}{5}\) × \(\frac{5}{7}\) = –\(\frac{1}{7}\)

Question 3.
\(\frac{56}{-7}\) = _____________
Answer:
The quotient will be negative because the signs are different.
\(\frac{56}{-7}\) = -8

Question 4.
\(\frac{251}{4} \div\left(-\frac{3}{8}\right)\) = ____________
Answer:
The quotient will be negative because the complex fraction is negative.
Rewrite using multiplication:
– \(\frac{251}{4}\) × \(\frac{8}{3}\) = –\(\frac{502}{3}\)

Texas Go Math Grade 7 Answer Key Pdf Lesson 1.6 Question 5.
\(\frac{75}{-\frac{1}{5}}\) = ____________
Answer:
The quotient will be negative because the signs are different
Write complex fractions as division:
-75 ÷ \(\frac{1}{5}\)
Rewrite using multiplication:
-75 × 5 = -375

Question 6.
\(\frac{-91}{-13}\) = ____________
Answer:
The quotient will be positive because the signs are the same.
\(\frac{-91}{-13}\) = \(\frac{91}{13}\)
= 7

Question 7.
\(\frac{-\frac{3}{7}}{\frac{9}{4}}\) = _____________
Answer:
The quotient will be negative because the signs are different.
Write complex fraction as division:
–\(\frac{3}{7}\) ÷ \(\frac{9}{4}\)
Rewrite using multiplication:
–\(\frac{3}{7}\) × \(\frac{4}{9}\) = –\(\frac{4}{21}\)

Question 8.
–\(\frac{12}{0.03}\) = ____________
Answer:
The quotient will be negative because the fraction has a negative sign.
Write decimal numbers as fraction:
–\(\frac{12}{\frac{3}{100}}\)
Write complex fraction as division:
-12 ÷ \(\frac{3}{100}\)
Rewrite using multiplication:
-12 × \(\frac{100}{3}\) = -400

Question 9.
A water pail in your backyard has a small hole in it. You notice that it has drained a total of 3.5 liters in 4 days. What is the average change in water volume each day? (Example 1)
Answer:
Use a negative number to represent spiLLage of water
Find \(\frac{-3.5}{4}\).
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(-\frac{\frac{35}{10}}{4}\)
Write complex fraction as division:
– \(\frac{35}{10}\) ÷ 4
Rewrite using multiplication:
–\(\frac{35}{10}\) × \(\frac{1}{4}\) = – \(\frac{35}{40}\)
= –\(\frac{7}{8}\)
The average change in water volume each day is –\(\frac{7}{8}\) liters.

Question 10.
The price of one share of ABC Company declined a total of $45.75 in 5 days. What was the average change of the price of one share per day? (Example 1)
Answer:
Use a negative number to represent decline in share price.
Find \(\frac{-45.75}{5}\)
The quotient will be negative because signs are different
Write decimal numbers as fraction:
\(-\frac{\frac{4575}{100}}{5}\)
Write complex fraction as division:
–\(\frac{4575}{100}\) ÷ 5
Rewrite using multiplication:
–\(\frac{915}{100}\) × \(\frac{1}{5}\) = –\(\frac{915}{100}\)
= –\(\frac{183}{25}\)
The average change of the price of one share per day is –\(\frac{183}{25}\)

Question 11.
To avoid a storm, a passenger jet pilot descended 0.44 mile in 0.8 minute. What was the plane’s average change of altitude per minute? (Example 1)
Answer:
Use a negative number to represent descent
Find \(\frac{-0.44}{0.8}\).
UL
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(\frac{1}{2}\)
Write complex fraction as division:
–\(\frac{44}{100}\) ÷ \(\frac{8}{10}\)
Rewrite using multiplication:
–\(\frac{44}{100}\) × \(\frac{10}{8}\) = –\(\frac{11}{20}\)
The average change of altitude per minute is –\(\frac{11}{20}\) miles.

Essential Question Check-In

Question 12.
Explain how you would find the sign of the quotient \(\frac{32 \div(-2)}{-16 \div 4}\).
Answer:
I would first find the sign of the numerator and denominator separately, and then the sign of the whole fraction.
Numerator: Negative, because signs are different
Denominator: Negative, because signs are different.
Whole fraction: Positive, because signs are the same.

Texas Go Math Grade 7 Lesson 1.6 Independent Practice Answer Key  

Question 13.
\(\frac{5}{-\frac{2}{8}}\) = __________
Answer:
The quotient will be negative because the signs are different
Write complex fraction as division: -5 ÷ \(\frac{2}{8}\)
Rewrite using multiplication:
-5 × \(\frac{8}{2}\) = -5 × 4
= -20

7th Grade Go Math Answer Key Lesson 1.6 Question 14.
\(5 \frac{1}{3} \div\left(-1 \frac{1}{2}\right)\) = __________
Answer:
Write mixed fractions as proper fractions:
\(\frac{16}{3}\) ÷ (-\(\frac{3}{2}\))
The quotient will be negative because the complex fraction is negative
Rewrite using multiplication:
– \(\frac{16}{3}\) × \(\frac{2}{3}\) = –\(\frac{32}{9}\)

Question 15.
\(\frac{-120}{-6}\) = ___________
Answer:
The quotient will be positive because the signs are the same.
\(\frac{-120}{-6}\) = \(\frac{120}{6}\)
= 20

Question 16.
\(\frac{-\frac{4}{5}}{-\frac{2}{3}}\) = _____________
Answer:
The quotient will be positive because the signs are the same.
Write complex fraction as division:
\(\frac{4}{5}\) ÷ \(\frac{2}{3}\)
Rewrite using multiplication:
\(\frac{4}{5}\) × \(\frac{3}{2}\) = \(\frac{6}{5}\)

Question 17.
1.03 ÷ (-10.3) = _____________
Answer:
Write decimal numbers as fractions.
\(\frac{103}{100}\) ÷ (-\(\frac{103}{10}\))
The quotient will be negative because the signs are different.
Rewrite using multiplication:
–\(\frac{103}{100}\) × \(\frac{10}{103}\) = –\(\frac{1}{10}\)

Question 18.
\(\frac{-0.4}{80}\) = ____________
Answer:
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(\frac{-\frac{4}{10}}{80}\)
Write complex fraction as division:
–\(\frac{4}{10}\) ÷ 80
Rewrite using multiplication:
–\(\frac{4}{10}\) × \(\frac{1}{80}\) = –\(\frac{1}{200}\)

Question 19.
1 ÷ \(\frac{9}{5}\) = ___________
Answer:
The quotient will be positive because the signs are the same.
Rewrite using multiplication:
1 × \(\frac{5}{9}\) = \(\frac{5}{9}\)

