Tasc Math Exam 4

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Questions and Answers

1.

Which statement is true?
- A.
  
  A numeral is a symbol that represents a number.
- B.
  
  A number is a symbol that represents a numeral.
- C.
  
  Numerals and numbers are the same.
- D.
  
  None of the above.
Correct Answer
A. A numeral is a symbol that represents a number.

Explanation
A. The correct solution is a numeral is a symbol that represents a number. Recall that numbers are abstract quantities, but a numeral is a symbol that represents a number.

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2.

What is 1,078 + 0?
- A.
  
  1,078
- B.
  
  1,079
- C.
  
  2,156
- D.
  
  None of the above
Correct Answer
A. 1,078

Explanation
A. The correct solution is 1,078. Adding any number to 0 yields that number. On a number line, starting at a certain number and taking no steps in either direction yields the same number.

See Lesson: Basic Addition and Subtraction.

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3.

Which expression yields a quotient with no remainder?
- A.
  
  5 ÷ 5
- B.
  
  26 ÷ 5
- C.
  
  81 ÷ 40
- D.
  
  365 ÷ 87
Correct Answer
A. 5 ÷ 5

Explanation
A. By inspection, 5 ÷ 5 = 1, so it has no remainder. Using the division algorithm on the other expressions produces a remainder. See Lesson: Basic Multiplication and Division.

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4.

Which math statement is true?
- A.
  
  3 ÷ 1 = 0
- B.
  
  0 ÷ 3 = 1
- C.
  
  3 ÷ 0 = 3
- D.
  
  None of the above
Correct Answer
D. None of the above

Explanation
D. Division by 0 is undefined, and dividing a number by one yields that number. Also, 0 divided by any number is 0. See Lesson: Basic Multiplication and Division.

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5.

A tree has a circumference of 340 centimeters. Find the diameter to the nearest tenth of a centimeter. Use 3.14 for π.
- A.
  
  27.1
- B.
  
  54.1
- C.
  
  81.4
- D.
  
  108.3
Correct Answer
D. 108.3

Explanation
D. The correct solution is 108.3 because C = πd; 340 = 3.14d; d ≈ 108.3 centimeters. See Lesson: Circles.

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6.
- A.
  
  LM
- B.
  
  PN
- C.
  
  OJ
- D.
  
  LP
Correct Answer
A. LM

Explanation
A. The correct solution is LM because L and M are on the circle. See Lesson: Circles.

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7.

A tire has a circumference of 70 inches. Find the radius to the nearest tenth of an inch. Use 3.14 for π.
- A.
  
  11.1
- B.
  
  22.2
- C.
  
  33.3
- D.
  
  44.4
Correct Answer
A. 11.1

Explanation
A. The correct solution is 11.1 because C = 2πr; 70 = 23.14r; 70 = 6.28r; r ≈ 11.1 inches. See Lesson: Circles.

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8.

Select the figure that is translated (x – 4, y + 4).
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
D. The correct solution is D. The translation for the points is (x – 4, y + 4). The points of the original square, (–1, 5), (–1, –1), (5, –1) and (5, 5), become (–5, 9), (–5, 3), (1, 3) and (1, 9). See Lesson: Congruence.

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9.

ΔJKL has points J (5, -3), K (-2,4), and L (3, 0). After a transformation the points are J' (5, 3), K' (-2, -4), and L' (3, 0). What is the transformation between the points?
- A.
  
  Reflection across the x-axis
- B.
  
  Reflection across the y-axis
- C.
  
  Reflection across the y = x
- D.
  
  Reflection across the y = –x
Correct Answer
A. Reflection across the x-axis

Explanation
A. The correct solution is a reflection across the x-axis because the points (x, y) become (x, –y). See Lesson: Congruence.

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10.

Write 1.5 as a percent.
- A.
  
  0.15%
- B.
  
  1.5%
- C.
  
  15%
- D.
  
  150%
Correct Answer
D. 150%

Explanation
D. The correct answer is 150% because 1.5 as a percent is 1.5 × 100 = 150%. See Lesson: Decimals and Fractions.

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11.

Write 29% as a decimal.
- A.
  
  29
- B.
  
  2.9
- C.
  
  0.29
- D.
  
  0.029
Correct Answer
C. 0.29

Explanation
C. The correct answer is 0.29 because 29% as a decimal is 29 ÷ 100 = 0.29. See Lesson: Decimals and Fractions.

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12.

Solve the inequality for the unknown. 2(3x - 1 ) +5 ≥ 3x - 4 - 4x
- A.
  
  X ≥ -7
- B.
  
  X ≥ -4
- C.
  
