Texas Go Math

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 Unit 4 Study Guide Review Answer Key.

Texas Go Math Grade 7 Unit 4 Study Guide Review Answer Key

Linear Relationships

Essential Question
How can you use linear relationships to solve real-world problems?

Example
Ross earns a set rate of $10 for babysitting, plus $6 per hour. Represent the relationship using a table, an equation, and a graph of the linear relationship.


Write an equation for the amount y in dollars earned for x hours.
Amount = $10 + $6 per hour .
y = 10 + 6x

Texas Go Math Grade 7 Unit 4 Exercises Answer Key

Question 1.
The cost of a box of cupcakes is $1.50 per cupcake plus $3. Complete the table to represent the linear relationship. (Lesson 7.1)

Answer:

Box of cupcake + 1 cupcake = 1.5 + 1 . 3 = 4.5
Box of cupcake + 2 cupcake = 1.5 + 2 . 3 = 7.5
Box of cupcake + 3 cupcake = 1.5 + 3 . 3 = 10.5
Box of cupcake + 4 cupcake= 1.5 + 4 . 3 = 13.5

y = Box of cupcake + x cupcake

Texas Go Math Grade 7 Solutions Unit 4 Study Guide Question 2.
The score a student receives on a standardized test is based on the number of correct answers, as shown in the table. Use the table to give a verbal description of the relationship between correct answers and scores. (Lesson 7.1)

Answer:
The relationship between the correct answers and the score is:
The score is 200 plus an additional of the correct answer multiplied by 2.

Question 3.
Steve is saving for his daughter’s college education. He opens an account with $2,400 and deposits $40 per month. Represent the relationship using a table and an equation. (Lesson 7.2)
Answer:

y = 2400 + 40x
1 month
y = 2400 + 40 . 1 = 2440
2 months
y = 2400 + 40 . 2 = 2480
3 months
y = 2400 + 40 . 3 = 2520
4 months
y = 2400 + 40 . 4 = 2560

y = 2400 + 40x

7th Grade Math Study Guide Unit 4 Review Answer Key Question 4.
Tonya has a 2-page story she wants to expand. She plans to write 3 pages per day until it is done. Represent the relationship using a table, an equation, and a graph. (Les5on 7.2)

Answer:

y = 2 + 3x
1 day
y = 2 + 3 . 1 = 5
2 days
y = 2 + 3 . 2 = 8
3 days
y = 2 + 3 . 3 = 11
4 days
y = 2 + 3 . 4 = 14

y = 2 + 3x

Equations and Inequalities

Essential Question
How can you use equations and inequalities to solve real-world problems?

Example 1
A clothing store sells clothing for 2 times the wholesale cost plus $10. The store sells a pair of pants for $48. How much did the store pay for the pants? Represent the solution on a number line.
Let w represent the wholesale cost of the pants or the price paid by the store.

The store paid $19 for the pants.

Example 2
Determine which, if any, of these values makes the inequality
-7x + 42 ≤ 28 true: x = -1, x = 2, x = 5.

Texas Go Math Grade 7 Unit 4 Exercises Answer Key

Unit 4 Test Study Guide Answer Key 7th Grade Math Question 1.
The cost of a ticket to an amusement park is $42 per person. For groups of up to 8 people, the cost per ticket decreases by $3 for each person in the group. Marcos’s ticket cost $30. Write and solve an equation to find the number of people in Marcos’s group. (Lessons 8.1, 8.2)
Answer:
Assign a variable for the unknown value. Let x be the number of people in Marco’s group. The equation for the
given problem is:
42 – 3x = 30
Determine the number of people in Marco’s group.
42 – 3x = 30 Write the equation
42 – 3x – 42 = 30 – 42 Subtract 42 from both sides
-3x = -12 Simplify
\(\frac{-3 x}{-3}\) = \(\frac{-12}{-3}\) Divide both sides by -3
x = 4 Simplify
There are 4 people in Marco’s group.

Solve each equation. Graph the solution on a number line. (Lesson 8.2)

Grade 7 Mathematics Unit 4 Answer Key Question 2.
8x – 28 = 44

Answer:
Add 28 to both sides.
8x – 28 + 28 = 44 + 28
8x = 72 Divide both sides by 8.


x = 9

Question 3.
-5z + 4 = 34

Answer:
Subtract 4 from both sides.
– 5z + 4 – 4 = 34 – 4
– 5z = 30 Divide both sides by (-5).


z = -6

Texas Go Math Book 7th Grade Answer Key Unit 4 Study Guide Question 4.
Prudie needs $90 or more to be able to take her family out to dinner. She has already saved $30 and wants to take her family out to eat in 4 days. (Lesson 6.3)

a. Suppose that Prudie saves the same each day. Write an inequality to find how much she needs to save each day.
Answer:
a) Sum $30 Prudie already has and 1x, where r represents how much money
she needs to save each day to raise at least $90.
$30 + 4r ≥ 890 Subtract $30 from both sides.
-$30 + $30 + 4x ≥ -$30 + $90
4x ≥ $60 Divide both sides by 4.

x ≥ $15

b. Suppose that Prudie saves $18 each day. Will she have enough money to take her family to dinner in 4 days? Explain.
Answer:
Yes, she will, because $18 satisfies the inequation. Let’s check.

x ≥ $15

Solve each inequality. Graph and check the solution. (Lesson 8.4)

Question 5.
15 + 5y > 45

Answer:
Subtract 15 from both sides
-15 + 15 + 5y > – 15 + 45
5y > 30 Divide both sides by .

Check the solution for y > 6. For example, y = 7.

This inequality is shown in the picture.

y > 6

Texas Go Math Grade 7 Unit 4 Assessment Answers Question 6.
7x – 2 ≤ 61

Answer:
Add 2 to both sides
7x – 2 + 2 ≤ 61 + 2
7x ≤ 63 Divide both sides by 7.

Check the solution for x ≤ 9. For example, x = 8.

True
This inequality is shown in the picture.

x ≤ 9

Texas Go Math Grade 7 Unit 4 Performance Tasks Answer Key

Question 1.
Careers in Math Mechanical Engineer A mechanical engineer is testing the amount of force needed to make a spring stretch by a given amount. The force y is measured in units called Newtons, abbreviated N. The stretch x is measured in centimeters. Her results are shown in the graph.

a. Write an equation for the line. Explain, using the graph and then using the equation, why the relationship is proportional.
Answer:
Based on the graph, use (2, 16). This point represents the force (16 N) with a stretch (2 cm). Using this point,
determine the value of k in k = \(\frac{y}{x}\).
k = \(\frac{y}{x}\) = \(\frac{16}{2}\) = 8
Substitute the value of k in the given form y = kx. The equation for the given graph 5:
y = 8x
The graph is said to be proportional because the graph is a straight line through the origin. Furthermore, the rate
of change is constant.

b. Identify the rate of change and the constant of proportionality.
Answer:
Based on the equation y = 8x, the rate of change and constant of proportionality is 8. This is because the comparison between the force and stretch in the given graph is constant for every point on the Line.

c. What is the meaning of the constant of proportionality in the context of the problem?
Answer:
The constant of proportionality in the problem showed that when there is an increase ¡n the stretch of the spring the force also increases by 8.

Question 2.
A math tutor charges $30 for a consultation, and then $25 per hour. An online tutoring service charges $30 per hour.

a. Does either service represent a proportional relationship? Explain.
Answer:
The online tutoring service represents a proportion relationship. This is because the relationship between the two
quantities is constant or the ratio of one quantity to the other is constant

b. Write an equation for the cost c of h hours of tutoring for each service. Which service charges less for 4 hours of tutoring? Show your work.
Answer:
The equation for the math tutor is:
30 + 25h = c
The equation for the online tutoring service is:
30h = c
Using the two equations, determine which service will charge less
Math tutor:
30 + 25h = c Write the equation
30 + 25(4) = c Substitute the value
30 + 1oo = c Multiply the values
130 = c Add the values
Online Tutoring
30h = c Write the equation
30(4) = c Substitute the value
120 = c Multiply the values
The online tutoring service will charge less compared to a math tutor.

Texas Go Math Grade 7 Unit 4 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Which description corresponds to the relationship shown in the table?

(A) earning $10 per hour
(B) earning $8 per hour plus $10 in tips
(C) earning $7 per hour plus $15 in tips
(D) earning $8.50 per hour
Answer:
(C) earning $7 per hour plus $15 in tips

Explanation:
y = 15 + 7x
x = number of hours
y = amount of pay
C. earning $7 per hour plus $15 in tips.

Unit 4 End of Unit Assessment Answer Key 7th Grade Question 2.
Timothy began the week with $35. He bought lunch at school, paying $2.25 for each meal. Let x be the number of meals he bought at school and y be the amount of money he had left at the end of the week. Which equation represents the relationship in the situation?
(A) y = 2.25x + 35
(B) y = 35 – 2.25x
(C) x = 35 – 2.25y
(D) y = 2.25x – 35
Answer:
(B) y = 35 – 2.25x

Explanation:
Timothy has $35 and spend $2.25 for each meal at school, hence amount of money he has decreases for each meal he buys.
y = 35 – 2.25x

Question 3.
Which table represents the linear relationship described by the equation y = 3x + 9?

Answer:

x = 2
y = 3(2) + 9 = 15
x = 3
y = 3(3) + 9 = 18
x = 4
y = 3(4) + 9 = 21
x = 5
y = 3(5) + 9 = 24

y = 3x + 9 = 15

Question 4.
A taxi costs $1.65 for the first mile and $0.85 for each additional mile. Which equation could be solved to find the number x of additional miles traveled in a taxi given that the total cost of the trip is $20?
(A) 1.65x + 0.85 = 20
(B) 0.85x + 1.65 = 20
(C) 1.65x – 0.85 = 20
(D) 0.85x – 1.65 = 20
Answer:
(B) 0.85x + 1.65 = 20

Explanation:
The equation will be:
the cost of the first mile plus the number of miles multiplied by the cost of each mile equals to total cost of the trip.
Hence
0.85x + 1.65 = 20

Texas Go Math Grade 7 Unit 4 Test Answer Key Question 5.
A bag contains 7 purple beads, 4 blue beads, and 7 pink beads. What is the probability of not drawing a blue bead?
(A) \(\frac{4}{18}\)
(B) \(\frac{7}{18}\)
(C) \(\frac{11}{18}\)
(D) \(\frac{14}{18}\)
Answer:
(D) \(\frac{14}{18}\)

Explanation:
Total number of beads in a bag is 18.

The sum of the probabilities of an event and its complement equals 1.
P(event) + P(complement) = 1
P(blue) + P(not blue) = 1
\(\frac{4}{18}\) + P(not blue) = 1 Subtract \(\frac{4}{18}\) from both sides.
P(not blue) = 1 – \(\frac{4}{18}\)
P(not blue) = \(\frac{14}{18}\)
The probability of not drawing a blue bead is \(\frac{14}{18}\).

Question 6.
Which equation has the solution x = 12?
(A) 4x + 3 = 45
(B) 3x + 6 = 42
(C) 2x – 5 = 29
(D) 5x – 8 = 68
Answer:
(B) 3x + 6 = 42

Explanation:
The answer is 3x + 6 = 42
Proof:

3x + 6 = 42

Question 7.
The 23 members of the school jazz band are trying to raise at least $1,800 to cover the cost of traveling to a competition. The members have already raised $750. Which inequality could you solve to find the amount that each member should raise to meet the goal?
(A) 23x + 750 > 1,800
(B) 23x + 750 ≥ 1,800
(C) 23x + 750 < 1,800
(D) 23x + 750 ≤ 1,800
Answer:
(B) 23x + 750 ≥ 1,800

Explanation:
Sum the amount they already have and a number of members multiplied by the amount each member should raise to collect at least $1800.
23x + 750 ≥ 1800

Question 8.
What is the solution of the inequality 2x – 9 < 7?
(A) x < 8 (B) x ≤ 8 (C) x > 8
(D) x ≥ 8
Answer:
Add 9 to both sides.
2x – 9 + 9 < 7 + 9
2x < 16 Divide both sides by 2
\(\frac{2 x}{2}\) < \(\frac{16}{2}\)
x < 8

Grade 7 Mathematics Unit 4 Answer Key Question 9.
Carter rolls a fair number cube 18 times. Which is the best prediction for the number of times he will roll a number that is odd and less than 3?
(A) 2
(B) 3
(C) 4
(D) 5
Answer:
(B) 3

Explanation:
Total number of outcome in a fair dice = 6
Number of outcome which is odd and less than 3 = 1
Probability of outcome which is odd and less than 3 = \(\frac{1}{6}\)
But it is given in the problem that dice is rolled for 18 times. So the probability of outcome which is an odd number and Less than 3 will be in the same proportion.
Let the number of rolls which results in an odd number and less than 3 be x.
\(\frac{x}{18}\) = \(\frac{1}{6}\) (By proportion)
x = \(\frac{18}{6}\) (Cross-multiplying)
x = 3 (Simplifying)
So, 3 rolls are expected for result of an odd number and less than 3
Hence, option B is correct answer.

