Nokea
Solve the equation 2(4x + 3) = 7x + 5 for x. Which of the following is correct?
- A. -1
- B. 1
- C. 11
- D. 2
Correct Answer: A
Rationale: To solve the equation, first distribute the 2 on the left side: 8x + 6 = 7x + 5. Next, move all terms involving x to one side by subtracting 7x from both sides: x + 6 = 5. Then, subtract 6 from both sides to isolate x: x = -1. Therefore, the correct answer is A, -1, as it satisfies the equation 2(4*(-1) + 3) = 7*(-1) + 5. Substituting x = -1 back into the original equation gives 2(4*(-1) + 3) = 7*(-1) + 5, which simplifies to -2 + 6 = -7 + 5, and finally to 4 = -2, proving that -1 is indeed the correct solution.
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Which of the following percentages is equivalent to the fraction 5/8?
- A. 160%
- B. 65.25%
- C. 62.50%
- D. 1.60%
Correct Answer: C
Rationale: To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100. For the fraction 5/8, it equals 0.625 when divided, which when multiplied by 100 results in 62.50%. Therefore, choice C, 62.50%, is the correct percentage equivalent to the fraction 5/8.
What is the best decimal approximation of 10 times the positive square root of 20?
- A. 89.4
- B. 200
- C. 44.7
- D. 100
Correct Answer: C
Rationale: To find 10 times the positive square root of 20, first calculate the square root of 20, which is approximately 4.472. Then, multiply this by 10: 10 * 4.472 ≈ 44.7. The best decimal approximation of 10 times the positive square root of 20 is 44.7, which corresponds to Option C.
A student performs the following estimations: 24 + 190 = 210, 151 + 319 = 470, 974 + 1022 = 1990. Based on these estimations, what is the student's estimate of 452 + 5017?
- A. 5430
- B. 5470
- C. 5500
- D. 5400
Correct Answer: B
Rationale: The student's pattern involves rounding numbers to the nearest tens or hundreds to simplify calculations. By analyzing the given examples, it is evident that the student tends to round numbers up or down, leading to slight variations from the exact sum. Applying the same strategy to 452 and 5017, we can estimate 450 + 5020 = 5470. Therefore, choice B is the correct estimate for the sum of 452 + 5017.
What is the metric equivalent of 7 inches in measurements used for appointments?
- A. 3.2 cm
- B. 17.8 cm
- C. 15.4 cm
- D. 2.8 cm
Correct Answer: B
Rationale: To convert inches to centimeters, you can use the conversion factor that 1 inch is equal to 2.54 centimeters. Therefore, 7 inches is equivalent to 7 * 2.54 = 17.78 cm, which is closest to 17.8 cm (Choice B). This conversion is commonly used in various fields to provide accurate measurements across different systems. In this case, for appointments, knowing the metric equivalent of inches is important for precise measurements and communication, ensuring accurate scheduling and planning.
A sports utility vehicle travels 386.4 miles on 14 gallons of gas. Which of the following represents the constant of proportionality in miles per gallon?
- A. 5,409.60
- B. 13.8
- C. 372.4
- D. 27.6
Correct Answer: D
Rationale: The constant of proportionality in miles per gallon is calculated by dividing the total miles traveled by the total gallons used. In this case, 386.4 miles · 14 gallons = 27.6 miles per gallon. Therefore, option D, 27.6, correctly represents the constant of proportionality in miles per gallon.