  X ≥ -1
- D.
  
  X ≥ 0
Correct Answer
C. X ≥ -1
13.

Solve the equation for the unknown, -6d = 36.
- A.
  
  -216
- B.
  
  -6
- C.
  
  30
- D.
  
  42
Correct Answer
B. -6

Explanation
B. The correct solution is –6 because both sides of the equation are divided by –6.
See Lesson: Equations with One Variable.

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14.

Solve the system of equations by graphing. 6x + 5y = -7 2x - 4y = -8
- A.
- B.
- C.
- D.
Correct Answer
A.

Explanation
A. The correct graph has the two lines intersect at (-2, 1). See Lesson: Equations with Two Variables.

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15.

Solve the system of equations. x + 2y = 10 x + y = 5
- A.
  
  (5, 0)
- B.
  
  (0, 5)
- C.
  
  (-5, 0)
- D.
  
  (0, -5)
Correct Answer
B. (0, 5)
16.

Which number is a multiple of 123?
- A.
  
  -123
- B.
  
  1
- C.
  
  247
- D.
  
  359
Correct Answer
A. -123

Explanation
A. Any product of a number and an integer is a multiple of that number. Since 123 x -1 is -123, one multiple of 123 is -123. See Lesson: Factors and Multiples.

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17.

If x is divisible by y, which statement best relates x and y?
- A.
  
  Y is a factor of x.
- B.
  
  X is a multiple of y.
- C.
  
  X and y are whole numbers.
- D.
  
  All of the above.
Correct Answer
D. All of the above.

Explanation
D. Each statement about x and y is true. By definition, if one number is a factor of another, both are whole numbers. See Lesson: Factors and Multiples.

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18.

The dot plot shows the number of hours a group of students volunteered. How are the mean and median affected when removing the outliers?
- A.
  
  The mean and median decrease.
- B.
  
  The mean decreases, but the median increases.
- C.
  
  The mean decreases, but the median does not change.
- D.
  
  The median decreases, but the mean does not change.
Correct Answer
C. The mean decreases, but the median does not change.

Explanation
C. The correct solution is the mean decreases, but the median does not change. The mean decreases by removal of the outlier values, but the median is still 20 hours. See Lesson: Interpreting Categorical and Quantitative Data.

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19.

The test scores in a class are 82, 83, 84, 84, 85, 86, 88, 89, 90. The last test is a score of 105. Compare the mean and median before and after the last test score is included.
- A.
  
  The mean and median increase.
- B.
  
  The mean and median decrease.
- C.
  
  The mean increases, and the median does not change.
- D.
  
  The mean decreases, and the median does not change.
Correct Answer
A. The mean and median increase.

Explanation
A. The correct solution is the mean and median increase. The test score of 105 increases the mean from 85.67 to 87.6 and increases the median from 85 to 85.5. See Lesson: Interpreting Categorical and Quantitative Data.

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20.

A college class had one group use a traditional textbook and another group use an online textbook. The attendance for the class was compared. Determine the independent variable.
- A.
  
  Class attendance
- B.
  
  Type of textbook
- C.
  
  Grade for the class
- D.
  
  Online version of the textbook
Correct Answer
B. Type of textbook

Explanation
B. The correct solution is the type of textbook because the other variables do not change the type of textbook. See Lesson: Interpreting Graphics.

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21.

The mean of eight numbers is 71. The numbers in the data set are 72, 75, 64, 80, 79, and 68. What is the other number in the data set if the number is the mode of the set?
- A.
  
  65
- B.
  
  68
- C.
  
  70
- D.
  
  71
Correct Answer
A. 65

Explanation
A. The correct solution is 65. The sum of the entire data set is 568, and the sum of the given items is 438. The difference between the sums is 130. Divide the result by 2 to get the missing value of 65. See Lesson: Interpreting Graphics.

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22.

The table shows the weight of 100 laptops. Find the mean weight to the nearest hundredth of a pound.
- A.
  
  3.79
- B.
  
  4.09
- C.
  
  4.39
- D.
  
  4.69
Correct Answer
C. 4.39

Explanation
C. The correct solution is 4.39 pounds. The sum of the weights is 3 × 35 + 4 × 24 + 5 × 19 + 6 × 11 + 7 × 11 = 105 + 96 + 95 + 66 + 77 = 439. The average weight is 439 divided by 100, or 4.39 pounds. See Lesson: Interpreting Graphics.

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23.

A cone has a diameter of 12 feet and a height of 5 feet. What is the volume in cubic feet? State the answer in terms of π.
- A.
  
  60π
- B.
  
  120π
- C.
  
  180π
- D.
  