Question 10.
Which inequality has the solution shown?

(A) 3x + 5 < 2
(B) 4x + 12 < 4
(C) 2x + 5 ≤ 1
(D) 3x + 6 ≤ 3
Answer:
(A) 3x + 5 < 2

Explanation:
Subtract 5 from both sides
3x + 5 – 5 < 2 – 5
3x < – 3 Divide both sides by 3.
\(\frac{3 x}{3}\) < \(\frac{-3}{3}\)
x < -1

Gridded Response

Question 11.
What is the greatest whole number value that makes the inequality 4x + 4 ≤ 12 true?

Answer:
Subtract 4 from both sides.
4x + 4 – 4 ≤ 12 – 4
4x ≤ 8 Divide both sides by 4.
\(\frac{4 x}{4}\) ≤ \(\frac{8}{4}\)
x ≤ 2
The number 2 is the greatest whole number that makes the inequality true.

7th Grade Unit 4 Study Guide Grade 7 Question 12.
The rectangles shown are similar. The dimensions are given in inches.

What is the width of the smaller rectangle?

Answer:
The bigger rectangle
l₁ = 50 in.
w₁ = 25 in.
The smaller rectangle
l₂ = 25 in.
w₂ = x in.
Because they are similar, the corresponding lengths of the sides are proportional.

The width of the smaller rectangle is 12.5 in.

Hot Tip!
Gridded responses can be positive or negative numbers. Enter any negative signs in the first column. Check your work!

Question 13.
What is the solution to the equation 8x – 11 = 77?

Answer:
Add 11 to both sides.
8x – 11 + 11 = 77 + 11
8x = 88 Divide both sides by 8.

The solution is 11

Vocabulary Preview

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

As one quantity changes by a constant amount, the other quantity also changes by a constant amount. (Lesson 7.1)

A special type of linear relationship in which the rate of change is constant, or one in which the ratio of one quantity to the other is constant. (Lesson 7.1)

An equation with more than one operation. (Lesson 8.1)

A variable whose value is less than zero. (Lesson 8.1)

A variable whose value is greater than zero. (Lesson 8.1)

Q: Why does the sum of -4 and 3 complain more than the sum of -3 and 5?
A: It’s the ___ ___ ___ __ ___ ___ ___ ___ ___ __ ___ !
Answer:

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 9 Answer Key Applications of Geometry Concepts.

Texas Go Math Grade 7 Module 9 Answer Key Applications of Geometry Concepts

Essential Question
How can you apply geometry concepts to solve real-world problems?

Texas Go Math Grade 7 Module 9 Are You Ready? Answer Key

Complete these exercises to review skills you will need for this chapter.

Multiply with Fractions and Decimals

Multiply.

Question 1.

Answer:
We multiply as a whole number

Since there are two decimal digits in the factor 4.16, there must be two decimal digits in the product 54.08.

Module 9 Answer Key Grade 7 Geometry Question 2.

Answer:
We mutiply as a whole number

Since there are two decimal digits in the factor 6.47 and one decimal digit in the factor 0.4, there must be three
decimal digits in the product 2.588.

Question 3.

Answer:
We multiply as a whole number.

Since there are two decimal digits in the factor 7.05 and one decimal digit in the factor 9.4, there must be three
decimal digits in the product 66.270.

Question 4.

Answer:
We multiply as a whole number

Since there are two decimal digits in the factor 0.49 and one decimal digit in the factor 25.6, there must be three
decimal digits in the product 12.544

Area of Squares, Rectangles, and Triangles

Find the area of each figure.

7th Grade Geometry Test Module 9 Review Answer Key Question 5.
triangle with a base of 14 in. and a height of 10 in. ____________________
Answer:
The formula for the area of a triangle, where b is base and h is height is
A = \(\frac{1}{2}\) b . h Substitute 14 in. for b, and 10 in. for h.
A = \(\frac{1}{2}\) . 14 . 10
A = \(\frac{1}{2}\) . 140

Question 6.
square with sides of 3.5 ft . ___________
Answer:
Formula for area of a square, where a represents side of a square, is
A = a² Substitute 3.5 ft for a.
= (3.5)²
A = 12.25 ft²

Question 7.
rectangle with length 8\(\frac{1}{2}\) in. and width 6 in. __________________
Answer:
The formula for the area of a rectangle, where a represents length and b represents the width, is
A = a . b Substitute 8\(\frac{1}{2}\) in. for a, and 6 in for b.
A = 8\(\frac{1}{2}\) . 6
A = \(\frac{17}{2}\) . 6

Geometry Concepts and Applications Answer Key Pdf Question 8.
triangle with base 12.5 m and height 2.4 m _________________
Answer:
The formula for the area of a triangle, where b is base and h is height is
A = \(\frac{1}{2}\) . b . h Substitute 12.5 m for b, and 2.4 m for h.
A = \(\frac{1}{2}\) . 12.5 . 2.4
A = \(\frac{1}{2}\) . 30

Texas Go Math Grade 7 Module 9 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the graphic. You will put one word in each oval.

Understand Vocabulary

Complete each sentence, using the preview words.

7th Grade Geometry Test Pdf Module 9 Test Answers Question 1.
____ are angles that have the same measure.
Answer:
Congruent angles.

Question 2.
___ are two angles whose measures have a sum of 90°.
Answer:
Complementary angles.

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 8.2 Answer Key Solving Two-Step Equations.

Texas Go Math Grade 7 Lesson 8.2 Answer Key Solving Two-Step Equations

Your Turn

Use algebra tiles to model and solve each equation.

Question 1.
2x + 5 = -11 __________
Answer:

First step
On the left side put 2 positive variables and 5 +1 tiles. On the right side put 11 + 1 tiles.

Second step
Remove 5 + 1 tiles from each side of the mat.

Third step
Divide each side into 2 groups.
The solution is x = 3

Texas Go Math Grade 7 Solutions Lesson 8.2 Question 2.
3n – 1 = 8 ___________
Answer:

First step
On the left side put 3 positive variables and 1 – 1 tiles. On the right side put 8 + 1 tiles.

Second step
Add 1 + 1 tiles to each side of the mat.
The sum of the +1 and 1 tiles is 0.

Third step
Divide each side into 3 groups.
The solution is n = 3.

Question 3.
2a – 3 = -5 __________
Answer:

First step
On the left side put 2 positive variables and 3 – 1 tiles. On the right side put 5 – 1 tiles.

Second step
Add 3 + 1 tiles to each side of the mat.
The sum of the +1 and 1 tiles is 0.

Third step
Divide each side into 2 groups.
The solution is a = -1.

Go Math Grade 7 Answer Key Pdf Solving Two Step Equations Question 4.
-4y + 2 = -2 ___________
Answer:

First step
On the left side put 4 negative variable and 2 + 1 tiles. On the right side put 2 – 1 tiles.

Second step
Remove 2 + 1 tiles from each side of the mat.
The sum of the +1 and -1 tiles is 0.

Third step
Divide each side into 4 groups.
The solution is -y = -4, hence y = 4.

Example 2

Tony carried 5 identical baseball bats to a ball game inside a carrying case weighing 12 ounces. The combined weight of the bats and the case was 162 ounces. How much did each bat weigh? Graph the solution on a number line.

Reflect

Question 5.
Analyze Relationships Describe how you could find the weight of one baseball bat using only arithmetic. Compare your method with the one used in Example 2.
Answer:
Using the arithmetic method, first subtract the weight of the case from the combined weight of the bats and case.
162 – 12 = 150
Then, divide the result by 5, since there are 5 identical bats.
150 ÷ 5 = 30
Each bat weighs 30 ounces. The two methods gave the same result. For some, it would be easier to use arithmetic and for some using an equation is easier. It will always depend on who is answering the problem which method they would prefer.

Your Turn

Write and solve an equation that represents the situation. Graph the solution on the number line.

Question 6.
Maureen wants to buy a $198 camera. She has $30 and plans to save $12 each week. In how many weeks will she be able to buy the camera?

Answer:
Sum $30 that Maureen has, and $12x, where x represents the number of weeks, to get the amount. of money she needs for the camera.
$30 + $12 ∙ x = $198 Subtract $30 from both sides.
-$30 + $30 + $12 ∙ x = $30 + $198
$12∙ x = $168 Divide both sides by $12.
\(\frac{\$ 12 \cdot x}{\$ 12}=\frac{14 \cdot \$ 12}{\$ 12}\)
x = 14

$30 + $12 ∙ x = $198

Texas Go Math Grade 7 Solving Two-Step Equations Answer Key Question 7.
A rectangular picture frame has a perimeter of 58 inches. The height of the frame is 18 inches. What is the width of the frame?

Answer:
A perimeter of a rectanguLar is equal the sum 2 × height and 2 × width. Let x be the width of the frame.
18 + 2 ∙ x = 58 Subtract 18 from both sides.
-18 + 18 + 2 ∙ x = -18 + 58
2 ∙ x = 40 Divide both sides by 2.
\(\frac{2 \cdot x}{2}=\frac{20 \cdot 2}{2}\)
x = 20 inches

18 + 2 ∙ x = 58

Determine which, if any, of the given values is a solution.

Question 8.
3k + 15 = 66
k = -7; k = 17; k = 27
Answer:
Substitute 7 for k in the given equation.
k = 7
3 ∙ (-7) + 15 ≟ 66
-21 + 15 ≟66
-6 ≟ 66
Not true.

Substitute 17 for k in the given equation.
k = 17
3 ∙ (17) + 15 ≟ 66
51 + 15 ≟ 66
66 ≟ 66
True.

Substitute 27 for k in the given equation.
k = 27
3 ∙ (27) + 15 ≟ 66
81 + 15 ≟ 66
96 ≟ 66
Not True.

Question 9.
\(\frac{p}{2}\) – 5 = 7
p = -72; p = 18; p = 108
Answer:
Substitute 72 for p in the given equation.
p = 72
\(\frac{-72}{9}\) – 5 ≟ 7 Multiply by 9 both sides
\(\frac{-72 \cdot 9}{9}\) – 5 ∙ 9 ≟ 7 ∙ 9
-72 – 45 ≟ 63
-117 ≟ 63
Not true.

Substitute 18 for p in the given equation.
p = 18
\(\frac{18}{9}\) – 5 ≟ 7 Multiply by 9 both sides
\(\frac{18 \cdot 9}{9}\) – 5 ∙ 9 ≟ 7 ∙ 9
18 – 45 ≟ 63
-27 ≟ 63
Not true.

Substitute 108 for p in the given equation.
p = 108
\(\frac{108}{9}\) – 5 ≟ 7 Multiply by 9 both sides
\(\frac{108 \cdot 9}{9}\) – 5 ∙ 9 ≟ 7 ∙ 9
108 – 45 ≟ 63
63 ≟ 63
True.

