Nursing Elites

1. Simplify (x^2 - y^2) / (x - y)

• A. x + y
• B. x - y
• C. 1
• D. (x + y)/(x - y)

Correct answer: A

Rationale: The expression 𝑥^2 - 𝑦^2 is a difference of squares, which follows the identity: 𝑥^2 - 𝑦^2 = (𝑥 + 𝑦)(𝑥 - 𝑦). Therefore, the given expression becomes: (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) = (𝑥 + 𝑦)(𝑥 - 𝑦) / (𝑥 - 𝑦). Since (𝑥 - 𝑦) appears in both the numerator and the denominator, they cancel each other out, leaving 𝑥 + 𝑦. Thus, the simplified form of (𝑥^2 - 𝑦^2) / (𝑥 - 𝑦) is 𝑥 + 𝑦. Therefore, the correct answer is A (x + y). Option B (x - y) is incorrect as it does not result from simplifying the given expression. Option C (1) is incorrect as it does not account for the variables x and y present in the expression. Option D ((x + y)/(x - y)) is incorrect as it presents the simplified form in a different format than the correct answer.

2. How many kilometers is 4382 feet?

• A. 1.336 kilometers
• B. 14.376 kilometers
• C. 1.437 kilometers
• D. 13.336 kilometers

Correct answer: A

Rationale: To convert feet to kilometers, you need to divide the number of feet by 3280.84 (the number of feet in a kilometer). Therefore, 4382 feet is equal to 4382/3280.84 ≈ 1.336 kilometers. Choice B, 14.376 kilometers, is incorrect as it seems to be a miscalculation. Choice C, 1.437 kilometers, is also incorrect, as it is slightly off from the correct conversion. Choice D, 13.336 kilometers, is significantly higher than the correct answer and does not align with the conversion factor.

3. If a train travels 60 miles per hour for 2 hours, how far does the train travel?

• A. 60 miles
• B. 100 miles
• C. 120 miles
• D. 200 miles

Correct answer: C

Rationale: To find the distance traveled by the train, we use the formula Distance = Speed x Time. Given that the train travels at 60 miles per hour for 2 hours, the calculation would be 60 miles/hour x 2 hours = 120 miles. Therefore, the correct answer is 120 miles. Choice A (60 miles) is incorrect because it only represents the speed of the train, not the total distance traveled. Choice B (100 miles) is incorrect as it does not account for the full 2 hours of travel. Choice D (200 miles) is incorrect as it overestimates the distance by multiplying the speed by the time incorrectly.

4. Adrian measures the circumference of a circular picture frame with a radius of 3 inches. Which of the following is the best estimate for the circumference of the frame?

• A. 12 inches
• B. 16 inches
• C. 18 inches
• D. 24 inches

Correct answer: C

Rationale: To calculate the circumference of a circle, use the formula 2πr, where r is the radius. In this case, with a radius of 3 inches, the estimated circumference would be 2 x π x 3 = 6π ≈ 18.85 inches. Therefore, the best estimate for the circumference of the frame is 18 inches (Choice C). Choice A (12 inches) is too small as it corresponds to the diameter rather than the circumference. Choice B (16 inches) and Choice D (24 inches) are also incorrect as they do not reflect the accurate calculation based on the given radius.

5. 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.

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