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A book has a width of 5 decimeters. What is the width of the book in centimeters?
- A. 0.25 centimeters
- B. 25 centimeters
- C. 250 centimeters
- D. 0.025 centimeters
Correct Answer: B
Rationale: To convert decimeters to centimeters, you need to multiply by 10 since 1 decimeter is equal to 10 centimeters. Therefore, to find the width of the book in centimeters, multiply 5 decimeters by 10: 5 decimeters * 10 = 50 centimeters. This means the width of the book is 50 centimeters, making choice B, "25 centimeters," the correct answer. Choices A, C, and D are incorrect because they do not correctly convert decimeters to centimeters.
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Robert secures three new clients every eight months. After how many months has he secured 24 new clients?
- A. 64
- B. 58
- C. 52
- D. 66
Correct Answer: C
Rationale: To determine the number of months it takes for Robert to secure 24 new clients, we set up a proportion: 3 clients / 8 months = 24 clients / x months. Cross multiplying gives 3x = 8 * 24. Solving for x results in x = 64 / 3 = 52. Therefore, after 52 months, Robert has secured 24 new clients. Choice A (64) is incorrect as it miscalculates the solution. Choices B (58) and D (66) are also incorrect as they do not reflect the accurate calculation based on the given information.
What is the simplest way to write the following expression? 5x - 2y + 4x + y
- A. 9x - y
- B. 9x - 3y
- C. 9x + 3y
- D. x; y
Correct Answer: A
Rationale: To simplify the given expression 5x - 2y + 4x + y, we combine like terms. Grouping the x terms together and the y terms together, we have 5x + 4x - 2y + y. Combining like terms results in 9x - y. Therefore, the simplest form of the expression is 9x - y, which corresponds to option A. Option B is incorrect because it incorrectly subtracts 3y instead of just y. Option C is incorrect because it adds 3y instead of subtracting y. Option D is incorrect as it separates x and y with a semicolon instead of an operation, providing no simplified expression.
A triangle has dimensions of 9 cm, 4 cm, and 7 cm. The triangle is reduced by a scale factor of x. Which of the following represents the dimensions of the dilated triangle?
- A. 8.25 cm, 3.25 cm, 6.25 cm
- B. 4.5 cm, 2 cm, 3.5 cm
- C. 6.75 cm, 3 cm, 5.25 cm
- D. 4.95 cm, 2.2 cm, 3.85 cm
Correct Answer: C
Rationale: When reducing a figure by a scale factor, each dimension is multiplied by the same scale factor. In this case, the scale factor is not provided in the question. To find the scale factor, you would divide the new lengths of the sides by the original lengths. The scaled-down triangle's dimensions are the original dimensions multiplied by the scale factor. By performing the calculations, the dimensions of the dilated triangle are 6.75 cm, 3 cm, and 5.25 cm, which matches choice C. Choices A, B, and D have incorrect dimensions as they do not result from the correct application of the scale factor to the original triangle's dimensions.
What is the volume of a ball with a diameter of 7 inches?
- A. 165.7 in³
- B. 179.6 in³
- C. 184.5 in³
- D. 192.3 in³
Correct Answer: A
Rationale: To find the volume of a sphere, the formula V = (4/3)πr³ is used, where r is the radius of the sphere. Given that the diameter of the ball is 7 inches, the radius (r) would be half of the diameter, which is 3.5 inches. Plugging this value into the formula: V = (4/3)π(3.5)³ = (4/3)π(42.875) ≈ 165.7 in³. Therefore, the correct answer is A. Choice B, C, and D are incorrect as they do not accurately represent the volume of the ball with a diameter of 7 inches.
University X requires some of its nursing students to take an exam before being admitted into the nursing program. In this year's class, the nursing students were required to take the exam, and all of those who took the exam passed. If this year's class has 200 students, how many students passed the exam?
- A. 120
- B. 100
- C. 60
- D. 50
Correct Answer: B
Rationale: Since all nursing students who took the exam passed, it means 100% of the students who took the exam passed. As the total number of students in this year's class is 200, the number of students who passed the exam would be 100% of 200, equaling 200 * 100% = 200. Therefore, 200 students passed the exam.