Texas Go Math Grade 7 Lesson 8.2 Guided Practice Answer Key

The equation 2x + 1 = 9 is modeled below. (Example 1)

Question 1.
To solve the equation with algebra tiles, first remove. ____________.
Then divide each side into ______________
Answer:

• first remove +1 tile from each side
• then divide each side into 2 equal groups

Two Step Equations Answer Key Go Math Lesson 8.2 7th Grade Question 2.
The solution is x = ________________
Answer:
The solution is x = 4

Solve each equation. Then graph the solution on the number line. (Example 2)

Question 3.
8m – 15 = 41
m = ___________

Answer:
Add 15 to both sides.
8m – 15 + 15 = 41 + 15
8m = 56 Divide both sides by 8.
\(\frac{8 \cdot m}{8}=\frac{56}{8}\)
m = 7

Question 4.
\(\frac{k}{3}\) + 21 = 27
k = ____________

Answer:
Subtract 21 from both sides.
\(\frac{k}{3}\) + 21 – 21 = 27 – 21
\(\frac{k}{3}\) = 6 Multiply both sides by 3.
3 ∙ \(\frac{k}{3}\) = 3 ∙ 6
k = 18

Determine which, if any, of the given values is a solution. (Example 3)

Question 5.
9p – 18 = 27
p = 3; p = 5; p = 7
Answer:
Substitute 3 for p in the given equation.
p = 3
9 ∙ (3) – 18 ≟ 27
27 – 18 ≟ 27
9 ≟ 27
Not true.

Substitute 5 for p in the given equation.
p = 5
9 ∙ (5) – 18 ≟ 27
45 – 18 ≟ 27
27 ≟ 27
True.

Substitute 7 for p in the given equation.
p = 7
9 ∙ (7) – 18 ≟ 27
63 – 18 ≟ 27
45 ≟ 27
Not true.

Grade 7 Go Math Answer Key Solving Two Step Equations Question 6.
\(\frac{a}{-2}\) – 5 = 0
a = -10; a = 0; a = 10
Answer:
Substitute 10 for a in the given equation
a = -10
\(\frac{-10}{-2}\) – 5 ≟ 0
\(\frac{-10 \cdot(-2)}{-2}\) – 5 ∙ (-2) ≟ 0 ∙ (-2) Multiply both sides by (-2)
– 10 + 10 ≟ 0
0 ≟ 0
True.

Substitute 0 for a in the given equation
a = 0
\(\frac{0}{-2}\) – 5 ≟ 0
0 – 5 ≟ 0
-5 ≟ 0
Not true.

Substitute 10 for a in the given equation
a = -10
\(\frac{10}{-2}\) – 5 ≟ 0
\(\frac{10 \cdot(-2)}{-2}\) – 5 ∙ (-2) ≟ 0 ∙ (-2) Multiply both sides by (-2)
10 + 10 ≟ 0
20 ≟ 0
Not true.

Essential Question Check-In

Question 7.
How can you decide which operations to use to solve a two-step equation?
Answer:
If we have variable multiplied by some number, we divide both sides of the equation by that number.
If we have variable divided by some number, we multiply both sides of the equation by that number.
If some number is added to variable, we subtract that number from both sides of the equation.
If some number is subtracted from variable, we add that number to the both sides of the equation.

Texas Go Math Grade 7 Lesson 8.2 Independent Practice Answer Key

Solve.

Question 8.
9s + 3 = 57
Answer:
Subtract 3 from both sides.
9 ∙ s + 3 – 3 = 57 – 3
9 ∙ s = 54 Divide both sides by 9.
\(\frac{s \cdot 9}{9}=\frac{6 \cdot 9}{9}\)
s = 6

Question 9.
4d + 6 = 42
Answer:
Subtract 6 from both sides.
4 ∙ d + 6 – 6 = 42 – 6
4 ∙ d = 36 Divide both sides by 4.
\(\frac{d \cdot 4}{4}=\frac{9 \cdot 4}{4}\)
d = 9

Question 10.
-3y + 12 = -48
Answer:
Subtract 12 from both sides.
-3 ∙ y + 12 – 12 = 48 – 12
-3 ∙ y = 60 Divide both sides by 4.
\(\frac{y \cdot(-3)}{3}=\frac{20 \cdot(-3)}{3}\)
y = 20

Question 11.
\(\frac{k}{2}\) + 9 = 30
Answer:
Multiply both sides by 2.
\(\frac{k \cdot 2}{2}\) + 9 ∙ 2 = 30 ∙ 2
k + 18 = 60 Subtract 18 from both sides
k + 18 – 18 = 60 – 18
k = 42

Question 12.
\(\frac{g}{3}\) – 7 = 15
Answer:
Multiply both sides by 3.
\(\frac{g \cdot 3}{3}\) + 7 ∙ 3 = 15 ∙ 3
g – 21 = 45 Subtract 21 from both sides
g – 21 + 21 = 45 + 21
g = 66

Go Math Answer Key 7th Grade Practice and Homework Lesson 8.2 Question 13.
\(\frac{z}{5}\) + 3 = -35
Answer:
Multiply both sides by 5.
\(\frac{z \cdot 5}{5}\) + 3 ∙ 5 = (-35) ∙ 2
z + 15 = -105 Subtract 15 from both sides
z + 15 – 15 = -105 – 15
k = -120

Question 14.
-9h – 15 = 93
Answer:
Add 15 to both sides.
-9 ∙ h – 15 + 15 = 93 + 15
-9 ∙ h = 108 Divide both sides by (-9)
\(\frac{h \cdot(-9)}{-9}=\frac{(-12) \cdot(-9)}{-9}\)
h = -12

Question 15.
24 + \(\frac{n}{4}\) = 10
Answer:
Multiply both sides by 4.
24 ∙ 4 + \(\frac{n \cdot 4}{4}\) = 10 ∙ 4
96 + n = 40 Subtract 96 from both sides.
-96 + 96 + n = -96 + 40
n = – 56

Question 16.
-17 + \(\frac{b}{8}\) = 13
Answer:
MuLtiply both sides by 8.
(-17) ∙ 8 + \(\frac{b \cdot 8}{8}\) = 13 ∙ 8
-136 + b = 104 Add 136 to both sides.
136 – 136 + b = 136 + 104
b = 240

Question 17.
-5 = 9 + \(\frac{c}{4}\)
Answer:
Multiply both sides by 4.
(-5) ∙ 4 = 9 ∙ 4 + \(\frac{c \cdot 4}{4}\)
-20 = 36 + c Subtract 36 from both sides
-36 – 20 = -36 + 36 + c
-56 = c
c = -56

Question 18.
-3 + \(\frac{p}{7}\) = -5
Answer:
Multiply both sides by 7.
(-3) ∙ 7 + \(\frac{p \cdot 7}{7}\) = ( 5) ∙ 4
-21 + p = -35 Add 21 to both sides.
21 – 21 + p = 21 – 35
p = -14

Question 19.
46 =-6t – 8
Answer:
Divide by (-6) both sides

Question 20.
After making a deposit, Puja had $264 in her savings account. She noticed that if she added $26 to the amount originally in the account and doubled the sum, she would get the new amount. How much did she originally have in the account?
Answer:
Let x be the amount originally in the account.
If she added $26 to x and double it, she’ll get 264 in lier’s saves account.
Hence, the equation will be
(x + 26)2 = 264 Divide both sides by 2.
\(\frac{(x+26) 2}{2}=\frac{264}{2}\)
x + 26 = 132 Subtract 26 from both sides.
x + 26 – 26= 132 – 26
x = 106
She originally had 106 dollars in the account.

Question 21.
The current temperature in Smalltown is 20 °F. This is 6 degrees less than twice the temperature that it was six hours ago. What was the temperature in Smalltown six hours ago?
Answer:
Let x be the temperature in Smalltown six hours ago.
20° + 60° = 2 ∙ x
26° = 2 ∙ x Divide both sides by 2.
\(\frac{26^{\circ}}{2}=\frac{2 \cdot x}{2}\)
13° = x
x = 13°

Question 22.
Daphpe gave away 3 more than half of her apples. She gave away 17 apples in all. How many apples did Daphne have originally?.
Answer:
Multiply both sides by 2
3 ∙ 2 + \(\frac{x \cdot 2}{2}\) = 17 ∙ 2
6 + x = 34 Subtract 6 from both sides.
-6 + 6 + x = 6 + 34
x = 28

Question 23.
Artaud noticed that if he takes the opposite of his age and adds 40 he gets the number 28. How old is Artaud?
Answer:
Subtract 40 from both sides
-x + 40 – 40 = 28 – 40
-x = -12 Multiply both sides by (-1)
(-1) ∙ x = (-1) ∙ (-12)
x = 12

Go Math Grade 7 Lesson 8.2 Answer Key Question 24.
Sven has 11 more than twice as many customers as when he started selling newspapers. He now has 73 customers. How many did he have when he started?
Answer:
Subtract 11 from both sides
-11 + 11 + 2x = -11 + 73
2x = 62 Divide both sides by 2.
\(\frac{2 \cdot x}{2}=\frac{62}{2}\)
x = 31

Question 25.
Paula bought a ski jacket on sale for $6 less than half its original price. She paid $88 for the jacket. What was the original price?
Answer:
Multiply both sides by 2.
\(\frac{x \cdot 2}{2}\) – 6 ∙ 2 = 88 ∙ 2
x – 12 = 176 Add 12 to both sides
x – 12 + 12 = 176 + 12
x = 188

Question 26.
Michelle has a starting balance on a gift card for $300. She buys several dresses at $40 a piece. After her purchases she has $140 left on the gift card. How many dresses did she buy?
Answer:
Divide by (-40) both sides.

Use a calculator to solve each equation.

Question 27.
-5.5x + 0.56 = -1.64
Answer:
Subtract 0.56 from both sides.
-5.5 ∙ x + 0.56 – 0.56 = -1.64 – 0.56
-5.5 ∙ x = -2.2 Divide both sides by (-5.5).
\(\frac{(-5.5) \cdot x}{(-5.5)}=\frac{-2.2}{-5.5}\)
x = 0.4

Question 28.
-4.2x + 31.5 = -65.1
Answer:
Subtract 31.5 from both sides.
-4.2 x + 31.5 – 31.5 = -65, 1 – 31,5
-4.2 x = -96.6 Divide both sides by (-4.2).
\(\frac{(-4.2) \cdot x}{(-4.2)}=\frac{-96.6}{-4.2}\)
x = 23

Question 29.
\(\frac{k}{5.2}\) + 81.9 = 47.2
Answer:
Subtract 81.9 from both sides
\(\frac{k}{5.2}\) + 81.9 – 81.9 = 47.2 – 81.9
\(\frac{k}{5.2}\) = -34.7 Multiply both sides by 5.2
\(\frac{5 \cdot 2 \cdot k}{5.2}\) = (-34.7) ∙ 5.2
k = -180.44

Question 30.
Write a two-step equation involving multiplication and subtraction that has a solution of x = 7.
Answer:
First, we multiply x by 10, and then we subtract 20 from 10x. So, we have multiplication and subtraction in following equation.
10 ∙ x – 20 = 50

Question 31.
Write a two-step equation involving division and addition that has a solution of x = -25
Answer:
First, we divide x by 5, and then we add 20 to 5x. So, we have division and addition in following equation.
\(\frac{x}{5}\) + 20 = 15

Question 32.
Reason Abstractly The formula F = 1,8C + 32 allows you to find the Fahrenheit (F) temperature for a given Celsius (C) temperature. Solve the equation for C to produce a formula for finding the Celsius temperature for a given Fahrenheit temperature.
Answer:
Subtract 32 from both sides
F – 32 = 18C + 32 – 32
F – 32 = 18C Divide both sides by 18.
\(\frac{F}{18}\) – \(\frac{32}{18}\) = \(\frac{18 \cdot C}{18}\)
\(\frac{1}{18}\) ∙ F – 1.78 = C
0.55F – 1.78 = C
C = 0.55F – 1.78

Texas Go Math Grade 7 Pdf Two Step Equations Question 33.
Reason Abstractly The equation P = 2(l + w) can be used to find the perimeter P of a rectangle with length l and width w. Solve the equation for w to produce a formula for finding the width of a rectangle given its perimeter and length.
Answer:
Divide both sides by 2

H.O.T. Focus on Higher Order Thinking

Question 34.
Critique Reasoning A student’s solution to the equation 3x + 2 = 15 is shown. Describe the error that the student made.
3x + 2 = 15 Divide both sides by 3.
x + 2 = 5 Subtract 2 from both sides,
x = 3
Answer:
When the student had divided both sides by 3, he didn’t divide number 2 on the left side.