Question 20.
\(\frac{\frac{-1}{4}}{\frac{23}{24}}\) = _____________
Answer:
The quotient will be negative because the signs are different
Write complex fractions as division:
–\(\frac{1}{4}\) ÷ \(\frac{23}{24}\)
Rewrite using multipLication:
–\(\frac{1}{4}\) × \(\frac{24}{23}\) = –\(\frac{6}{23}\)

Lesson 1.6 Go Math 7th Grade Dividing Rational Numbers Answer Key Question 21.
\(\frac{-10.35}{-2.3}\) = ___________
Answer:
The quotient will be positive because the signs are the same.
Write decimal numbers as fractions:
\(\frac{-\frac{1035}{100}}{-\frac{23}{10}}\)
Write complex fractions as division:
\(\frac{1035}{100}\) ÷ \(\frac{23}{10}\)
Rewrite using muLtiplication:
\(\frac{1035}{100}\) × \(\frac{10}{23}\) = \(\frac{45}{10}\)
= \(\frac{9}{2}\)

Question 22.
Alex usually runs for 21 hours a week, training for a marathon. If he is unable to run for 3 days, describe how to find out how many hours of training time he loses, and write the appropriate integer to describe how it affects his time.
Answer:
If Alex runs 21 hours for a week, that means he runs \(\frac{21}{7}\) = 3 hours per day. If he is unable to run for 3 days, that means he loses 3 × 3 = 9 hours.

Question 23.
The running back for the Bulldogs football team carried the ball 9 times for a total loss of 15\(\frac{3}{4}\) yards. Find the average change in field position on each run.
Answer:
Use negative number to represent loss of yards
Find \(\frac{-15 \frac{3}{4}}{9} .\)
Write mixed fractions as proper fractions:
\(\frac{-\frac{63}{4}}{9}\)
The quotient will be negative because the signs are different.
Write complex fraction as division:
–\(\frac{63}{4}\) ÷ 9
Rewrite using multiplication:
–\(\frac{63}{4}\) × \(\frac{1}{9}\) = –\(\frac{7}{4}\)
Averange change in field position on each run is –\(\frac{7}{4}\) yards.

Question 24.
The 6:00 a.m. temperatures for four consecutive days in the town of Lincoln were -12.1°C, -7.8°C, -14.3°C, and -7.2 °C. What was the average 6:00 a.m. temperature for the four days?
Answer:
First we need to add the temperatures up.
12.1 + (- 7.8) + (- 14.3) + (- 7.2) = 19.9 + (- 14.3) + (- 7.2)
= 34.2 + (- 7.2)
= 41.4
Now, we need to divide the result with the count of temperature measurements.
Find \(\frac{-41.4}{4}\).
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(\frac{-\frac{414}{10}}{4}\)
Write complex fraction as division:
–\(\frac{414}{10}\) ÷ 4
Rewrite using multiplication:
–\(\frac{414}{10}\) × \(\frac{1}{4}\) = –\(\frac{207}{20}\)
The average 6.00 a.m temperature for four days was –\(\frac{207}{20}\) degrees Celsius.

Question 25.
Multistep A seafood restaurant claims an increase of $1,750.00 over its average profit during a week where it introduced a special of baked clams.
a. If this is true, how much extra profit did it receive per day?
Answer:
Find \(\frac{1750}{7}\).
\(\frac{1750}{7}\) = 250
They received $250 extra profit per day.

b. If it had, instead, lost $150 per day, how much money would it have lost for the week?
Answer:
Find -150 × 7
-150 × 7 = -1050
They would have lost $1050 for the week.

c. If its total loss was $490 for the week, what was its average daily change?
Answer:
Find \(\frac{-490}{7}\)
\(\frac{-490}{7}\) = -70
The average daily change was -$70.

Question 26.
A hot air balloon descended 99.6 meters in 12 seconds. What was the balloon’s average rate of descent in meters per second?

Answer:
Use a negative number to represent descent.
Find \(\frac{-99.6}{12}\)
The quotient will be negative because signs are different.
Write decimal numbers as fraction:
\(-\frac{\frac{996}{10}}{12}\)
Write complex fraction as division:
–\(\frac{996}{10}\) ÷ 12
Rewrite using multiplication:
–\(\frac{996}{10}\) × \(\frac{1}{12}\) = –\(\frac{83}{10}\)
= -8.3
The average rate of descent is 8.3 meters per second

Question 27.
Sanderson is having trouble with his assignment. His work is as follows:
\(\frac{-\frac{3}{4}}{\frac{4}{3}}=-\frac{3}{4} \times \frac{4}{3}=-\frac{12}{12}=-1\)
However, his answer does not match the answer that his teacher gave him. What is Sanderson’s mistake? Find the correct answer.
Answer:
Sanderson jumped over one step. He should have written complex fractions using division.
\(\frac{3}{4}\) ÷ \(\frac{4}{3}\)
And then rewrite it using multiplication.
\(\frac{3}{4}\) × \(\frac{3}{4}\)

Go Math Answer Key Grade 7 Lesson 1.6 Question 28.
Science Beginning in 1996, a glacier lost an average of 3.7 meters of thickness each year. Find the total change in its thickness by the end of 2012.
Answer:
First, find out how many years have passed in the period 1996-2012.
2012 – 1996 = 16
Find -3.7 × 16.
-3.7 × 16 = -59.2
The total change in thickness by the end of 2012 is -59.2 inches.

H.O.T. Focus on Higher Order Thinking

Question 29.
Represent Real-World Problems Describe a real-world situation that can be represented by the quotient -85 ÷ 15. Then find the quotient and explain what the quotient means in terms of the real-world situation.
Answer:
A group of 15 people lost 85 dollars. If every person lost the same amount of dollars, how many dollars have each person lost?
–\(\frac{85}{15}\) = –\(\frac{17}{3}\)
Each person lost –\(\frac{17}{3}\)

Question 30.
Construct an Argument Divided 5 by 4. Is your answer a rational number? Explain.
Answer:
Yes, it is a Quotient of dividing 5 by 4 is a fraction, and every fraction is a rational number.

Question 31.
Critical Thinking Is the quotient of an integer divided by a nonzero integer always a rational number? Explain.
Answer:
Yes, it is. A quotient of any two integers can be written as a fraction, the denominator being a nonzero integer. Thus, it is a rational. number.

Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Module 1 Answer Key Rational Numbers.

Texas Go Math Grade 7 Module 1 Answer Key Rational Numbers

Texas Go Math Grade 7 Module 1 Are You Ready? Answer Key

Multiply. Write the product in simplest form.