  240π
Correct Answer
A. 60π
24.

Multiply.
- A.
- B.
- C.
- D.
Correct Answer
B.
25.

Divide.
- A.
- B.
- C.
- D.
Correct Answer
C.
26.

A sphere has a volume of 972π cubic millimeters. Find the radius in millimeters.
- A.
  
  3
- B.
  
  9
- C.
  
  27
- D.
  
  81
Correct Answer
B. 9

Explanation
B. The correct solution is 9 millimeters. Substitute the values into the formula, , then multiply by the reciprocal, 729 = r3, and apply the cube root, r = 9 millimeters. See Lesson: Measurement and Dimension.

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27.

Apply the polynomial identity to rewrite 27x³ - 8.
- A.
  
  (3x - 2)(9x² - 6x + 4)
- B.
  
  (3x - 2)(9x² + 6x + 4)
- C.
  
  (3x - 2)(9x² + 6x - 4)
- D.
  
  (3x - 2)(9x² - 6x - 4)
Correct Answer
B. (3x - 2)(9x² + 6x + 4)
28.

Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)
- A.
  
  3x³ - 6x² + 8x + 1
- B.
  
  3x³ - 2x² + 8x + 1
- C.
  
  3x³ + 6x² + 8x + 1
- D.
  
  3x³ + 2x² + 8x + 1
Correct Answer
A. 3x³ - 6x² + 8x + 1
29.
- A.
- B.
- C.
- D.
Correct Answer
B.
30.

Solve x² = 225.
- A.
  
  -5, 5
- B.
  
  -10, 10
- C.
  
  -15, 15
- D.
  
  -20, 20
Correct Answer
C. -15, 15

Explanation
C. The correct solution is -15, 15 because the square root of 225 is 15. The values of -15 and 15 make the equation true. See Lesson: Powers, Exponents, Roots, and Radicals.

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31.

If the ratio of women to men in a certain industry is 5:4, how many people are in that industry?
- A.
  
  9
- B.
  
  20
- C.
  
  900
- D.
  
  Not enough information
Correct Answer
D. Not enough information

Explanation
D. The ratio 5:4 is the industry’s relative number of women to men. But the industry could have 10 women and 8 men, 100 women and 80 men, or any other breakdown whose ratio is 5:4. Therefore, the question provides too little information to answer. Had it provided the total number of people in the industry, it would have been possible to determine how many women and how many men are in the industry. See Lesson: Ratios, Proportions, and Percentages.

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32.

If a truck’s initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed
- A.
  
  17%
- B.
  
  33%
- C.
  
  40%
- D.
  
  67%
Correct Answer
D. 67%
33.

Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
B. The first point is in the second quadrant, the second point is in the third quadrant, the third point is in the fourth quadrant, and the last point is in the first quadrant. See Lesson: Similarity, Right Triangles, and Trigonometry.

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34.

An outdoor game board is 20 feet by 30 feet. One corner of the game board on the coordinate plane is (-10, -20). What could be a second coordinate of the game board?
- A.
  
  (-20, -10)
- B.
  
  (-10, 10)
- C.
  
  (10, -10)
- D.
  
  (-20, 10)
Correct Answer
B. (-10, 10)

Explanation
B. The correct solution is (-10, 10) because 30 can be added to the y-coordinate, -20+30=10. See Lesson: Similarity, Right Triangles, and Trigonometry.

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35.

Solve the equation by the square root method. 2x² = 162
- A.
  
  ±8
- B.
  
  ±9
- C.
  
  ±10
- D.
  
  ±11
Correct Answer
B. ±9

Explanation
B. The correct solution is ±9.

See Lesson: Solving Quadratic Equations.

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36.

Solve the equation by factoring. 6x² - 11x - 35 = 0
- A.
- B.
- C.
- D.
Correct Answer
B.
37.

Solve the equation by the quadratic formula. 6x² - 4x - 3 = 0
- A.
  
  -1.12 and -0.45
- B.
  
  1.12 and -0.45
- C.
  
  -1.12 and 0.45
- D.
  
  1.12 and 0.45
Correct Answer
B. 1.12 and -0.45
38.
- A.
- B.
- C.
- D.
Correct Answer
B.
39.

The original height of a plant is 1.75 inches. The plant grows an average of 1.08 inches each month for 6 months. What is the new height of the plant in inches?
- A.
  
  7.13
- B.
  
  7.23
- C.
  
  8.13
- D.
  
  8.23
Correct Answer
D. 8.23

Explanation
D. The correct solution is 8.23 because 1.75 + 1.08(6) = 1.75 + 6.48 = 8.23 inches. See Lesson: Solving Real World Mathematical Problems.