Question 35.
Multiple Representations Explain how you could use the work backward problem-solving strategy to solve the equation \(\frac{x}{4}\) – 6 = 2.
Answer:
Translating the given equation to words, 6 was subtracted to a number divided by 4 and the result will be 2. Using the backward problem-solving strategy, add 6 to 2, which is 8 then multiply it by 4 and the result is 32.

Question 36.
Reason Abstractly Solve the equation ax + b = c for x.
Answer:
Divide both sides by a.

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 Unit 3 Study Guide Review Answer Key.

Texas Go Math Grade 7 Unit 3 Study Guide Review Answer Key

Texas Go Math Grade 7 Unit 3 Exercises Answer Key

Module 5 Experimental Probability

Find the probability of each event. (Lesson 5.1)

Question 1.
Rolling a 5 on a fair number cube.
Answer:
Total number of cube: Possibilities 1, 2, 3, 4, 5, 6, so 6.
Number: A regular cube has only one side with the number five, so 1 possibility.
P (rolling a 5) =
The probability of rolling a 5 is \(\frac{1}{6}\).

7th Grade Unit 3 Study Guide Test Answer Key Question 2.
Picking a 7 from a standard deck of 52 cards. A standard deck includes 4 cards of each number from 2 to 10.
Answer:
There are 4 cards with 7, so number of cards with 7 is 4.
P (picking a 7) =
The probability of picking a number 7 is \(\frac{1}{13}\).

Question 3.
Picking a blue marble from a bag of 4 red marbles, 6 blue marbles, and 1 white marble.
Answer:
Total number of marbles in all color: 4 + 6 + 1 = 11
P (picking a blue marble) =
The probability of picking a blue marble is \(\frac{6}{11}\).

Question 4.
Rolling a number greater than 7 on a 12-sided number cube.
Answer:
Number of sides with number greater than 7 is side with 8, 9, 10, 11, 12, so 5 possibilities for number greater than 7.
P(greater than 7) =
The probability of rolling a number greater than 7 is \(\frac{5}{12}\).

Question 5.
Christopher picked coins randomly from his piggy Penny Nickel Dime Quarter bank and got the numbers of coins shown in the table. Find each experimental probability. (Lessons 5.2, 5.3)

Answer:
Total number of possible outcomes is:
7 + 2 + 8 + 6 = 23

a. The next coin that Christopher picks is a quarter. __________________
Answer:
P (picking a quarter) =
The probabiLity of picking a quarter is \(\frac{6}{23}\)

b. The next coin that Christopher picks is not a quarter. _______________
Answer:
P (not picking a quarter) = 1 – P (picking a quarter) = 1 – \(\frac{6}{23}\) = \(\frac{23}{23}\) – \(\frac{6}{23}\) = \(\frac{17}{23}\)
The probability of not picking a quarter is \(\frac{17}{23}\)

c. The next coin that Christopher picks is a penny or a nickel. __________
Answer:
P (picking a penny or nickel) =
The probability of picking a penny or nickel is \(\frac{9}{23}\)

Unit 3 Study Guide Grade 7 Answer Key Question 6.
A grocery store manager found that 54% of customers usually bring their own bags. In one afternoon, 82 out of 124 customers brought their own grocery bags. Did a greater or lesser number of people than usual bring their own bags? (Lesson 5.4)
Answer:
Use proportion

The number of people that usually bring their own bags is greater that afternoon because 82 > 67

Module 6 Theoretical Probability

Find the probability of each event. (Lessons 6.1, 6.2)

Question 1.
Graciela picks a white mouse at random from a bin of 8 white mice, 2 gray mice, and 2 brown mice.
Answer:
The number of possible ways is 8 because we have 8 white mice.
The total number of possible outcomes is 12 because we have in total 12 miles in white, grey, and brown color.
P (picking a white mouse) =
The probability of picking a white mouse is \(\frac{2}{3}\)

Question 2.
Theo spins a spinner that has 12 equal sections marked 1 through 12. It does not land on 1.
Answer:

The probability not to land on 1 is \(\frac{11}{12}\).

Question 3.
Tania flips a coin three times. The coin lands on heads twice and on tails once, not necessarily in that order.
Answer:
Number of possible ways is 3 because we can flip HHT, HTH, THH
Total number of possible outcomes is 8 because we can flip HHH, HTT, HHT, TTT, THH, TTH, THT, HTH.
P (lands on heads twice and on tails once) =
The probability that a coin lands on heads twice and on tails once is \(\frac{3}{8}\).

Texas Go Math Book 7th Grade Answer Key Question 4.
Students are randomly assigned two-digit codes. Each digit is either 1, 2, 3, or 4. The guy is given the number 11.
Answer:
Number of possible ways is 1 because to have 1 on each digit of the code is only one.
Total number of possible outcomes is 16 because for the first digit, we have 4 possibilities and also for the second, 4 ∙ 4 = 16.
P (two-digit code is 11) =
The probability to give a number is 11 is \(\frac{1}{16}\).

Question 5.
Patty tosses a coin and rolls a number cube. (Lesson 6.3)
a. Find the probability that the coin lands on heads and the cube lands on an even number.
Answer:
Number of possible ways is 3 because there are three ways to flip a head and roll a even number: H-2,H-4, H-6.
Total number of possible outcomes is 12 because: for coin we have 2 possibilities and for cube 6, so 2 ∙ 6 = 12.
P (flip a head and a cube is on an even number) =
The probability to flip a head and a cube is on an even number is \(\frac{1}{4}\).

b. Patty tosses the coin and rolls the number cube 60 times. Predict how many times the coin will land on heads and the cube will land on an even number.
Answer:
Use proportion

The coin will land on head and a cube on an even number about 15 times out of 60.

Question 6.
Rajan’s school is having a raffle. The school sold raffle tickets with 3-digit numbers. Each digit is either 1, 2, or 3. The school also sold 2 tickets with the number 000. Which number is more likely to be picked, 123 or 000? (Lesson 6.3)
Answer:
For total number of possible outcomes we have for the first digit 3 possibilities, for the second and third and we have also 2 possibilities with 000, so 29 possibilities.

It is more likely to pick a ticket numerated with 000 than a ticket numerated with 123.

Unit 3 Study Guide Math 7th Grade Question 7.
Suppose you know that over the last 10 years, the probability that your town would have at least one major storm was 40%. Describe a simulation that you could use to find the experimental probability that your town will have at least one major storm in at least 3 of the next 5 years. (Lesson 6.4)
Answer:
The probability that the city will have at least one major storm is \(\frac{40}{100}\) = \(\frac{2}{5}\).
Let numbers 1 and 2 represent that there was a major storm and 3 4 and 5 that not We generate five numbers in each of 10 trials Find the experimental probability that the major storm occurred at least three times over the five years.

Texas Go Math Grade 7 Unit 3 Performance Task Answer Key

Question 1.
CAREERS IN MATH Meteorologist A meteorologist predicts a 20% chance of rain for the next two nights and a 75% chance of rain on the third night.
a. On which night is it most likely to rain? On that night, is it likely to rain or unlikely to rain?
Answer:
P (chance to rain to the next two nights) = \(\frac{1}{5}\)
P (chance to rain third night) = \(\frac{3}{4}\)
Chance to rain is more likely third day than first two nights. It is likely to rain that night.

b. Tara would like to go camping for the next 3 nights, but will not go if it is likely to rain on all 3 nights. Should she go? Use probability to justify your answer.
Answer:
P (chance to rain all three nights is) : \(\frac{1}{5}\) ∙ \(\frac{3}{4}\) = \(\frac{3}{20}\)
It is not likely to rain all three nights.

Question 2.
Sinead tossed 4 coins at the same time. She did this 50 times, and 6 of those times, all 4 coins showed the same result (heads or tails).
a. Find the experimental probability that all 4 coins show the same result when tossed.
Answer:
The experimental probability that all 4 coins show the same result when tossed is:

b. Can you determine the experimental probability that no coin shows heads? Explain.
Answer:
The experimental probability that all 4 coins shows heads is P = \(\frac{3}{25}\).
The experimental probability that no coin shows the heads is:
1 – P = 1 – \(\frac{3}{25}\) = \(\frac{25}{25}\) – \(\frac{3}{25}\) = \(\frac{22}{25}\)

c. Suppose Sinead tosses the coins 125 more times. Use experimental probability to predict the number of times that all 4 coins will show heads or tails. Show your work.
Answer:
Use proportion.

You can expect that all 4 coins will show heads or tails about 15 times out of 125.

Texas Go Math Grade 7 Unit 3 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1
A pizza parlor offers thin, thick, and traditional-style pizza crusts. You can get pepperoni, beef, mushrooms, olives, or peppers for toppings. You order a one-topping pizza. How many outcomes are in the sample space?
(A) 3
(B) 5
(C) 8
(D) 15
Answer:
(D) 15

Explanation:
3 possibilities for the crust and 5 possibilities for topping are 3 ∙ 5 = 15 possibilities for pizza.
The sample space is 15.

Unit 3 Assessment Answer Key 7th Grade Question 2.
A bag contains 9 purple marbles, 2 blue marbles, and 4 pink marbles, The probability of randomly drawing a blue marble is \(\frac{2}{15}\). What is the probability of not drawing a blue marble?
(A) \(\frac{2}{15}\)
(B) \(\frac{4}{15}\)
(C) \(\frac{11}{15}\)
(D) \(\frac{13}{15}\)
Answer:
(D) \(\frac{13}{15}\)

Explanation:

The probability of not picking a blue marble is \(\frac{13}{15}\).

Question 3.
During the month of April, Dora kept track of the bugs she saw in her garden. She saw a ladybug on 23 days of the month. What is the experimental probability that she will see a ladybug on May 1?
(A) \(\frac{1}{23}\)
(B) \(\frac{7}{30}\)
(C) \(\frac{1}{2}\)
(D) \(\frac{23}{30}\)
Answer:
(D) \(\frac{23}{30}\)

Explanation:
Number of times the event occurs represents how many times a ladybug appeared in April.
The total number of trials represents how many days she kept track of the bugs in her garden.
The experimental probability that she will see a ladybug on May 1 is:

Question 4.
Ryan flips a coin 8 times and gets tails all 8 times. What is the experimental probability that Ryan will get heads the next time he flips the coin?
(A) 1
(B) \(\frac{1}{2}\)
(C) \(\frac{1}{8}\)
(D) 0
Answer:
(D) 0

Explanation:
The experimental probability that Rayan flip a head next time is:
P (flip a head) =

Question 5.
Jay tossed two coins several times and then recorded the results in the table below.

What is the experimental probability that the coins will land on different sides on his next toss?
(A) \(\frac{1}{5}\)
(B) \(\frac{2}{5}\)
(C) \(\frac{3}{5}\)
(D) \(\frac{4}{5}\)
Answer:
(C) \(\frac{3}{5}\)

Explanation:
The number of possible ways is 3 because in toss 1, 3, 5 we have that possibility.
P (the coins land on different sides) = \(\frac{3}{5}\)
The experimental probability that the coins land on different sides is \(\frac{3}{5}\).

Unit 3 Test Math Answer Key Grade 7 Question 6.
A used guitar is on sale for $280. Derek offers the seller \(\frac{3}{4}\) of the advertised price. How much does Derek offer for the guitar?
(A) $180
(B) $210
(C) $240
(D) $270
Answer:
\(\frac{3}{5}\)

Explanation:
Derek offer’s:
2800 ∙ \(\frac{3}{4}\) = 210
Derek offer’s for the guitar $ 210.

Question 7.
What is the probability of tossing two fair coins and having exactly one land tails side up?
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{1}{2}\)
Answer:
(D) \(\frac{1}{2}\)

Explanation:
Number of possible ways is 2 because we have HT or TH.
P (one land tails side up) =
The probability of tossing two fair coins and having exactly one land tails side up is \(\frac{1}{2}\).