Question 1.
\(\frac{9}{14}\) × \(\frac{7}{6}\) ____________
Answer:
Start with dividing by the common factors:
\(\frac{9}{14}\) × \(\frac{7}{6}\)
= \(\frac{3}{4}\)

Question 2.
\(\frac{3}{5}\) × \(\frac{4}{7}\) ____________
Answer:
We do not have any common factors here to divide with.
Simplify:
= \(\frac{12}{35}\)

Grade 7 Go Math Texas Module 1 Answer Key Question 3.
\(\frac{11}{8}\) × \(\frac{10}{33}\) ____________
Answer:
Start with dividing by the common factors:
\(\frac{11}{8}\) × \(\frac{10}{33}\)
= \(\frac{5}{12}\)

Question 4.
\(\frac{4}{9}\) × 3 ____________
Answer:
Start with dividing by the common factors:
Write 3 as \(\frac{3}{1}\)
\(\frac{4}{9}\) × \(\frac{3}{1}\)
= \(\frac{4}{3}\)

Divide.

Question 5.
\(\frac{1}{2}\) ÷ \(\frac{1}{4}\) ____________
Answer:
= \(\frac{1}{2}\) × \(\frac{4}{1}\) Multiply by the reciprocal of the divisor.
= \(\frac{1}{2}\) × \(\frac{4}{1}\) Divide by the common factors.
= \(\frac{2}{1}\) = 2 Simplify
= 2

Question 6.
\(\frac{3}{8}\) ÷ \(\frac{13}{16}\) ____________
Answer:
= \(\frac{3}{8}\) × \(\frac{16}{13}\) Multiply by the reciprocal of the divisor.
= \(\frac{3}{8}\) × \(\frac{16}{12}\) Divide by the common factors.
= \(\frac{6}{13}\) Simplify
= \(\frac{6}{13}\)

Question 7.
\(\frac{2}{5}\) ÷ \(\frac{14}{15}\) ____________
Answer:
= \(\frac{2}{5}\) × \(\frac{15}{14}\) Multiply by the reciprocal of the divisor.
= \(\frac{2}{5}\) × \(\frac{15}{15}\) Divide by the common factors.
= \(\frac{3}{7}\) Simplify
= \(\frac{3}{7}\)

Module 1 Grade 7 Answer Key Texas Go Math Question 8.
\(\frac{4}{9}\) ÷ \(\frac{16}{27}\) ____________
Answer:
= \(\frac{4}{9}\) × \(\frac{27}{16}\) Multiply by the reciprocal of the divisor.
= \(\frac{4}{9}\) × \(\frac{27}{16}\) Divide by the common factors.
= \(\frac{3}{4}\) Simplify
= \(\frac{3}{4}\)

Question 9.
\(\frac{3}{5}\) ÷ \(\frac{5}{6}\) ____________
Answer:
= \(\frac{3}{5}\) × \(\frac{6}{5}\) Multiply by the reciprocal of the divisor.
= \(\frac{18}{25}\) No common factors. Simplify
= \(\frac{18}{25}\)

Question 10.
\(\frac{1}{4}\) ÷ \(\frac{23}{24}\) ____________
Answer:
= \(\frac{1}{4}\) × \(\frac{24}{23}\) Multiply by the reciprocal of the divisor.
= \(\frac{1}{4}\) × \(\frac{24}{23}\) Divide by the common factors.
= \(\frac{6}{23}\) Simplify
= \(\frac{6}{23}\)

Question 11.
6 ÷ \(\frac{3}{5}\) ____________
Answer:
Write 6 as \(\frac{6}{1}\)
= \(\frac{6}{1}\) × \(\frac{5}{3}\) Multiply by the reciprocal of the divisor.
= \(\frac{6}{1}\) × \(\frac{5}{3}\) Divide by the common factors.
= \(\frac{10}{1}\) = 10 Simplify
= 10

Texas Go Math Grade 7 Module 1 Answer Key Pdf Question 12.
\(\frac{4}{5}\) ÷ 10 ____________
Answer:
Write 10 as \(\frac{10}{1}\)
= \(\frac{4}{5}\) × \(\frac{10}{1}\) Multiply by the reciprocal of the divisor.
= \(\frac{4}{5}\) × \(\frac{10}{1}\) Divide by the common factors.
= \(\frac{8}{1}\) = 8 Simplify
= 8

Evaluate each expression.

Question 13.
21 – 6 ÷ 3 _________
Answer:
= 21 – 2 MultipLy and divide from Left to right.
= 19 Add and substract from left to right
= 19

Question 14.
18 + (7 – 4) × 3 _________
Answer:
If first step get rid of parentheses to obtain:
18 + (7 – 3) • 3 = 18 + 3 • 3
In second step multiply from left to right.
18 + 3 • = 18 + 9
Third step is where we add from left to right.
18 + 9 = 27
= 27

Question 15.
5 + (8 – 3)² ___________
Answer:
= 5 + (5)² Operate within parenthesis.
= 5 + 25 SimpLify exponents
= 30 Add and subtract from Left to right.
= 30

Texas Go Math Rational Numbers Test Grade 7 Pdf with Answers Question 16.
9 + 18 ÷ 3 + 10 ________
Answer:
= 9 + 6 + 10 MuLtiply and divide from Left to right
= 15 + 10 Add and subtract from Left to right.
= 25

Question 17.
60 – (3 – 1)⁴ × 3 _________
Answer:
= 60 – (2)⁴ × 3 Operate within parenthesis.
= 60 – 16 × 3 SimpLify exponents
= 60 – 48 MuLtiply and divide from Left to right
= 12 Add and subtract from left to right.
= 12

Grade 7 Texas Go Math Module 1 Answer Key Question 18.
10 – 16 ÷ 4 × 2 + 6 _________
Answer:
= 10 – 4 × 2 + 6 MuLtipLy and divide from Left to right
= 10 – 8 + 6 Add and subtract from Left to right.
= 2 + 6
= 8

Texas Go Math Grade 7 Module 1 Reading Start-Up Answer Key

Visualize Vocabulary
Use the ✓ words to complete the graphic. You can put more than one word in each section of the triangle.

Understand Vocabulary

Complete the sentences using the preview words.

Question 1.
A group of items is a __________. A set contained within another set is a __________.
Answer:
set, subset

Texas Go Math Grade 7 Answer Key Pdf Module 1 Question 2.
The ___________ of a number is the same distance from 0 on a number line as the original number but on the other side of 0.
Answer:
opposite

Question 3.
A ___________ can be expressed as a ratio of two integers.
Answer:
rational number

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 14.2 Answer Key Trend Lines and Predictions.

Texas Go Math Grade 8 Lesson 14.2 Answer Key Trend Lines and Predictions

Texas Go Math Grade 8 Lesson 14.2 Explore Activity Answer Key

Explore Activity 1

Drawing a Trend Line

When a scatter plot shows a linear association, you can use a line to model the relationship between the variables. A trend line is a straight line that comes closest to the points on a scatter plot.