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40.

A county contains 25 villages, 12 towns, and 3 cities. There is an average of 6 stoplights in a village, 27 in a town, and 148 in a city. Estimate the total number of stoplights.
- A.
  
  800
- B.
  
  900
- C.
  
  1,200
- D.
  
  1,300
Correct Answer
B. 900

Explanation
B. The correct solution is 900 because the expression for estimation is 25(6) + 10(30) + 150(3). The expression simplifies to 150 + 300 + 450 = 900 stoplights. See Lesson: Solving Real World Mathematical Problems.

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41.

Convert 1,000 fluid ounces to gallons.
- A.
  
  7.8125 gallons
- B.
  
  15.625 gallons
- C.
  
  31.25 gallons
- D.
  
  62.5 gallons
Correct Answer
A. 7.8125 gallons

Explanation
A. The correct solution is 7.8125 gallons.

See Lesson: Standards of Measure.

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42.

Convert 0.5 kiloliter to milliliters.
- A.
  
  50,000 milliliters
- B.
  
  500,000 milliliters
- C.
  
  5,000,000 milliliters
- D.
  
  50,000,000 milliliters
Correct Answer
B. 500,000 milliliters

Explanation
B. The correct solution is 500,000 milliliters.

See Lesson: Standards of Measure.

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43.

At a school, the probability a student has a study hall is two-thirds. What object and results could be used for a simulation of 1,000 times?
- A.
  
  A. Flipping a coin
- B.
  
  Playing rock, paper, scissors and looking for rock
- C.
  
  Using a four-sided spinner and spinning 1, 2, or 3
- D.
  
  Throwing a six-sided number cube and looking for 1, 2, 3, or 4
Correct Answer
D. Throwing a six-sided number cube and looking for 1, 2, 3, or 4

Explanation
D. The correct solution is throwing a six-sided number cube and looking for 1, 2, 3, or 4 because the dice has 4 out of 6, or two-thirds, options to match the probability of the event. See Lesson: Statistical Measures.

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44.

Identify the sampling technique that is a convenience sample.
- A.
  
  A group of students selected by a principal
- B.
  
  A group of students selected by their grade point average
- C.
  
  A group of students selected by their after-school availability
- D.
  
  A group of students selected by a random number generator
Correct Answer
C. A group of students selected by their after-school availability

Explanation
C. The correct solution is a group of students selected by their after-school availability because the students are only available after school. See Lesson: Statistical Measures.

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45.

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the union of the first 10 cards.
- A.
  
  Green cards
- B.
  
  Cards 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- C.
  
  Green cards and Red cards; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
- D.
  
  Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10
Correct Answer
D. Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10

Explanation
D. The correct solution is Green cards 1, 2, 3, 4, 5; Red cards 6, 7, 8, 9, 10. The union is listing out all options of the sample space. See Lesson: Statistics & Probability: The Rules of Probability.

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46.

There are 12 boys’ and 14 girls’ names in a hat. What is the probability of selecting a boy’s name twice in a row without replacement?
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
See Lesson: Statistics & Probability: The Rules of Probability.

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47.

Karida has a part-time job. She works 4.25 hours on Thursday and Friday and 6.5 hours on Saturday and Sunday. What is her hourly rate if her check is $268.75?
- A.
  
  $8.50
- B.
  
  $12.50
- C.
  
  $14.50
- D.
  
  $21.50
Correct Answer
B. $12.50

Explanation
B. The correct solution is $12.50 because she worked a total of 4.25(2) + 6.5(2) = 8.5 + 13 = 21.5 hours. The hourly rate is 268.75 ÷ 21.50 = $12.50. See Lesson: Solving Real World Mathematical Problems.

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48.

Select the statement that is true for the angles.
- A.
  
  Points X and Y are vertices of angles.
- B.
  
  Points X and U are vertices of angles.
- C.
  
  Points W and Y are vertices of angles.
- D.
  
  Points W and U are vertices of angles.
Correct Answer
B. Points X and U are vertices of angles.

Explanation
B. The correct solution is points X and U are vertices of angles because these points are the intersection of two rays. See Lesson: Congruence.

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49.

The volume of a hemi-sphere is cubic feet. What is the diameter in feet?
- A.
  
  1
- B.
  
  2
- C.
  
  3
- D.
  
  4
Correct Answer
D. 4
50.

A teacher wants to know if seat location affects test scores. What data needs to be collected for an experiment?
- A.
  
  The teacher should collect data on one seat for every class.
- B.
  
  The teacher should collect data on one student for every class.
- C.
  
  The teacher should collect data on a random sample of students for the final exam.
- D.
  