Question 8.
Find the percent change from 60 to 96.
(A) 37.5% decrease
(B) 37.5% increase
(C) 60% decrease
(D) 60% increase
Answer:
(D) 60% increase

Explanation
Use proportion

Subtract 100 % of the last result. In this way, we will get a percentage of increase because we have taken away the original price from the increased price.
160 – 100 = 60%
The percent of change is 60% increase.

Unit 3 Study Guide Math 7th Grade Texas Go Math Question 9.
Jason, Erik, and Jamie are friends in art class. The teacher randomly chooses 2 of the 21 students in the class to work together on a project. What is the probability that two of these three friends will be chosen?
(A) \(\frac{1}{105}\)
(B) \(\frac{1}{70}\)
(C) \(\frac{34}{140}\)
(D) \(\frac{4}{50}\)
Answer:
(B) \(\frac{1}{70}\)

Explanation:
Number of favorable possibilities:
3 for first student and 2 for second 6
Total number of possible outcomes:
21 for first student and 20 for second = 420.
P (two of three friends are chosen) =
The probability that two of these three students will be chosen is \(\frac{1}{70}\).

Question 10.
Philip rolls a number cube 12 times. Which is the best prediction for the number of times that he will roll a number that is odd and less than 5?
(A) 2
(B) 3
(C) 4
(D) 6
Answer:
(C) 4

Explanation:

Phillip can expect that he will roll a number that is odd and less than 5 about 4.

Gridded Response

Question 11.
A bag contains 6 white beads and 4 black beads. You pick out a bead at random, record its color, and put the bead back in the bag. You repeat this process 35 times. How many times would you expect to remove a white bead from the bag?

Answer:

How we get the value of 21 in the fourth column from the left we round the number 2, in the column to the right of it 1. In the columns after the column with a decimal point, we do not round anything because it is an integer.
You can expect that you will pick a white bead about 21 times

Unit 3 End of Unit Assessment Grade 7 Answer Key Question 12.
A set of cards includes 20 yellow cards, 16 green cards, and 24 blue cards. What is the probability, written in decimal form, that a blue card is chosen at random?

Answer:

As we get the decimal number 0.4 in the column in front of the column with a decimal point, we will round the number 0, while in the column after the decimal point we will round the number 4.
The probability of choosing blue card is 0.4.

Hot Tips! Estimate your answer before solving the problem. Use your estimate to check the reasonableness of your answer.

Probability Unit Study Guide Answer Key Question 13.
A survey reveals that one airline’s flights have a 92% probability of being on time. Out of 4,000 flights in a year, how many flights would you predict to arrive on time?

Answer:
P (flight arrive on time) = \(\frac{92}{100}\) = \(\frac{23}{25}\)
To predict how many flights will arrive on time we use proportion. In that proportion equalize the probability that the flight will arrive on time with a fraction, whose numerator is unknown and mean the number of flight which arrive on time out of 4000 flights, denominator 4000 which is the total number of flights

Texas Go Math Grade 7 Unit 3 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.

• An activity based on chance in which results are observed. (Lesson 5-1)
• The set of all outcomes that are not included in the event. (Lesson 5-1)
• Each observation of an experiment. (Lesson 5-1)
• A model of an experiment that would be difficult or too time-consuming to perform. (Lesson 5-2) .
• Measures the likelihood that the event will occur. (Lesson 5-1)
• An event with only one outcome (2 words). (Lesson 5-2)
• A set of all possible outcomes for an event (2 words), (Lesson 5-1)

Question.
Why was there little chance of success for the clumsy thieves?
Answer:
Because they had low _____ _____ _____ – _____ _____ _____ _____ _____ _____ _____!

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 7 Quiz Answer Key.

Texas Go Math Grade 7 Module 7 Quiz Answer Key

Texas Go Math Grade 7 Module 7 Ready to Go On? Answer Key

7.1 Linear Relationships in the Form y = mx + b

Question 1.
Darice also took a break after riding 10 miles. The table below shows the rate at which Darice rides her bicycle after the break.

Write a verbal description of the relationship between the time she rides and the distance she travels.
Answer:
Dance was riding a bike 10 miles plus an additional 0.25 miles after each break.

7.2 Writing and Graphing Equations in the Form y = mx + b

Emir started out a card game with 500 points. For every hand he won, he gained 100 points.

Module Quiz Ready to go on Answers 7th Grade Question 2.
Complete the table.

Answer:

y = 100 ∙ x + 500

Question 3.
Plot the points on the graph.

Answer:

y = 100 ∙ x + 500

Question 4.
Write an equation for the linear relationship.
Answer:
y = 100 ∙ x + 500

Essential Question

Grade 7 Math Module 7 Answer Key Question 5.
What are some of the ways you can represent real-world linear relationships?
Answer:
Real-world relationships can be represented by graphics. tables, and equations.

Texas Go Math Grade 7 Module 7 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
Which description corresponds to the relationship shown in the table?

(A) earning $10 an hour
(B) earning $8 an hour plus a $10 bonus
(C) earning $7 an hour plus a $15 bonus
(D) earning $9 an hour
Answer:
(B) earning $8 an hour plus a $10 bonus

Explanation:
90 – 50 = 40 Find the difference between two payments.
\(\frac{40}{5}\) = 8 Find how much is paid for 1 hour.
50 – 40 = 10 Find a bonus.

Question 2.
Which equation represents the same linear relationship as the graph below?

Answer:
(A) y = 1.2x + 32
(B) y = 1.5x + 20
(C) y = 0.75x + 50
(D) y = 0.8x + 45
Answer:
(C) y = 0.75 ∙ x + 50

Explanation:
Our points on the graph are:
A = (40,80)
B = (80,110)
C = (120, 140)
D = (160, 170)
Replacing the value of point A in the solution under (A) we get:
80 = 1.2 ∙ 40 + 32 = 80
This is correct
Replacing the value of point B in the solution under (A) we get:
110 = 1.2 ∙ 80 + 32 = 128
This isn’t correct.

By repeating the procedure, we will conclude that alt points are solutions of the equation under (C)

Go Math Grade 7 Module 7 Answer Key Question 3.
Omar began the week with $25. He took a city bus to and from school, paying $1.25 for each trip. Let x be the number of trips he took and y be the amount of money he had left at the end of the week. Which equation represents the relationship in the situation?
(A) y = 1.25x + 25
(B) y = 25 – 1.25x
(C) x = 25 – 1.25y
(D) y = 1.25x – 25
Answer:
(B) y = 25 – 1.25x

Explanation:
The right answer is (B) y = 25 – 1.25 ∙ x, because he spends money on the bus, so the sum of money that remains to be reduced after each payment of trip.

Question 4.
Which table represents the same linear relationship as the equation y = 5x + 7?

Answer:
Table (B)

Explanation:
The table represent the equation
y = 5 ∙ x + 7

Question 5.
Selina is planning to paint a large picture on a wall. She draws a smaller version first. The drawing is 8 inches by 6 inches. If the scale of the drawing is 2 in: 1 ft, what is the area of the actual picture on the wall?
(A) 4 feet
(B) 3 feet
(C) 48 square inches
(D) 12 square feet
Answer:
(D) 12 square feet

Explanation:
The answer is (D) 12 square feet
The area of the drawing is 8 ∙ 6 = 48 in.
Because scale of the drawing, the area of the actual picture on the wall is
\(\frac{8}{2} \cdot \frac{6}{2}\) = 4 ∙ 3 = 12 square feet

Gridded Response

Module 7 Go Math Answer Key Grade 7 Question 6.
The equation y = 3.5x – 210 represents the profit made by a manufacturer that sells products for $3.50 each, where y is the profit and x is the number of units sold. What is the profit in dollars when 80 units are sold?

Answer:
y= 3.5 ∙ x – 210 ……….. (1)
Variable x is the number of sold units
Variable y represents the profit.
We have 80 sold units so x = 80.
Substitute this value for x in equation (1):
y = 3.5 ∙ 80 – 210 = 70
y = 70

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 7.2 Answer Key Writing and Graphing Equations in the Form y = mx + b.

Texas Go Math Grade 7 Lesson 7.2 Answer Key Writing and Graphing Equations in the Form y = mx + b

Texas Go Math Grade 7 Lesson 7.2 Explore Activity Answer Key

Graphing Linear Relationships

Teresa signs up for a membership to rent video games. The company charges $5 per month and $2 per video game. Graph a linear relationship between the number of games Teresa rents and her monthly cost.

STEP 1: Make a table. Record different values for the linear relationship.

STEP 2: Use the table to create ordered pairs:
(0, 5), (1, 7), (2, 9), (3, 11), (4, 13)
Plot each ordered pair on the coordinate grid.

Reflect

Texas Go Math Grade 7 Solutions Lesson 7.2 Answer Key Question 1.
Do the values between the points make sense in this context? Explain.
Answer:
This makes sense because the graphics show that when the number of lending increases, the price rises.

Your Turn

Write an equation to describe the linear relationship.

Question 2.
The temperature of a pot of water is 45°F. The temperature increases by 20°F per minute when being heated.
Answer:

y = 20 ∙ x + 45

Question 3.
A bamboo reed is planted when it is 12 centimeters tall. It grows 2.2 centimeters per week.
Answer:

y = 22 ∙ x + 12

Example 2
Charlie starts with $350 in his savings account. He withdraws $15 per week from his account. Represent the relationship using a table, an equation, and a graph.
STEP 1: Make a table. Record different values for the linear relationship.

STEP 2: Write an equation for the amount of money y in the savings after x weeks. $350 minus $15 times the number of weeks
y = 350 – 15x
STEP 3: Use the table to create ordered pairs and then plot the data.

Reflect

Question 4.
Does it make sense to connect the points on the graph with a line? Explain.
Answer:
It makes sense because in this way it is easier to see that when withdrawing money, the saved amount is reduced.

Lesson 7.2 Homework Texas Go Math Grade 7 Answer Key Question 5.
Does an ordered pair with a negative y-value make sense in the situation?
Answer:
It makes no sense to take negative values for y because it would mean that he takes more money than what he has on the account, which is impossible.

Your Turn

Question 6.
A bicycle rental company charges $18 to rent a bicycle, plus $7 for every two hours of rental time. Represent the relationship using a table, an equation, and a graph.

Answer:

Equation: 18 + 7 ∙ x = y

Texas Go Math Grade 7 Lesson 7.2 Guided Practice Answer Key

Graph the linear relationship. (Explore Activity)

Question 1.
A pool contains 5 liters of water, and 10 liters of water are being poured into the pool every 5 minutes.

Answer:
y = 2 ∙ x + 5
Ploted pairs on the coordinate grid are:
A = (0, 5)
More precisely in equation replace x with 0, and y with 5 for point A;
B = (10, 25)
Replace in equation x with 10, and y with 25 for point B.

Write an equation to describe the linear relationships. (Example 1)

Question 2.
A moving company charges a $50 flat fee and $55 per hour to move.
y = _______ x + _______
Answer:
y = 55 ∙ x + 50

Question 3.
Anne has $250 in a savings account. She withdraws $5 per month.
y = _______ x + _______
Answer:
y = -5 ∙ x + 250

Lesson 7.2 Texas Go Math Grade 7 Answers Question 4.
Erin owns $375 worth of comic books. She spends $15 every week on new comic books. Represent the relationship using a table and an equation. (Example 2)
y = _______x + _______

Answer:

y = 15 ∙ x + 375

Essential Question Check-In

Question 5.
How can you use a table of data to write and graph a linear relationship?
Answer:
All the initial values that we get actually represent x, while all the values obtained based on the initial conditions by solving the equation represent y.

Texas Go Math Grade 7 Lesson 7.2 Independent Practice Answer Key

A cab company charges a $3.50 boarding fee and $0.50 per mile.

Question 6.
Write an equation to describe the relationship between the cost of the cab ride and the number of miles traveled.
Answer:
y = 0.5 ∙ x + 3.5

Question 7.
Graph the linear relationship.