Joyce is training for a 10K race. For some of her training runs, she records the distance she ran and how many minutes she ran.
A. Make a scatter plot of joyce’s running data.

B. To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. Ignore any outliers.

C. Use your trend line to predict how long it would take Joyce to run 4.5 miles.

Reflect

Question 1.
How well does your trend line fit the data? Explain.
Answer:
Draw a trend line.

The trend line fits the data very well, because we can draw a straight line that has about the same number of points above and below. We can ignore one point that present a outlier.

Go Math Grade 8 Trend Lines and Predictions Answer Key Question 2.
Do you think you can use a scatter plot that shows no association to make a prediction? Explain your answer.
Answer:
You can not use a scatter plot that shows no association to make a prediction. Because association describes how sets of data are related and when there is no association that means that there is no relationship between them.

Example 1

The scatter plot and trend line show the relationship between the number of chapters and the total number of pages for several books. Write an equation for the trend line.

STEP 1: Find the slope of the trend line. The line passes through points (5, 50) and (17, 170).

STEP 2: Find the y-intercept of the trend line.

STEP 3: Use your slope and y-intercept values to write the equation.
y = mx + b Slope-intercept form
y = 10x + 0 Substitute 10 for m and 0 for y.
The equation for the trend line is y = 10x.

Reflect

Question 3.
What type(s) of association does the scatter plot show?
Answer:
The scatter plot shows a positive and linear association.

Question 4.
What is the meaning of the slope in this situation?
Answer:
For every increase of two chapters, there is an increase of 20 pages.

Question 5.
What is the meaning of the y-intercept in this situation?
Answer:
The y-intercept represents the total number of pages for several books. There are about 10 pages in a chapter.

Your Turn

Grade 8 Lesson 14.2 Trend Lines and Predictions Answer Key Go Math Question 6.
The scatter plot and trend line shows the relationship between the number of rainy days in a month and the number of umbrellas sold each month. Write an equation for the trend line.

Answer:
The Line passes through (0, 0) and (10, 9).
Use the slope formula to find the slope
slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{9-0}{10-0}=\frac{9}{10}\)
The Line crosses the y-axis at (0, 0) so the y-intercept is 0
Form an equation for the trend line by substituting the value of the slope for m and the value of the y-intercept for b in the slope-intercept formula.
y = mx + b
y = \(\frac{9}{10}\)x + 0
y = \(\frac{9}{10}\)x

Explore Activity 2

Making Predictions

When you use a trend line or its equation to predict a value between data points that you already know, you interpolate the predicted value. When you make a prediction that is outside the data that you know, you extrapolate the predicted value.

Use the equation of the trend line in Example 1 to predict how many pages would be in a book with 26 chapters.
Is this prediction an example of interpolation or extrapolation? ____________
y = __________ Write the equation for your trend line.
y = __________ Substitute the number of chapters for x.
y = __________ Simplify.
I predict that a book with 26 chapters will have ____________ pages.

Reflect

Question 7.
Make a Prediction Predict how many pages would be in a book with 14 chapters. Is this prediction an example of interpolation or extrapolation?
Answer:
Using the equation y = 10x, substitute 14 (chapters) for x to predict how many pages.
y = 10x = 10(14)
I predict there will be 140 pages.
Interpolation

Question 8.
Do you think that extrapolation or interpolation is more accurate? Explain.
Answer:
Interpolation might be more accurate for linear data. With the given data, you can see the difference between points. If the surrounding points are close to the line, your prediction will be more accurate.

However, if the points have a large difference, interpolation may not give a good estimate.

Texas Go Math Grade 8 Lesson 14.2 Guided Practice Answer Key

Angela recorded the price of different weights of several bulk grains. She made a scatter plot of her data. Use the scatter plot for 1-4.

Question 1.
Draw a trend line for the scatter plot. (Explore Activity 1)
Answer:
Draw a trend line

Question 2.
How do you know whether your trend line is a good fit for the data? (Explore Activity 1)
Answer:
Most of the data points are close to the trend line. The trend line has about the same number of points above and below it.

Go Math Lesson 14.2 Trend Lines and Predictions Question 3.
Write an equation for your trend line. (Example 1)
Answer:
Step 1: The trend line passes through (0, 0) and (19, 1.80).

Step 2: Find the slope by using the slope formula.
slope = m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{1.80-0}{19-0}=\frac{1.80}{19}\) = 0.09

Step 3: The Line passes through the origin so the y-intercept is 0.

Step 4: Form an equation for the trend line by substituting the slope value for m and the value of the y-intercept for b in the stop-intercept formula.
y = mx + b
y = 0.09x + 0
y = 0.09x

Question 4.
Use the equation for your trend line to interpolate the price of 7 ounces and extrapolate the price of 50 ounces. (Explore Activity 2)
Answer:
Use the equation for the trend Line (y = 0.09x) to interpolate the price of 7 ounces by substituting 7 for x (y = 0.09 ∙ 7) and solving for y.
Use the equation for the trend line (y = 0.09x) to extrapoLate the price of 50 ounces by substituting 50 for x (y = 0.09 ∙ 50)and solving for y.

Essential Question Check-In

Question 5.
A trend line passes through two points on a scatter plot. How can you use the trend line to make a prediction between or outside the given data points?
Answer:
Use two points on the line. Find the slope and y-intercept. Substitute the vaLues of the slope (in) and y-intercept (b) to form an equation using y = mx + b. Substitute the value of x for which you want to make a prediction and solve for y OR substitute your prediction for y and solve for x to find its value.

Texas Go Math Grade 8 Lesson 14.2 Independent Practice Answer Key

Use the data in the table for Exercises 6-10.

Question 6.
Make a scatter plot of the data and draw a trend line.

Answer:
Make a scatter plot of the data and draw a trend line.

Question 7.
What type of association does the trend line show?
Answer:
One data set increases (Wind Speed) and the other (Wind Chill) decreases so the trend line shows a Negative Association.

Question 8.
Write an equation for your trend line.
Answer:
Step 1:
m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) Find the slope using the slope Formula.
= \(\frac{(-10)-(5)}{50-30}\)
= \(\frac{-5}{20}\)
= -0.25

Step 2:
y = mx + b Find the y-intercept using the Slope Intercept Formula.
-5 = -0.25(30) + b
-5 = -7.5 + b
2.5 = b

Step 3:
y = -0.25x + 2.5 Substitute the value of m and b into the Slope Intercept Formula to form an equation for the trend line.

Question 9.
Make a Prediction Use the trend line to predict the wind chill at these wind speeds.
a. 36 mi/h ___________
Answer:
Use the trend line to predict the wind chill at 36 mi/h
y = -0.25x + 2.5
y = -0.25(36) + 2.5
y = – 9 + 2.5
y = -6.5
The wind chill at 36 mi/h is -6.5 °F.

b. 100 mi/h ____________
Answer:
Use the trend line to predict the wind chill at 100 mi/h
y = -0.25x + 2.5
y = -0.25(100) + 2.5
y = -25 + 2.5
y = -22.5
The wind chill at 100 mi/h is 22.5 °F.