  The teacher should collect data on a random sample of students of test scores and seat location.
Correct Answer
D. The teacher should collect data on a random sample of students of test scores and seat location.

Explanation
D. The correct solution is that the teacher should collect data on a random sample of students of test scores and seat location because there are specific groups based on seat location. See Lesson: Statistical Measures.

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Tasc Math Exam 4

Which statement is true?

What is 1,078 + 0?

Which expression yields a quotient with no remainder?

Which math statement is true?

A tree has a circumference of 340 centimeters. Find the diameter to the nearest tenth of a centimeter. Use 3.14 for π.

A tire has a circumference of 70 inches. Find the radius to the nearest tenth of an inch. Use 3.14 for π.

Select the figure that is translated (x – 4, y + 4).

ΔJKL has points J (5, -3), K (-2,4), and L (3, 0). After a transformation the points are J' (5, 3), K' (-2, -4), and L' (3, 0). What is the transformation between the points?

Write 1.5 as a percent.

Write 29% as a decimal.

Solve the inequality for the unknown. 2(3x - 1 ) +5 ≥ 3x - 4 - 4x

Solve the equation for the unknown, -6d = 36.

Solve the system of equations by graphing. 6x + 5y = -7 2x - 4y = -8

Solve the system of equations. x + 2y = 10 x + y = 5

Which number is a multiple of 123?

If x is divisible by y, which statement best relates x and y?

The dot plot shows the number of hours a group of students volunteered. How are the mean and median affected when removing the outliers?

The test scores in a class are 82, 83, 84, 84, 85, 86, 88, 89, 90. The last test is a score of 105. Compare the mean and median before and after the last test score is included.

A college class had one group use a traditional textbook and another group use an online textbook. The attendance for the class was compared. Determine the independent variable.

The mean of eight numbers is 71. The numbers in the data set are 72, 75, 64, 80, 79, and 68. What is the other number in the data set if the number is the mode of the set?

The table shows the weight of 100 laptops. Find the mean weight to the nearest hundredth of a pound.

A cone has a diameter of 12 feet and a height of 5 feet. What is the volume in cubic feet? State the answer in terms of π.

Multiply.

Divide.

A sphere has a volume of 972π cubic millimeters. Find the radius in millimeters.

Apply the polynomial identity to rewrite 27x3 - 8.

Perform the operation. (-2x2 + 8x) + (3x3 - 4x2 + 1)

Solve x2 = 225.

If the ratio of women to men in a certain industry is 5:4, how many people are in that industry?

If a truck’s initial speed is 60 mph and its final speed is 100 mph, what is its percent change in speed

Draw a square with the coordinates (-3, 4), (-3, -2), (3, -2), (3, 4).

An outdoor game board is 20 feet by 30 feet. One corner of the game board on the coordinate plane is (-10, -20). What could be a second coordinate of the game board?

Solve the equation by the square root method. 2x2 = 162

Solve the equation by factoring. 6x2 - 11x - 35 = 0

Solve the equation by the quadratic formula. 6x2 - 4x - 3 = 0

The original height of a plant is 1.75 inches. The plant grows an average of 1.08 inches each month for 6 months. What is the new height of the plant in inches?

A county contains 25 villages, 12 towns, and 3 cities. There is an average of 6 stoplights in a village, 27 in a town, and 148 in a city. Estimate the total number of stoplights.

Convert 1,000 fluid ounces to gallons.

Convert 0.5 kiloliter to milliliters.

At a school, the probability a student has a study hall is two-thirds. What object and results could be used for a simulation of 1,000 times?

Identify the sampling technique that is a convenience sample.

In a deck of 20 number cards, cards 1–5 are green, cards 6–10 are red, cards 11–15 are yellow, and cards 16–20 are blue. Describe the union of the first 10 cards.

There are 12 boys’ and 14 girls’ names in a hat. What is the probability of selecting a boy’s name twice in a row without replacement?

Karida has a part-time job. She works 4.25 hours on Thursday and Friday and 6.5 hours on Saturday and Sunday. What is her hourly rate if her check is $268.75?

Select the statement that is true for the angles.

The volume of a hemi-sphere is cubic feet. What is the diameter in feet?

A teacher wants to know if seat location affects test scores. What data needs to be collected for an experiment?

Apply the polynomial identity to rewrite 27x³ - 8.

Perform the operation. (-2x² + 8x) + (3x³ - 4x² + 1)

Solve x² = 225.

Solve the equation by the square root method. 2x² = 162

Solve the equation by factoring. 6x² - 11x - 35 = 0

Solve the equation by the quadratic formula. 6x² - 4x - 3 = 0