Answer:


y = 0.5 ∙ x + 3.5

Go Math Answer Key Grade 7 Lesson 7.2 Answer Key Question 8.
Draw Conclusions Does it make sense to draw a line through the points? Explain.
Answer:
It makes sense because in this way we easily notice how the billing increases in the miles ahead.

Question 9.
What If? Suppose that the boarding fee was changed to $5. How would the graph change?
Answer:

y1 = 0.5 ∙ x + 3.5
y2 = 0.5 ∙ x + 5
The value of the variable y1 has increased
(with that increase we got a variable y_2)
so the points on the graph are above the points before increasing the variable y1.

For 10-13 write an equation to represent the given linear relationship. Then state the meaning of the given ordered pair.

Question 10.
A plain medium pizza costs $8.00. Additional toppings cost $0.85 each. (4, 11.4)
Answer:
y = 0.85 ∙ x + 8
For x = 4 in the equation we get y = 11.4

Question 11.
Luis joined a gym that charges a membership fee of $99.95 plus $7.95 per month. (9, 171.5)
Answer:
y = 7.95 ∙ x + 99.95
For x = 9 in the equation we get y = 171.5

Practice and Homework Lesson 7.2 Answer Key Question 12.
A tank currently holds 35 liters of water, and water is pouring into the tank at 15 liters per minute. (5.5, 117.5)
Answer:
y = 15 ∙ x + 35
For x = 5.5 in the equation we get y = 117.5

Question 13.
Jonas is riding his bicycle at 18 kilometers per hour, and he has already ridden for 40 kilometers. (6, 148)
Answer:
y = 18 ∙ x 40
For x = 6 in the equation we get y = 148

Question 14.
Analyze Relationships How can you use an equation of a linear relationship to verify the points on the graph of the relationship?
Answer:
Let the point A= (p, q) from the graph. By replacing the value in the equation y = mx + b, where x = p, y = q, if the left and right sides are equal, we have confirmed the relation between the equation and the graph.

Question 15.
Multiple Representations A furniture salesperson earns $750 per week plus a 15% commission on all sales made during the week.
a. Complete the table of data.

Answer:

b. Graph the values in the table.

Answer:

c. Write a linear equation to describe the relationship.
Answer:
y = 0.15 ∙ x + 750

Go Math Grade 7 Lesson 7.2 Answer Key Question 16.
Make a Conjecture Can you draw a straight line through the points? Explain.
Answer:
We can for the reason that all points are solutions of the same equation.

H.O.T. Focus on Higher Order Thinking

Question 17.
Analyze Relationships What are the advantages of portraying a linear relationship as a table, graph, or equation?
Answer:
The advantage of graphics, tables and equations is that it helps us to see the changes and understand them in easy way.

Question 18.
Critical Thinking Describe when it would be more useful to represent a linear relationship with an equation than with a graph.
Answer:
It would be more useful to present it through the equation because from the equation for the given value we can easily get points on the graph.

Question 19.
Communicate Mathematical Ideas How can you determine when to draw a line through the points on the graph of a linear relationship?
Answer:
Linear relationship can represent with equation. If all the points on graph are the solutions of the equation, then we can draw a line through them.

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 6 Quiz Answer Key.

Texas Go Math Grade 7 Module 6 Quiz Answer Key

Texas Go Math Grade 7 Module 6 Ready to Go On? Answer Key

6.1, 6.2 Theoretical Probability of Simple and Compound Events

Find the probability of each event. Write your answer as a fraction, as a decimal, and as a percent.

Question 1.
You choose a marble at random from a bag containing 12 red, 12 blue, 15 green, 9 yellow, and 12 black marbles. The marble is red.
Answer:
The number of possible outcomes is:
12 + 12 + 15 + 9 + 12 = 61
P (choose a red marble) =
The probability of choosing a red marble is \(\frac{12}{61}\).

Go Math Grade 7 Module 6 Answer Key Question 2.
You draw a card at random from a shuffled deck of 52 cards. The deck has four 13-card suits (diamonds, hearts, clubs, spades). The card is a diamond or a spade.
Answer:
The total number of possible outcomes is: 4 ∙ 13 = 52
P (diamond or a spade) =
The probability to draw a diamond or spide is \(\frac{1}{2}\).

6.3 Making Predictions with Theoretical Probability

Question 3.
A bag contains 23 red marbles, 25 green marbles, and 18 blue marbles. You choose a marble at random from the bag. What color marble will you most likely choose?
Answer:
The total number of possible outcomes is: 23 + 25 + 18 = 66

It is more likely to pick a green marble than marble in other color.

6.4 Using Technology to Conduct a Simulation

Question 4.
Bay City has a 20% chance of having a flood in any given decade. The table shows the results of a simulation using random numbers to find the experimental probability that there will be a flood in Bay City in at least 1 of the next 5 decades. In the table, the number 1 represents a decade with a flood. The numbers 2 through 5 represent a decade without a flood.

According to the simulation, what is the experimental probability of a flood in Bay City in at least 1 of the next 5 decades?
Answer:

The experimental probability of a flood in Bay City in at least 1 of the next 5 decades is \(\frac{4}{10}\) = \(\frac{2}{5}\).

Essential Question

Grade 7 Module 6 Topic Quiz Go Math Question 5.
How can you use theoretical probability to make predictions in real-world situations?
Answer:
Theoretical probability is a ratio that describes what should happen, so we can make prediction about all possible situations which helps us to find the answer in real-world situations.

Texas Go Math Grade 7 Module 6 Mixed Review Texas Test Prep Answer Key

Selected Response

Question 1.
What is the probability of flipping two fair coins and having both show tails?
(A) \(\frac{1}{8}\)
(B) \(\frac{1}{4}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{1}{2}\)
Answer:
(B) \(\frac{1}{4}\)

Explanation:
Total numbers of possible outcomes is:
HT, HH, TT, TH = 4
Number of flips with tail on each coin The only way to fall two tails is to get tails on both coins.
P (flip on each tail) =
The probability of picking two tails is \(\frac{1}{4}\).

Grade 7 Module 6 Quiz Answers Go Math Question 2.
A bag contains 8 white marbles and 2 black marbles. You pick out a marble, record its color, and put the marble back in the bag. If you repeat this process 45 times, how many times would you expect to remove a white marble from the bag?
(A) 9
(B) 32
(C) 36
(D) 40
Answer:
(A) 9 times

Explanation:

You can expect to remove a white marble about 9 times.

Question 3.
Philip rolls a standard number cube 24 times. Which is the best prediction for the number of times he will roll a number that is even and less than 4?
(A) 2
(B) 3
(C) 4
(D) 6
Answer:
(C) 4

Explanation:
A number that is even and less than 4 is number 2

The best prediction for the number of times to roll number that is even and less than 4 is 4.

Question 4.
A set of cards includes 24 yellow cards, 18 green cards, and 18 blue cards. What is the probability that a card chosen at random is not green?
(A) \(\frac{3}{10}\)
(B) \(\frac{4}{10}\)
(C) \(\frac{3}{5}\)
(D) \(\frac{7}{10}\)
Answer:
(D) \(\frac{7}{10}\)

Explanation:
Total number of possible outcomes is:
24 + 18 + 18 = 60
P (choose a green card) =
P (not to choose a green card) = 1 – P (choose a green card) = 1 – \(\frac{3}{10}\) = \(\frac{10}{10}\) – \(\frac{3}{10}\) = \(\frac{7}{10}\)
The probability that the chosen card at random is not green is \(\frac{7}{10}\).

Grade 7 Module 6 Review Answer Key Go Math Question 5.
A rectangle made of square tiles measures 10 tiles long and 8 tiles wide. What is the width of a similar rectangle whose length is 15 tiles?
(A) 3 tiles
(B) 12 tiles
(C) 13 tiles
(D) 18.75 tiles
Answer:
(B) 12 tiles

Explanation:
Use Proportion.

The width of a similar rectangle is 12 tiles.

Question 6.
You buy a game that originally cost $35. It was on sale at 20% off. You paid 6% tax on the sale price. What was the total amount that you paid?
(A) $29.68
(B) $37.10
(C) $44.10
(D) $44.52
Answer:
(A) $29.68

Explanation:
Originally price is $35.
Sale is 20%.
Tax is 6%.
Calculate how ¡iiicIi a game on sale costs.
35 – 35 ∙ \(\frac{20}{100}\) = 35 – 35 ∙ \(\frac{1}{5}\) = 35 – 7 = $28
Find a tax on the sale price.
28 ∙ \(\frac{6}{100}\) = $1.68
Total amount is: sale price + tax = 28 + 1.68 = $29.68
The total amount that you paid is $29.68.

Grade 7 Math Module 6 Answer Key With Solution Question 7.
The Fernandez family drove 273 miles in 5.25 hours. How far would they have driven at that rate in 4 hours?
(A) 208 miles
(B) 220 miles
(C) 280 miles
(D) 358 miles
Answer:
(A) 208 miles

Explanation:
To find how much he drove for one hour, number of miles divide by number of hours that he drove.
\(\frac{273}{5.25}\) = 52
He drove about 52 miles per hour
For 4 hours he will drive 4 ∙ 52 = 208 miles.
The right answer is 208 miles.

Question 8.
There are 20 tennis balls in a bag. Five are orange, 7 are white, 2 are yellow, and 6 are green. You choose one at random. Which color ball are you least likely to choose?
(A) green
(B) orange
(C) white
(D) yellow
Answer:
(D) yellow

Explanation:
Total number of possible outcomes is:
5 + 7 + 2 + 6 = 20

It is least likely to choose a yellow ball.

Gridded Response

Grade 7 Module 6 Topic Quiz Answer Key Question 9.
Gibley’s frozen yogurt cones come in 3 flavors (chocolate, vanilla, and strawberry) with 4 choices of topping (sprinkles, strawberries, nuts, and granola). You choose a cone at random. What is the probability, expressed as a decimal, that you get a cone with strawberry topping?

Answer:
Number of favorable outcomes: Chocolate-strawberry, vanilla-strawberry, strawberry-strawberry.
Total number of possible outcomes: 3 possibilities for flavor and 4 possibiLities for topping = 3 ∙ 4 = 12

The probability of getting a cone with strawberry topping is 0.25

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 6.4 Answer Key Using Technology to Conduct a Simulation.

Texas Go Math Grade 7 Lesson 6.4 Answer Key Using Technology to Conduct a Simulation

Your Turn

Question 1.
An elephant has a 50% chance of giving birth to either a male or to a female calf. Use a simulation to find the experimental probability that the elephant gives birth to 3 male calves before having a female calf. (Hint: Use 0s and 1s. Let 0 represent a male calf, and 1 represent a female calf. Generate random numbers until you get a 1.)

Answer:

The probability that the elephant gives birth to three male calves before having a female calf is \(\frac{7}{10}\).

Texas Go Math Grade 7 Solutions Lesson 6.4 Answer Key Question 2.
Matt guesses the answers on a quiz with 5 true-false questions. The probability of guessing a correct answer on each question is 50%. Use a simulation to find an experimental probability that he gets at least 2 questions right. (Hint: Use 0s and is. Let 0s represent incorrect answers, and 1s represent correct answers. Perform 10 trials, generating 5 random numbers in each, and count the number of 1s.)
Answer:

The probability to get at least 2 question right is \(\frac{7}{10}\).

Texas Go Math Grade 7 Lesson 6.4 Guided Practice Answer Key

There is a 30% chance that T’Shana’s county will have a drought during any given year. She performs a simulation to find the experimental probability of a drought in at least 1 of the next 4 years. (Examples 1 and 2)

Question 1.
T’Shana’s model involves the whole numbers from 1 to 10. Complete the description of her model.
Let the numbers 1 to 3 represent _____________ and the numbers 4 to 10 represent _____________
Perform multiple trials, generating _______ random numbers each time.
Answer:
Let the numbers 1 to 3 represent that will be drought during any given year, and the numbers 4 to 10 represent that will not have drought during any year.
Perform multiple trials, generating 4 random numbers each time.

Question 2.
Suppose T’Shana used the model described in Exercise 1 and got the results shown in the table. Complete the table.