Lesson 14.2 Trend Lines and Predictions Answer Key Question 10.
What is the meaning of the slope of the line?
Answer:
The slope means that the wind chill falls about 1°F for every 4 mph increase in wind speed.

Use the data in the table for Exercises 11-14.

Question 11.
Make a scatter plot of the data and draw a trend line.

Answer:
Make a scatter plot and draw a trend line.

Question 12.
Write an equation for your trend line.
Answer:
Step 1:
Find the slope by using two points using the slope formula.
For example: (0, 64) and (60, 72).
m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\)
= \(\frac{72-64}{60-0}\)
= \(\frac{8}{60}\)
= –\(\frac{2}{15}\)

Step 2:
The Line passes the y-axis at (0, 64).
The y-intercept = b = 64

Step 3:
Use the slope-intercept formula to form an equation for the trend line Substitute the slope value for m and the value of the y-intercept for b.
y = mx + b
y = –\(\frac{2}{15}\)x + 64

Question 13.
Make a Prediction Use the trend line to predict the apparent temperature at 70% humidity.
Answer:
Use the equation of the trend line Substitute 70 (for 70%) into the equation for x.
y = –\(\frac{2}{15}\)x + 64
y = –\(\frac{2}{15}\)(70) + 64

Solve for y
y = –\(\frac{140}{5}\) + 64
y ≈ –\(9 . \overline{3}\) + 64
y ≈ \(73 . \overline{3}\)
The apparent temperature is 73.3° F.

Question 14.
What is the meaning of the y-intercept of the line?
Answer:
The y-intercept means that at 0% humidity, the apparent temperature is 64°F.

H.O.T. Focus on Higher Order Thinking

Question 15.
Communicate Mathematical Ideas Is it possible to draw a trend line on a scatter plot that shows no association? Explain.
Answer:
It is not possible to draw a trend line on a scatter plot that shows no association.

If the scatter plot shows no association, the data points have no relationships to one another. You can draw a trend line if there is a linear association.

Trend Lines and Predictions Worksheet Answer Key Question 16.
Critique Reasoning Sam drew a trend line that had about the same number of data points above it as below it, but did not pass through any data points. He then picked two data points to write the equation for the line. Is this the correct way to write the equation? Explain.
Answer:
Sam did not use the correct way to write an equation.
Sam may have drawn a correct trend line but using the data points that are not on the trend line may have an incorrect equation for the line. He should use two points on that trend line to write the equation.

Question 17.
Marlene wanted to find a relationship between the areas and populations • of counties in Texas. She plotted x (area in square miles) and y (population) for two counties on a scatter plot:
Kent County (903, 808)
Edwards County (2118, 2002)
She concluded that the population of Texas counties is approximately equal to their area in square miles and drew a trend line through her points.

a. Critique Reasoning Do you agree with Marlene’s method of creating: a scatter plot and a trend line? Explain why or why not.
Answer:
I do not agree with Marlene’s method of creating a scatter plot and a trend line. She did not have enough data. Marlene should have collected and plotted data for many more counties.

b. Counterexamples Harris County has an area of 1778 square miles and a population of about 4.3 million people. Dallas County has an area of 908 square miles and a population of about 2.5 million people. What do these data show about Marlene’s conjecture that the population of Texas counties is approximately equal to their area?
Answer:
The data collected are only of two counties whose populations are nearly equal to their area. The fact that the populations of Harris and Dallas counties are in the millions, Marlene’s conjecture about the population of Texas counties being equivalent to their area is invalid.

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Module 14 Answer Key Scatter Plots.

Texas Go Math Grade 8 Module 14 Answer Key Scatter Plots

Texas Go Math Grade 8 Module 14 Are You Ready? Answer Key

Evaluate each expression for the given value of x.

Question 1.
6x – 5 for x = 4
Answer:
Substitute the given value for x
6x – 5 = 6(4) – 5
= 24 – 5
= 19

Question 2.
-2x + 7 for x = 2
Answer:
Substitute the given value for x
-2x + 7 = -2(2) + 7
= -4 + 7
= 3

Grade 8 Go Math Module 14 Answer Key Question 3.
5x – 6 for x = 3
Answer:
Substitute the given value for x
5x – 6 = 5(3) – 6
= 15 – 6
= 9

Question 4.
0.5x + 8.4 for x = -1
Answer:
Substitute the given value for x
0.5x + 8.4 = 0.5(-1) + 8.4
= -0.5 + 8.4
= 7.9

Question 5.
\(\frac{3}{4}\)x – 9 for x = -20
Answer:
Substitute the given value for x
\(\frac{3}{4}\)x – 9 = \(\frac{3}{4}\)(-20) – 9
= -15 – 9
= -24

Question 6.
1.4x + 3.5 for x = -4
Answer:
Substitute the given value for x
1.4x + 3.5 = 1.4(-4) + 3.5
= -5.6 + 3.5
= -2.1

Solve for x.

Question 7.
3x + 4 = 10
Answer:
3x + 4 = 10
-4 = -4 Subtract 4 from both sides.
3x = 6
\(\frac{3 x}{3}=\frac{6}{3}\) Divide both sides by 3
x = 2

Question 8.
5x – 11 = 34
Answer:
5x – 11 = 34
+11 = +11 Add 11 from both sides.
5x = 45
\(\frac{5 x}{5}=\frac{45}{5}\) Divide both sides by 5.
x = 9

Question 9.
-2x + 5 = -9
Answer:
-2x + 5 = -9
-5 = -5 Subtract 5 from both sides.
-2x = -14
\(\frac{-2 x}{-2}=\frac{-14}{-2}\) Divide both sides by -2.
x = 7

Go Math Grade 8 Answer Key Pdf Module 14 Scatter Plots Question 10.
8x + 13 = -11
Answer:
8x + 13 = 11
-13 = -13 Subtract 13 from both sides.
8x = 24
\(\frac{8 x}{8}=\frac{-24}{8}\) Divide both sides by 8.
x = -3

Question 11.
4x – 7 = -27
Answer:
4x – 7 = 27
+7 = +7 Add 7 to both sides
4x = 20
\(\frac{4 x}{4}=\frac{-20}{4}\) Divide both sides by 4.
x = -5

Question 12.
\(\frac{1}{2}\)x + 16 = 39
Answer:
\(\frac{1}{2}\)x + 16 = 39
-16 = – 16 Subtract 16 from both sides.
\(\frac{1}{2}\)x = 23
\(\frac{1}{2}\)x ∙ 2 = 23 ∙ 2 Multiply both sides by 2.
x = 46

