Nokea
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.
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Solve for x: 3(x - 5) = 2(x + 3)
- A. x = 3
- B. x = 6
- C. x = 9
- D. x = 12
Correct Answer: A
Rationale: To solve the equation 3(x - 5) = 2(x + 3) for x, start by distributing the terms inside the parentheses. This gives you 3x - 15 = 2x + 6. Next, combine like terms by moving all terms with x to one side and the constants to the other side. Subtracting 2x from both sides gives x - 15 = 6. Finally, adding 15 to both sides results in x = 21. Therefore, the correct answer is A: x = 3. Choices B, C, and D are incorrect as they do not result from the correct calculations of the equation.
Simplify the following expression: 5/9 15/36
- A. 5/36
- B. 8/27
- C. 10/17
- D. 15/27
Correct Answer: A
Rationale: To simplify the given expression, multiply the numerators together and the denominators together.
5/9 15/36 = (5 15) / (9 36) = 75 / 324.
Now, simplify the resulting fraction by finding the greatest common divisor (GCD) of 75 and 324, which is 3. Divide both the numerator and denominator by 3 to get the simplified fraction: 75 · 3 / 324 · 3 = 25 / 108.
Therefore, the simplified form of 5/9 15/36 is 25/108, which is equivalent to 5/36.
Choice A, 5/36, is the correct answer.
Choice B, 8/27, is incorrect as it does not match the simplified form of the expression.
Choice C, 10/17, is unrelated and does not result from the given multiplication.
Choice D, 15/27, does not correspond to the simplification of the given expression.
Juan wishes to compare the percentages of time he spends on different tasks during the workday. Which of the following representations is the most appropriate choice for displaying the data?
- A. Line plot
- B. Bar graph
- C. Line graph
- D. Pie chart
Correct Answer: D
Rationale: A pie chart is the most appropriate choice for displaying the percentages of time spent on different tasks during the workday because it visually represents parts of a whole. In this case, each task's percentage represents a part of the entire workday, making a pie chart an ideal way to compare these percentages. Line plots, bar graphs, and line graphs are not suitable for showing percentages of a whole; they are more commonly used for tracking trends, comparing values, or showing relationships between variables but do not efficiently represent parts of a whole like a pie chart does.
After taking a certain antibiotic, Dr. Lee observed that 30% of all his patients developed an infection. He further noticed that 5% of those patients required hospitalization to recover from the infection. What percentage of Dr. Lee's patients were hospitalized after taking the antibiotic?
- A. 1.50%
- B. 5%
- C. 15%
- D. 30%
Correct Answer: A
Rationale: To find the percentage of Dr. Lee's patients hospitalized, you need to calculate 5% of the 30% who developed an infection. 5% of 30% is 1.5%. Therefore, 1.5% of Dr. Lee's patients were hospitalized. Choice A is correct. Choices B, C, and D are incorrect because they do not accurately reflect the calculation of the percentage of patients requiring hospitalization after taking the antibiotic.
If Sarah reads at an average rate of 21 pages in four nights, how long will it take her to read 140 pages?
- A. 6 nights
- B. 26 nights
- C. 8 nights
- D. 27 nights
Correct Answer: D
Rationale: If Sarah reads 21 pages in four nights, she reads at a rate of 21 / 4 = 5.25 pages per night. To read 140 pages, she would need 140 / 5.25 = 26.67 nights. Since she cannot read a fraction of a night, it would take her 27 nights to read 140 pages, making option D the correct answer. Option A is incorrect as it does not accurately reflect the calculation. Option B is incorrect as it does not consider the fractional part of the calculation, resulting in an inaccurate answer. Option C is incorrect as it does not align with the correct calculation based on Sarah's reading rate.