Answer:

The probability that there will be a drought in the country at least 1 of the next 4 years is \(\frac{8}{10}\).

Question 3.
According to the simulation, what is the experimental probability that there will be a drought in the county in at least 1 of the next 4 years?
Answer:
The probability that there will be a drought in the country at least 1 of the next 4 years is \(\frac{8}{10}\).

Essential Question Check-In

Lesson 6.4 Texas Go Math Grade 7 Answers Question 4.
You want to generate random numbers to simulate an event with a 75% chance of occurring. Describe a model you could use.
Answer:
The probability of some event is = \(\frac{75}{100}\) = \(\frac{3}{4}\).
We can use numbers 1, 2, 3 which represent that the chosen event is happen and 4 that is not.
Generating a random number in every trial until you get 1 or 2 or 3.

Texas Go Math Grade 7 Lesson 6.4 Independent Practice Answer Key

Every contestant on a game show has a 40% chance of winning. In the simulation below, the numbers 1-4 represent a winner, and the numbers 5-10 represent a non winner. Numbers were generated until one that represented a winner was produced.

Question 5.
In how many of the trials did it take exactly 4 contestants to get a winner?
Answer:
Only in one. In the eighth trial, it was taken exactly 4 contestants to get a winner.

Lesson 6.4 Answer Key 7th Grade Go Math Question 6.
Based on the simulation, what is the experimental probability that it will take exactly 4 contestants to get a winner?
Answer:
The probability of taking exactly 4 contestants to get a winner is \(\frac{1}{10}\).

Over a 100-year period, the probability that a hurricane struck Rob’s city in any given year was 20%. Rob performed a simulation to find an experimental probability that a hurricane would strike the city in at least 4 of the next 10 years. In Rob’s simulation, 1 represents a year with a hurricane.

Question 7.
According to Rob’s simulation, what was the experimental probability that a hurricane would strike the city in at least 4 of the next 10 years?
Answer:
The experimental probability that a hurricane would strike the city in at last 4 of the next 10 years is \(\frac{2}{10}\) = \(\frac{1}{5}\).

Question 8.
Analyze Relationships Suppose that over the 10 years following Rob’s simulation, there was actually 1 year in which a hurricane struck. How did this compare to the results of Rob’s simulation?
Answer:
The probability that over the 10 years, where was 1 year in which hurricane struck is \(\frac{3}{10}\).
How is the experimental probability of Rob’s simulation \(\frac{1}{5}\), the probability that over the 10 years, where was 1 year in. which hurricane struck is greater.

Question 9.
Communicate Mathematical Ideas You generate three random whole numbers from 1 to 10. Do you think that it is unlikely or even impossible that all of the numbers could be 10? Explain?
Answer:
The probability that in three generated numbers all of three is 10 is:
P (in each is 10) = \(\frac{1}{1000}\)
Because we have 10 possibilities for first ∙ 10 possibilities for second ∙ 10 possibilities for third = 1000, but only one that all of three are 10.

Go Math Lesson 6.4 Answer Key Homework 7th Grade Question 10.
Erika collects baseball cards, and 60% of the packs contain a player from her favorite team. Use a simulation to find an experimental probability that she has to buy exactly 2 packs before she gets a player from her favorite team.
Answer:

The probability that she has to buy exactly 2 packs before she gets a player from fer favorite time is \(\frac{3}{10}\).

H.O.T. Focus on Higher Order Thinking

Question 11.
Represent Real-World Problems When Kate plays basketball, she usually makes 37.5% of her shots. Describe a simulation that you could use to find the experimental probability that she makes at least 3 of her next 10 shots.
Answer:
The probability that Kate makes a shot is \(\frac{3}{8}\).
Let 1, 2 and 3 represent that she makes a shot and 4, 5, 6, 7, and 8 that not. Generate 5 numbers in each of 10 trials and find an experimental probability that she makes at least 3 of the 10 shots.

Go Math Lesson 6.4 4th Grade Answer Key Question 12.
Justify Reasoning George and Susannah used a simulation to simulate the flipping of 8 coins 50 times. In all of the trials, at least 5 heads came up. What can you say about their simulation? Explain.
Answer:
The experimental probability that Susannah and George flip at least 5 heads in every trial is greater than flipping tails, because in every attempt if they flip at least 5 heads, there are 3 or fewer possibilities for the tails.

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 6 Answer Key Theoretical Probability and Simulations.

Texas Go Math Grade 7 Module 6 Answer Key Theoretical Probability and Simulations

Texas Go Math Grade 7 Module 6 Are You Ready? Answer Key

Write each fraction as a decimal and a percent.

Question 1.
\(\frac{3}{4}\) ____________
Answer:
Divide 3 by 4. Write a decimal point and insert extra zeros in the dividend.

The result is 0.75.
Move the decimal point two places to the right and add the “%” sign.
0.75 = 75%
\(\frac{3}{4}\) = 75%

Go Math Grade 7 Module 6 Answer Key Question 2.
\(\frac{2}{5}\) ____________
Answer:
Divide 2 by 5. Write a decimal point and insert extra zeros in the dividend.

The result is 0.40.
Move the decimal point two places to the right and add the “%” sign.
0.40 = 40%
\(\frac{2}{5}\) = 40%

Question 3.
\(\frac{9}{10}\) ____________
Answer:
Divide 9 by 10. Write a decimal point and insert extra zeros in the dividend.

The result is 0.90.
Move the decimal point two places to the right and add the “%” sign.
0.90 = 90%
\(\frac{9}{10}\) = 90%

Question 4.
\(\frac{7}{20}\) ____________
Answer:
Divide 7 by 20. Write a decimal point and insert extra zeros in the dividend.

The result is 0.35.
Move the decimal point two places to the right and add the “%” sign.
0.35 = 35%
\(\frac{7}{20}\) = 35%

Grade 7 Go Math Module 6 Answer Key Question 5.
\(\frac{7}{8}\) ____________
Answer:
Divide 7 by 8. Write a decimal point and insert extra zeros in the dividend.

The result is 0.875.
Move the decimal point two places to the right and add the “%” sign.
0.875 = 87.5%
\(\frac{7}{8}\) = 87.5%

Question 6.
\(\frac{1}{20}\) ____________
Answer:
Divide 1 by 20. Write a decimal point and insert extra zeros in the dividend.

The result is 0.05.
Move the decimal point two places to the right and add the “%” sign.
0.05 = 5%
\(\frac{1}{20}\) = 5%

Question 7.
\(\frac{19}{25}\) ____________
Answer:
Divide 19 by 25. Write a decimal point and insert extra zeros in the dividend.

The result is 0.76.
Move the decimal point two places to the right and add the “%” sign.
0.76 = 76%
\(\frac{19}{25}\) = 76%

Question 8.
\(\frac{23}{50}\) ____________
Answer:
Divide 23 by 50. Write a decimal point and insert extra zeros in the dividend.

The result is 0.46.
Move the decimal point two places to the right and add the “%” sign.
0.46 = 46%
\(\frac{23}{50}\) = 46%

Find each difference.

Question 9.
1 – \(\frac{1}{5}\) ___________
Answer:
1 – \(\frac{1}{5}\) = \(\frac{5}{5}\) – \(\frac{1}{5}\) Write 1 as \(\frac{5}{5}\).
= \(\frac{5-1}{5}\) Subtract the numerators.
= \(\frac{4}{5}\)

Question 10.
1 – \(\frac{2}{9}\) ___________
Answer:
1 – \(\frac{2}{9}\) = \(\frac{9}{9}\) – \(\frac{2}{9}\) Write 1 as \(\frac{9}{9}\).
= \(\frac{9-2}{9}\) Subtract the numerators.
= \(\frac{7}{9}\)

Grade 7 Module 6 Answer Key Go Math Question 11.
1 – \(\frac{8}{13}\) ___________
Answer:
1 – \(\frac{8}{13}\) = \(\frac{13}{13}\) – \(\frac{8}{13}\) Write 1 as \(\frac{13}{13}\).
= \(\frac{13-8}{13}\) Subtract the numerators.
= \(\frac{5}{13}\)

Question 12.
1 – \(\frac{3}{20}\) ___________
Answer:
1 – \(\frac{3}{20}\) = \(\frac{20}{20}\) – \(\frac{3}{20}\) Write 1 as \(\frac{20}{20}\).
= \(\frac{20-3}{20}\) Subtract the numerators.
= \(\frac{17}{20}\)

Multiply. Write each product in simplest form.

Grade 7 Module 6 Answer Key Go Math Question 13.
\(\frac{8}{15}\) × \(\frac{5}{8}\) ___________
Answer:
\(\frac{8}{15}\) × \(\frac{5}{8}\) = \(\frac{8}{15}\) × \(\frac{5}{8}\) Divide numerators and denominators by the common factors.
= \(\frac{1}{3}\) × \(\frac{1}{1}\)
= \(\frac{1 \cdot 1}{3 \cdot 1}\)
= \(\frac{1}{3}\)

Question 14.
\(\frac{2}{9}\) × \(\frac{3}{4}\) ___________
Answer:
\(\frac{2}{9}\) × \(\frac{3}{4}\) = \(\frac{2}{9}\) × \(\frac{3}{4}\) Divide numerators and denominators by the common factors.
= \(\frac{1}{3}\) × \(\frac{1}{2}\)
= \(\frac{1 \cdot 1}{3 \cdot 2}\)
= \(\frac{1}{6}\)

Question 15.
\(\frac{9}{16}\) × \(\frac{12}{13}\) ___________
Answer:
\(\frac{9}{16}\) × \(\frac{12}{13}\) = \(\frac{9}{16}\) × \(\frac{12}{13}\) Divide numerators and denominators by the common factors.
= \(\frac{9}{4}\) × \(\frac{3}{13}\)
= \(\frac{9 \cdot 3}{4 \cdot 13}\)
= \(\frac{27}{52}\)

Module 6 Answer Key Go Math Grade 7 Question 16.
\(\frac{7}{10}\) × \(\frac{5}{28}\) ___________
Answer:
\(\frac{7}{10}\) × \(\frac{5}{28}\) = \(\frac{7}{10}\) × \(\frac{5}{28}\) Divide numerators and denominators by the common factors.
= \(\frac{1}{2}\) × \(\frac{1}{4}\)
= \(\frac{1 \cdot 1}{2 \cdot 4}\)
= \(\frac{1}{8}\)

Texas Go Math Grade 7 Module 6 Reading Start-Up Answer Key

Visualize Vocabulary

Use the ✓ words to complete the graphic.

Understand Vocabulary

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

Answer:
1. Compound event – an event made of two or more simple events.

2. Theoretical probability – the ratio of the number of equally likely outcomes in an event to the total number of possible outcomes.

3. Complement – the set of all outcomes that are not the desired event.

Active Reading
Two-Panel Flip Chart Create a two-panel flip chart, to help you understand the concepts in this module. Label one flap “Simple Events and the other flap “Compound Events’ As you study each lesson, write important ideas under the appropriate flap. Include information that will help you remember the concepts later when you look back at your notes.

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 7.1 Answer Key Linear Relationships in the Form y = mx + b.

Texas Go Math Grade 7 Lesson 7.1 Answer Key Linear Relationships in the Form y = mx + b

Texas Go Math Grade 7 Lesson 7.1 Explore Activity Answer Key

Discovering Linear Relationships

Many real-world situations can be described by linear relationships.

Jodie pays $5 per ticket for a play and a one-time $2 convenience fee. The table shows the total cost for different numbers of tickets.

A. Describe a pattern for the row showing the number of tickets bought.
B. Describe the pattern for the row showing total cost.
C. Out of the total cost paid, how much does the actual ticket account for?

Reflect

Question 1.
How much more than $5 does Jodie pay for one ticket? What if she buys 5 tickets? Explain.
Answer:
Jodie pays $2 more for one ticket. If she buys 5 tickets she will pay also $ 2 more because only at the first payment is charged $ 2.