Question 13.
\(\frac{2}{3}\)x – 16 = 12
Answer:
\(\frac{2}{3}\)x – 16 + 16 = 12 + 16 Add 16 to both sides
\(\frac{2}{3}\)x = 28

\(\frac{2}{3}\)x × \(\frac{3}{2}\) = 28 × \(\frac{3}{2}\) Multiply both sides by the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\).
x = \(\frac{3 \cdot 28}{2}\)

x = \(\frac{3 \cdot 28}{2}\) Multiply the numerator.
x = \(\frac{84}{2}\)

x = \(\frac{84}{2}\) Divide
x = 42

Module 14 Scatter Plots Answer Key Go Math Grade 8 Question 14.
0.5x – 1.5 = -6.5
Answer:
0.5x – 1.5 = -6.5
+1.5 = +1.5 Add 1.5 to both sides.
0.5x = 5
\(\frac{0.5 x}{0.5}=\frac{-5}{0.5}\) Divide both sides by 0.5.
x = – 10

Texas Go Math Grade 8 Module 14 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the right column of the chart.

Understand Vocabulary

Match the term on the left to the correct expression on the right.

1. cluster – A. A data point that is very different from the rest of the data in a set
2. outlier – B. A straight line that comes closest to the points on a scatter plot.
3. trend line – C. A set of closely grouped data.
Answer:
1. – C. A cluster is a set of closely grouped data.
2. – A. An outlier is a data point that is very different from the rest of the data in a set
3. – B. A trend line is a straight line that comes closest to the points on a scatter plot.

Active Reading
Two-Panel Flip Chart Create a two-panel flip chart, to help you understand the concepts in this module. Label each flap with the title of one of the lessons in the module. As you study each lesson, write important ideas under the appropriate flap. Include any sample problems or equations that will help you remember the concepts later when you look back at your notes.

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Unit 7 Study Guide Review Answer Key.

Texas Go Math Grade 8 Unit 7 Study Guide Review Answer Key

Texas Go Math Grade 8 Unit 7 Exercises Answer Key

Module 16 Managing Your Money and Planning for Your Future

Question 1.
Sheri is going to take out a loan for $4,000 that she plans to pay back in 2 years. She wants to know how much more it will cost her in interest if she uses her credit card at 18% interest instead of borrowing from the bank at 10% interest. Both loans require monthly payments. Use an online calculator to find the total repayment for each loan and the difference in the cost of these two choices. (Lesson 16.1)
Answer:
Given that,
Sheri took a loan = $4,000.
Sheri plans to come back in = 2 years.
Interest if she uses her credit card is = 18%.
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $4000
T = time = 2 years.
R = interest rate = 18%
Simple interest for using her credit card = $4000 × 2 × 18/100 = 1440.
2 years = 24 months.
For 1 month = 1440/24 = 60.
Total replacement of loan for 1 month = $4000 + 60 = $4060
Interest if she borrowing from the bank is 10%
P = actual money = $4000
T = time = 2 years.
R = interest rate = 10%
Simple interest for her borrowing from the bank is = $4000 × 2 × 10/100 = 800.
2 years = 24 months.
For 1 month = 800/24 = 33.3
Total replacement of loan for 1 month = $4000 + 33.3 = $4033.3
Difference in the cost of two loans for 1 month is $4060 – $4033.3 = $26.7.
The difference between the two loans is $26.7.

Go Math Unit 7 Review Answer Key Grade 8 Question 2.
You are trying to decide which account to put $3,500 into for the next 6 years. One account has an interest rate of 2.9%, compounded annually. The other account has a simple interest rate of 3.1 %. Which account will earn more interest over 6 years, and how much more interest will it earn? (Lesson 16.2)
Answer:
Given that,
The total amount = $3500.
The total number of years = 6 years.
One account an interest rate = 2.9% in compound interest.
Formula for compound interest = A = P(1 + R/1000)n
P = actual money = $3500
n = time = 6 years.
R = interest rate = 2.9%
Compound interest for 6 years = A = 3500(1 + 3.1/100)6
= 3500(1 + 0.031)6
= 3500(1.031)6
= 3500(1.20)
= $4200
The other account = 3.1% in simple interest.
The formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $3500
T = time = 6 years.
R = interest rate = 3.1%
Simple interest for 6 years = $3500 × 6 × 3.1/100 = $651.
The difference between the two loans is $4200 – $651 = $3549
The simple interest loan is $3549 more interest than compound interest.

Question 3.
Maria has $ 120 to spend on food for the week. She goes out to a restaurant to eat dinner with her friends and spends $62 on the meal. Did Maria make a financially responsible decision or a financially irresponsible decision? Explain your answer. (Lesson 16.3)
Answer:
Given that,
Maria spends on food for the week = $120.
1 week = 7 days
For 1 day meal = $120/7 = $17.14.
Maria goes out to a restaurant to eat dinner with friends and spends on meal = $62.
It is an irresponsible decision for her to go out to a restaurant and to spend $62 on a meal.
Maria spending $120 on food for the week is a responsible decision.

Go Math Grade 8 Answer Key Pdf Unit 7 Answer Key Question 4.
Use an online tool to estimate the cost for one year at a 4-year university and one year at a 2-year college in Texas. (Lesson 16.4)

a. Find the cost of attending the university for four years.
Answer:
Tuition and fees for 4 years university = 24,000.
Room and board for 4 year university = 14,000
Books for 4 year university = 1000
Others for 4 year university = 500
Tuition and fees for 2 years college = 12,000.
Room and board for 2 year college = 7,000
Books for 2 year college = 6000
Others for 2 year college = 300
The total cost of attending the university for 4 years = 24,000 + 14,000 + 1000 + 500 = 39,500.

b. Find the cost of attending the two-year college and transferring to the university for your final two years of school.
Answer:
Tuition and fees for 4 years university = 24,000.
For 2 years = 12000
Room and board for 4 year university = 14,000
For 2 years = 7000
Books for 4 year university = 1000
For 2 years = 500.
Others for 4 year university = 500
For 2 years = 250.
Tuition and fees for 2 years college = 12,000.
Room and board for 2 year college = 7,000
Books for 2 year college = 6000
Others for 2 year college = 300
The cost of attending the two-year college and transferring to the university for your final two years of school = 1200 + 7000 + 500 + 250 + 12000 + 7000 + 6000 + 300 = 45,050

