Nokea
What is 4.6 rounded to the nearest integer?
- A. 3
- B. 4
- C. 5
- D. 6
Correct Answer: C
Rationale: When rounding a decimal number to the nearest integer, if the decimal part is 0.5 or greater, we round up to the next integer; if it is less than 0.5, we round down. In this case, 4.6 is closer to 5 than to 4 because it is exactly halfway between the two integers. Therefore, when rounding 4.6 to the nearest integer, we round up to 5. Choice A (3), B (4), and D (6) are incorrect as they are not the nearest integer to 4.6.
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On a floor plan drawn at a scale of 1:100, the area of a rectangular room is 50 cm². What is the actual area of the room?
- A. 500 m²
- B. 50 m²
- C. 5000 cm²
- D. 500 cm²
Correct Answer: D
Rationale: The scale of 1:100 means that 1 cm² on the floor plan represents 100 cm² in real life. To find the actual area of the room, you need to multiply the area on the floor plan by the square of the scale factor. Since the scale is 1:100, the scale factor is 100. Therefore, 50 cm² on the floor plan represents 50 * 100 = 5000 cm² in real life. Choice A (500 m²) is incorrect as it converts the area from cm² to m² without considering the scale factor. Choice B (50 m²) is incorrect as it does not account for the scale factor. Choice C (5000 cm²) is incorrect as it gives the area on the floor plan, not the actual area.
What is the overall median of Dwayne's current scores: 78, 92, 83, 97?
- A. 19
- B. 85
- C. 83
- D. 87.5
Correct Answer: B
Rationale: To find the median of a set of numbers, first arrange the scores in ascending order: 78, 83, 92, 97. Since there is an even number of scores, we find the median by taking the average of the two middle values. In this case, the middle values are 83 and 92. Calculating (83 + 92) / 2 = 85, we determine that the overall median of Dwayne's scores is 85. Choice A (19) is incorrect as it does not correspond to any value in the given set of scores. Choice C (83) is the median of the original set but not the overall median once arranged. Choice D (87.5) is the average of all scores but not the median.
A certain exam has 30 questions. A student gets 1 point for each question answered correctly and loses half a point for each question answered incorrectly; no points are gained or lost for questions left blank. If x represents the number of questions a student answers correctly and y represents the number of questions left blank, which of the following expressions represents the student's score on the exam?
- A. x - y/2
- B. x - y
- C. 30 - (x + y)
- D. 30 - x - y/2
Correct Answer: A
Rationale: The student's score is calculated by adding the points earned for correct answers (x) and subtracting the points lost for incorrect answers (y/2). Therefore, the expression for the student's score on the exam is x - y/2. Option A is correct because it accurately represents this calculation. Option B (x - y) is incorrect as it does not account for the penalty of losing half a point for each incorrect answer. Option C (30 - (x + y)) is incorrect as it subtracts the total number of questions from the sum of correct and blank answers, which does not represent the scoring system. Option D (30 - x - y/2) is also incorrect as it incorrectly subtracts x from 30 and then deducts y divided by 2, which is not the correct scoring method for the exam.
What is the solution to 4 x 7 + (25 - 21)²?
- A. 512
- B. 36
- C. 44
- D. 22
Correct Answer: C
Rationale: To find the solution, first solve the expression inside the parentheses: 25 - 21 = 4. Then, square the result from the parentheses: 4² = 16. Next, perform the multiplication: 4 x 7 = 28. Finally, add the results: 28 + 16 = 44. Therefore, the correct answer is 44. Choice A (512), Choice B (36), and Choice D (22) are incorrect as they do not follow the correct order of operations for solving the given mathematical expression.
If a car travels 150 miles in 3 hours, what is the car's average speed in miles per hour?
- A. 45 mph
- B. 50 mph
- C. 55 mph
- D. 60 mph
Correct Answer: B
Rationale: To calculate the average speed, use the formula: Average speed = Total distance / Total time. In this case, Average speed = 150 miles / 3 hours = 50 mph. Therefore, the car's average speed is 50 miles per hour. Choice A (45 mph), Choice C (55 mph), and Choice D (60 mph) are incorrect as they do not match the correct calculation based on the given distance and time values.