Lesson 7.1 Modeling Linear Relationships Answer Key Question 2.
Analyze Relationships Describe the total amount paid in dollars based on the number of tickets.
Answer:
One ticket: 2 + 5= 7
Two tickets: 2 – 5 (2) = 12
Three tickets: 2 + 5 (3) = 17
Four tickets: 2 + 5 (4) = 22
Five tickets: 2 + 5 (5) = 27

One ticket cost $7.
Two tickets cost $12.
Three tickets cost $17.
Four tickets cost $ 22.
Five tickets $ 27.

Example 1

A man’s shoe size is approximately 3 times his foot length in inches minus 22. Use a table to represent the relationship between foot length and shoe size.

STEP 1: Make a table. Label the top row Foot length (in.) and the bottom row Shoe size.
STEP 2: Enter some foot lengths in inches. Since ¡t is impossible to have a negative shoe size, pick a foot length that when multiplied by 3 will be greater than 22.

Reflect

Question 3.
Analyze Relationships If someone had a foot length of 13 inches, how can you use the table to determine his shoe size?
Answer:
Multiply 13 by 3 and subtract 22 from that product
13 ∙ 3 = 39
39 – 22 = 17

Question 4.
Critical Thinking Foot lengths do not have to be whole numbers. Give an example of a non-whole number foot length you could have chosen when filling in the table and find the approximate shoe size. What should a person do if their foot length does not correspond to a whole or half shoe size? Explain.
Answer:
For example: Foot Length of 12A in.
12.4 ∙ 3 – 22 = 37.2 – 22 = 15.2
therefore, it will be chosen shoe with a size of 15.5.
Conclusion: If a number whose decimal is between 0 and 5 is obtained, then foot length corresponds to half shoe size, if a number whose decimal is between 5 and 9 is obtained then foot length corresponds to whole shoe size.

Your Turn

Go Math 7th Grade Answer Key Pdf Lesson 7.1 Question 5.
Lea’s house is 350 meters from her friend’s house. Lea walks to her friend’s house at a constant rate of 50 meters per minute. Use a table to represent the relationship between time and the distance Lea has left to walk to her friend’s house.

Answer:
At first divide 350 by 50.

In this way, we are calculated how many minutes she has to walk to the friend’s house with a constant rate of 50 meters per minute.
As we have five fields in the table for values of time and distance, divide 7 by 5.

The value of distance for each value of time in table we calculate as
Distance = 50 ∙ time

She has to walk 7 minutes.

Example 2

Luis will participate in a walkathon for charity. He received a pledge from his aunt, and the table shows the relationshipbetween the miles walked by Luis and the amount his aunt pledged.

Use the table to give a verbal description of the relationship between miles walked and amount pledged.

STEP 1: Look for patterns in the different values for miles walked and amount pledged.

In the table, each value for the number of miles walked is 1 greater than the previous one, and each amount pledged is $1.50 greater than the previous one.

STEP 3: Give a verbal description for the relationship between the miles walked by Luis and amount of money pledged by his aunt.
Luis’s aunt pledged $30 plus an additional $1.50 for each mile he walks.

Reflect

Question 6.
Make a Prediction How could you find the amount pledged by Luis’s aunt if Luis walks 7 miles? What is the amount pledged?
Answer:
If Luis walks 7 miles the amount of pledged will be:
37.5 + 1.5 (2)
= $40.5
If Luis walks 7 miles the amount of pledged will be $ 40.5.

Texas Go Math Grade 7 Linear Functions Answer Key Question 7.
What If…? Luis’s mother decides to also pledge $15 plus an additional $3 per mile. If Luis wants to earn the same amount from his mother and his aunt, how far must he walk? What is the amount he will earn?
Answer:
For aunt:

For mother:

He has to walk 10 miles to earn $45.

Your Turn

The relationship between the cost of an online advertisement for a movie and the number of times it is clicked on is shown in the table.

Question 8.
Use the table to give a verbal description of the relationship.

Answer:
To buy an online advertisement for a movie you will pay $150 plus an additional $ 0.5 for every tenth click.

Question 9.
What is the cost for the advertisement if it is clicked 1000 times?
Answer:
An online advertisement for a movie if it is clicked 1000 times will cost:
150 + 0.5 (1000)
= 150 + 500
= $650
An online advertisement for a movie if it is clicked 1000 times will cost $ 650.

Question 10.
Is there a lower limit for the number of clicks? Is there an upper limit? Explain.
Answer:
For every ten clicks, we’re paying half a dollar, dividing that half-dollar difference from 10 to get a one-click cost.
\(\frac{0.5}{10}\) = 0.05
The upper limit does not exist because each click increases the price.

Texas Go Math Grade 7 Lesson 7.1 Guided Practice Answer Key

Question 1.
The age of a cat 2 years or older can be approximately converted into human years by multiplying by 4 and adding 16. Use a table to represent the relationship between cat age and human years. (Example 1)
Label the rows of the table.
Choose numbers to represent the ages of the cat. Choose numbers that are 2 or greater, since the relationship described is only for cats 2 years or older.
Complete the table by calculating the value for Human years based on the description.

Answer:

Let X represent the age of a cat, and Y represent human years. To find human years we are solving the equation:
X ∙ 4 + 16 = Y

Go Math Grade 7 Lesson 7.1 Answer Key Question 2.
The yearly cost of a community college based on the number of credits taken is shown in the table. Use the table to give a verbal description of the relationship between credits and cost. (Explore Activity and Example 2)

STEP 1: Look for patterns in the different values for credits and cost.
Each value for credits is _________ greater than the previous one,
and each value for cost is _________ greater than the previous one.
This means that 1 credit corresponds to _________ in cost.

STEP 2: Determine how many more dollars than _________ that it costs to take 3 credits.
It costs _________ – _________ = _________ more than _________ to take 3 credits.

STEP 3: Give a verbal description for the relationship between credits and cost.
The yearly cost of the community college is _________ plus _________ for each credit taken.
Answer:
Each value for credits is 3 greater than the previous one.
Each value for cost is $75 greater than the previous one.
This mean one credit correspond to $25 in cost.

Determine how many more dollars than $75 that it costs to take 3 credits.
It cost 175 – 75 = $100 more than $75 to take 3 credits.

The yearly cost of community college is $100 plus $25 for each credit taken.

Essential Question Check-In

Question 3.
When using tables and verbal descriptions to describe a linear relationship, why is it useful to convert from one to another?
Answer:
Because in this way a connection is established and it is clearly explained how the connection has developed between them. It can be concluded quite a lot in case we know the value of one size and its relationship with another to accurately calculate the value of the other.

Texas Go Math Grade 7 Lesson 7.1 Independent Practice Answer Key

A teacher is making multiple copies of a 1 -page homework assignment. The time it takes her in seconds is 2 times the number of copies she makes plus 3.
Question 4.
What does the 3 represent in this scenario? What does the 2 represent?
Answer:
This scenario we can represent with next equation:
y = 2 ∙ x + 3
Therefore when we look general form y = m ∙ x + b, in our equation m = 2 and b = 3.

Texas Go Math Grade 7 Answers Lesson 7.1 Practice Answers Question 5.
What is the total number of seconds it takes for the teacher to make 1 copy? 2 copies? 3 copies? By how many seconds does the total time increase for each copy?
Answer:
For one copy: x = 1
y = 2 (1) + 3
y = 5
For two copies: x = 2
y = 2 (2) + 3
y = 7
For three copies: x = 3
y = 2 (3) + 3
y = 9
For each subsequent copy, it takes two seconds more.

Question 6.
Represent Real-World Problems Represent the relationship between the number of copies made and time in seconds in the table below.

Answer:
The equation is: y = 2 ∙ x + 3, where y represent seconds and x represent number of copies

Rosalee parks at a metered space that still has some time left. She adds some dimes to the meter. The table below represents the number of minutes left based on the number of dimes inserted into the meter.

Question 7.
How many minutes does 1 dime correspond to?
Answer:
First find the difference between the adjacent values expressed in minutes
38 – 22 = 16
Divide the result by 4.
\(\frac{16}{4}\) = 4
It takes 4 minutes for 1 dime.

Question 8.
Based on your answer to exercise 7, how many minutes should you receive for inserting 4 dimes?
Answer:
You should receive 4 ∙ 4 = 16 minutes

Question 9.
Analyze Relationships Give a verbal description of the relationship between dimes and the number of minutes left on the meter.
Answer:
Rosalee has 6 minutes left for parking plus an additional 4 minutes for each dime she adds.

Question 10.
Look at your answer for exercise 9. What does each of the numbers in the answer represent?
Answer:
If we Look at the equation y = m ∙ x + b, for our example m = 16, b = 6, y represent how many minutes left for parking space and x represents how meny dimes are added.

The cost in dollars of a loaf of bread in a bakery is equal to 2 minus 0.25 times the number of days since it was baked.
Question 11.
What is different about this description compared to most of the other descriptions you have seen in this lesson?
Answer:
The difference is that in our exercises it was mostly an increase for a certain value.
More precisely, we added a new value to the initial value, while in this case we deduct some value from the value.

Question 12.
Make a Conjecture Is there a point at which the linear relationship between days and dollars no longer makes sense?
Answer:
Equation is: y = 2 – 0.25 ∙ x
8 days after being baked, the Linear relationship between days and dollars no longer makes sense, because:
y = 2 – 0.25 ∙ 8 = 2 – 2 = 0
y represent the cost in dollars of a loaf of bread and x represent a number of days since it was baked.

7th Grade Go Math Lesson 7.1 Homework Answers Question 13.
Represent Real-World Problems Represent the relationship between days and dollars in the table below.

Answer:

y = 2 – 0.25 ∙ x

Question 14.
Find the number of days it will take the price to reach $0.25.
Answer:
In that case y = 0.25
Replace this in equation y = 2 – 0.25 ∙ x
y = 2 – 0.25 ∙ x
0.25 = 2 – 0.25 ∙ x Subtract 2 from each side.
0.25 – 2 = 2 – 0.25 ∙ x – 2
– 1.75 = 0.25 ∙ x Divide both sides by -0.25
\(\frac{-1.75}{-0.25}\) = x
7 = x
It will take 7 days for a price to reach $ 0.25.

The relationship between the number of years since a tree was transplanted and its height in inches is shown in the table.

Question 15.
What is different about this table compared to the other tables you have seen in this lesson?
Answer:
In this table, there is no constant increase between the values for the variable x, while in each preceding case, we had the same increase for the value of the variable x. In this case, x represents the number of years.

Question 16.
Analyze Relationships Can you give a description of the relationship between the years since the tree was transplanted and its height in inches? If so, what is it?
Answer:
The tree had a height of 18 in. before it was transplanted and plus an additional 8 in. for each year that follows.

H.O.T. Focus on Higher Order Thinking

Question 17.
Communicate Mathematical Ideas Suppose you are analyzing the relationship between time and distance given in a table, and there are 4 values for each quantity. You divide distance 2 minus distance 1 by time 2 minus time 1. You then divide distance 4 minus distance 3 by time 4 minus time-3 and get a different answer. What can you say about the relationship? Explain.
Answer:
If you get different answers that means its not about equal distance or time given in the table, as in exercise 15.

Question 18.
Persevere in Problem-Solving There is a linear relationship between a salesperson’s sales and her weekly income. If her sales are $200, her income is $500, and if her sales are $1,200, her income is $600. What is the relationship between sales and income?
Answer:
The relationship between sales and income is given by the equation
y = \(\frac{1}{10}\) ∙ x + 480
where y represents sales, and x represents income.

Question 19.
Critique Reasoning Molly orders necklace kits online. The cost of the necklace kits can be represented by a linear relationship. Molly’s order of 3 kits cost $12.50. Another order of 5 kits cost $17.50. Molly decides that the kits cost $5 each. Is she correct? Explain.
Answer:
Equation: y = \(\frac{5}{2}\) ∙ x + 5
The procedure for obtaining this equation 5: First find the difference between the number of necklaces in these orders 5 – 3 = 2.
Then find the difference between the prices 17.5 – 12.5 = 5
Divide this two values \(\frac{5}{2}\) = 2.5
That much costs one necklace kits
The kits cost $ 2.5 each. Molly’s answer is not correct.