Texas Go Math Grade 8 Unit 7 Performance Tasks Answer Key

Unit 7 End of Unit Assessment Answer Key Grade 8 Question 1.
CAREERS IN MATH Organic Farmer Carlos is an organic farmer, and his business is doing so well that he his thinking of expanding in the next few years. He decided to start saving for this expansion and is going to put $8,200 into a savings account. At his credit union, he has two choices for savings accounts: Simple Savers which earns 2% simple interest per year, and Super Savers which earns 1.95% interest, compounded annually.
a. How much will Carlos have after 2 years if he chooses the Simple Savers account? Show your work.
Answer:
Given that,
Organic Farmer Carlos’ money in the savings account is $8200.
Simple Savers that earns 2% simple interest per year.
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $8200
T = time = 2 years.
R = interest rate = 2%
Simple interest for 2 years = $8200 × 2 × 2/100 = $328.

b. How much will Carlos have after 2 years if he chooses the Super Savers account? Show your work.
Answer:
Given that,
Organic Farmer Carlos’ money in the savings account is $8200.
Super savers that earn 1.95 compounded interest per year.
Formula for compound interest = A = P(1 + R/100)n
P = actual money = $8200
n = time = 2 years.
R = interest rate = 1.95%
Compound interest for 2 years = A = 8200(1 + 1.95/100)2
= 8200(1 + 0.0195)2
= 8200(1.0195)2
= 8200(1.039)
Compounded interest for 2 years = $8519.8

c. Which account would you recommend Carlos use and why?
Answer:
Simple interest for 2 years = $8200 × 2 × 2/100 = $328.
Compounded interest for 2 years = $8519.8
I recommend the simple interest because its interest is less than the compounded interest.

d. If Carlos decides to keep the money in the savings account for 5 years, would you change your recommendation? Why or why not?
Answer:
Organic Farmer Carlos’ money in the savings account is $8200.
Simple Savers that earn 2% simple interest per year.
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $8200
T = time = 5 years.
R = interest rate = 2%
Simple interest for 2 years = $8200 × 2 × 5/100 = $820.
Organic Farmer Carlos’ money in the savings account is $8200.
Super savers that earn 1.95 compounded interest per year.
Formula for compound interest = A = P(1 + R/100)n
P = actual money = $8200
n = time = 2 years.
R = interest rate = 1.95%
Compound interest for 2 years = A = 8200(1 + 1.95/100)5
= 8200(1 + 0.0195)5
= 8200(1.0195)5
= 8200(1.101)
Compounded interest for 2 years = $9028.2.
There is no change in the recommendation because after 5 years also simple interest is less than compounded interest.

Question 2.
Kay wants a new television. She sees an advertisement in the newspaper for a rent-to-own store, where for $80 a month she can rent a new television. And, if she rents for 18 months, she will own the television outright. Kay is considering this option, because she doesn’t have enough money to purchase a television but she can pay $80 a month.
a. If Kay rents the television for 18 months, how much will she pay in total for the television?
Answer:
Given that,
Kay can rent a new television for 1 month = $80.
For 18 months = $80 × 18 = $1440.
Kay rents for 18 months = $1440.

b. The same television sells for $429 at an electronics store. How much more will Kay end up paying if she rents the television for 18 months than if she buys it outright?
Answer:
Given that,
The television sells at an electronic store is $429
Kay can rent a new television for 1 month = $80.
For 18 months = $80 × 18 = $1440.
Kay rents for 18 months = $1440.
Subtract $1440 – $ 429 = $1011.
Key will end up paying if she rents for 18 months = $1011.

c. What financially responsible recommendation would you give to Kay about purchasing the television?
Answer: I recommend that you purchase the television at the electronics shop. Because the cost of the television in the electronic shop is less than the rent for 18 months.

Unit 7 Test Review Answer Key Grade 8 Go Math Question 3.
Anastasia is a high school senior who wants to be an architect. She was accepted at a four-year university and was offered a scholarship of $17,800 per year. The costs per year at this university are shown in the table.

She can also attend a community college for the first two years. The tuition for the community college is $1,150 per year. She would need to rent an apartment and buy her food, which she estimates will cost $400 a month for the apartment and $210 a month for food. She would still need to buy books and materials at $850 a year.

a. How much will it cost Anastasia to attend the university for all four years of college, assuming she has her scholarship all four years, and she does not pay for housing and food during the summers? Show how you got your answer.
Answer:
Given that,
The amount of Anastasia scholarship is = $17800 per year.
For four years = 4 × $17800 = $71200
The total amount of tuition fee for one year is $17400
The total amount of tuition fee for four years = $17400 × 4 = $69600
The total amount of fee for room and board = $10,350
For four years = 4 × $10,350 = $41400
The total amount of fee for books and materials = $850
For four years = $850 × 4 = $3400
The total amount for the community tuition = $1150 per year.
For two years = $1150 × 2 = $2300
The total amount for the apartment = $400 per month
There is no need to pay money in the summer for food and an apartment.
1 year = 12 months in that 3 months are summer so 12 – 3 – 9.
For 4 years = 4 × 9 = 36 months.
For 4 years = 36 × $400 = $14400
The total amount for the food = $210 per month
For 4 years = 36 months.
For 4 years = 36 × $210 = $7560
She still needs to buy the books and materials = $850.
For 4 years = 4 × $850 = $3400
The total cost Anastasia to attend the university for all four years of college = $71200 + $69600 + $41400 + $3400 + $2300 + $14400 + $7560 + $3400 = $213,260

b. How much will it cost Anastasia to attend the community college for the first two years, and to attend the university for the last two years? Show your work.
Answer:
Given that,
The total amount of tuition fee for one year is $17400
The total amount of tuition fee for the last two years = $17400 × 2 = $34800
The total amount for the community tuition = $1150 per year.
For two years = $1150 × 2 = $2300.
The total cost for Anastasia to attend the community college for the first two years, and to attend the university for the last two years = $34800 + $2300 = $37100.

c. Give one reason in favor of going to the university for her entire college career, and one reason in favor of going two years to the community college and two years to the university.
Answer:
Given that,
The total amount of tuition fee for one year is $17400
The total amount of tuition fee for four years = $17400 × 4 = $69600
The total cost for Anastasia to attend the community college for the first two years, and to attend the university for the last two years = $34800 + $2300 = $37100.
The fee for four years of university college is more than the community college of two years and two years of university college.

Texas Go Math Grade 8 Unit 7 Mixed Review Texas Test Prep Answer Key

Selected Response

Grade 8 Unit 7 Study Guide Answer Key Question 1.
Which interest rate and time period result in the lowest total loan repayment for a $5,000 loan earning simple interest?
(A) 3 years at 10%
(B) 3 years at 13%
(C) 4 years at 8%
(D) 4 years at 11%
Answer:

(A) 3 years at 10%
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $5000
T = time = 3 years.
R = interest rate = 10%
Simple interest for 3 years = $5000 × 3 × 10/100 = $1500.

(B) 3 years at 13%
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $5000
T = time = 3 years.
R = interest rate = 13%
Simple interest for 3 years = $5000 × 3 × 13/100 = $1950
(C) 4 years at 8%
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $5000
T = time = 4 years.
R = interest rate = 8%
Simple interest for 4 years = $5000 × 4 × 8/100 = $1600
(D) 4 years at 11%
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $5000
T = time = 4 years.
R = interest rate = 11%
Simple interest for 4 years = $5000 × 4 × 11/100 = $2200
Option A is the correct answer.

Question 2.
Which of the relations below is a function?

Answer: Option C is a function

Question 3.
Amanda used her PIN to complete a transaction at a department store. Which payment method does this describe?
(A) gift card
(B) credit card
(C) debit card
(D) personal check
Answer:
A transaction at a department store payment method is a credit card.
A credit card is a card issued by the bank and it is used to purchase goods or services on credit.
Option B is the correct answer.

Geometry Unit 7 Test Answer Key Grade 8 Question 4.
What is the surface area of the rectangular prism?

(A) 160 cm²
(B) 164 cm²
(C) 328 cm²
(D) 392 cm²
Answer:
Formula for the surface area of the rectangular prism = 2(lw + lh + wh)
Length = 14cm
Width = 6cm
Height = 4cm
Surface area of the rectangular prism = 2(14 × 6 + 14 × 4 + 6 × 4)
= 2(84 + 56 + 24)
= 2(164)
= 328.
The surface area of the rectangular prism = 328 cm2
Option C is the correct answer.

Question 5.
Rianna opens a savings account with $900. Her account earns interest at a rate of 1.3%, compounded annually. How much money is in the account after 4 years?
(A) $46.80
(B) $47.72
(C) $946.80
(D) $947.72
Answer:
Given that,
Rianna opens a savings account = $900.
Interest at rate = 1.3%.
The total number of years = 4.
Formula for compound interest = A = P(1 + R/100)ⁿ
P = actual money = $900
n = time = 4 years.
R = interest rate = 1.3%
Compound interest for 4 years = A = 900(1 + 1.3/100)⁴
= 900(1 + 0.013)4
= 900(1.013)4
= 900(1.053022)
= $947.72
Money in the account after 4 years = $947.72.
Option D is the correct answer.

Hot Tips! Some answer choices, called distracters, may seem correct because they are based on common errors made in calculations.

Question 6.
Richard took a handful of pencils from a large box. Out of the 15 pencils in his hand, 4 were glittery. How many glittery pencils should Richard expect to find in the box if there are a total of 240 pencils?
(A) 16 glittery pencils
(B) 32 glittery pencils
(C) 64 glittery pencils
(D) 96 glittery pencils
Answer:
Given that,
Richard took a handful of pencils from a large box.
Out of 15 pencils, 4 are glittery.
Richard expects to find 240 pencils = 240/15 = 16.
There are 16 glittery pencils in the 240 pencils.
Option A is the correct answer.

Grade 8 Mathematics Study Guide Unit 7 Test Question 7.
Yvonne started running 8 minutes after Cassie started. Cassie was running at a rate of 500 feet per minute. Yvonne was running at a rate of 600 feet per minute. Which equation could you solve to find out how long it will take Yvonne to catch up to Cassie?
(A) 600t + 3 = 500t
(B) 600t + 4,800 = 500t
(C) 500t + 3 = 600t
(D) 500t + 4,000 = 600t
Answer:
Given that,
Cassie was running at a rate of 500 feet per minute.
Yvonne started running after 8 minutes of Cassie.
Yvonne was running at a rate of 600 feet per minute.
1 minute = 600 feets.
8 minutes = 6 × 600 = 4800 feets.
Yvonne to catch up to cassie = 4800 feet.
Option B is the correct answer.

Question 8.
Leah is planning on attending a public university to earn a four year bachelor’s degree. For one year, the tuition and fees are $10,220, room and board is $6250, and books are $540. At these rates, how much should Leah expect four years of school to cost?
(A) $16,470
(B) $17,010
(C) $34,020
(D) $68,040
Answer:
Given that,
Leah tuition and fees for one year = $10220.
For room and board = $6250.
For books for one year = $540.
The total amount for one year = $10220 + $6250 + $540 = $17010
Leah expects four years of school = $17010 × 4 = $68040.
Option D is the correct answer.

Question 9.
The square below is dilated under the dilation (x, y) →(0.25x, 0.25y).

What are the coordinates of A’?
(A) (-4, -4)
(B) (-1, -1)
(C) (-2, -2)
(D) (4, -4)
Answer:
Dilation means changing the positions and size of a figure but not the shape.
Coordinates of A(-4,4), B(4,4), C(4,-4) D(-4,-4)
The coordinates of A’ is (4,-4).

Gridded Response

Question 10.
Fletcher puts $4,500 in a savings account earning 1.5% interest compounded annually. He does not make any deposits or withdrawals for 3 years. How much interest does the account earn? Round to the nearest cent.

Answer:

Given that,
Fletcher puts in a savings account = $4500.
Interest compounded annually = 1.5%.
The total number of years = 3
Formula for compound interest = A = P(1 + R/100)ⁿ
P = actual money = $4500
n = time = 3 years.
R = interest rate = 1.5%
Compound interest for 3 years = A = 4500(1 + 1.5/100)³
= 4500(1 + 0.015)³
= 4500(1.015)³
= 4500(1.045)
= 4702.5

Hot Tips! Underline keywords given in the test question so you know for certain what the question is asking.

Grade 8 Mathematics Unit 7 Answer Key Question 11.
Pat puts $1,310 in a savings account earning 2% simple interest and does not make any deposits or withdrawals for 8 years. How much interest does the account earn?

Answer:

Given that,
Pat puts in a savings account = $1310.
Interest = 2%
Total number of years = 8 years.
Formula for simple interest equal to SI = PTR/100
Here,
P = actual money = $1310
T = time = 8 years.
R = interest rate = 2%
Simple interest for 8 years = 1310 × 8 × 2/100 = $209.6
Interest for the amount = $209.6

Texas Go Math Grade 8 Unit 7 Vocabulary Review Answer Key

Use the puzzle to preview key vocabulary from this unit. Unscramble the circled letters within found words to answer the riddle at the bottom of the page.

Across
2. College funding awards for students based on achievement. (Lesson 1.4)
4. Payment card you can use to make purchases, and the money is deducted immediately from a bank account. (Lesson 16.4)
5. College funding awards from the government or other organizations, usually for students who need money the most. (Lesson 16.4)

Down
1. The original amount of money deposited or saved. (Lesson 16.2)
3. Payment card you can use to make purchases, then pay a bill at the end of a billing cycle. (Lesson 16.4)

Question.
Why did the man put his money in the freezer?
Answer:
Because he wanted ____ ____ ____ ____, ____ ____ ____ ____ ____ ____ ____ ____!