Nursing Elites

1. Simplify the expression: 2x + 3x - 5.

• A. 5x - 5
• B. 5x
• C. x - 5
• D. 2x - 5

Correct answer: A

Rationale: To simplify the expression 2𝑥 + 3𝑥 - 5, follow these steps: Identify and combine like terms. The terms 2𝑥 and 3𝑥 are both 'like terms' because they both contain the variable 𝑥. Add the coefficients of the like terms: 2𝑥 + 3𝑥 = 5𝑥. Simplify the expression. After combining the like terms, the expression becomes 5𝑥 - 5, which includes the simplified term 5𝑥 and the constant -5. Thus, the fully simplified expression is 5𝑥 - 5, making Option A the correct answer. This method ensures all terms are correctly simplified by combining similar elements and retaining constants.

2. Curtis is taking a road trip through Germany, where all distance signs are in metric. He passes a sign that states the city of Dusseldorf is 45 kilometers away. Approximately how far is this in miles?

• A. 42 miles
• B. 37 miles
• C. 28 miles
• D. 16 miles

Correct answer: C

Rationale: To convert kilometers to miles, you can use the conversion factor of approximately 0.62 miles per kilometer. Therefore, 45 kilometers × 0.62 miles/kilometer = 27.9 miles, which is approximately 28 miles away. Choice A (42 miles), Choice B (37 miles), and Choice D (16 miles) are incorrect as they do not reflect the accurate conversion from kilometers to miles.

3. A rectangular field has an area of 1452 square feet. If the length is three times the width, what is the width of the field?

• A. 22 feet
• B. 44 feet
• C. 242 feet
• D. 1452 feet

Correct answer: A

Rationale: To find the width of the rectangular field, use the formula for the area of a rectangle: A = length × width. Given that the length is three times the width, you have A = 3w × w. Substituting the given area, 1452 = 3w^2. Solving for w, you get 484 = w^2. Taking the square root gives ±22, but since the width must be positive, the width of the field is 22 feet. Choice B, 44 feet, is incorrect because it represents the length, not the width. Choice C, 242 feet, is incorrect as it is not a factor of the area. Choice D, 1452 feet, is incorrect as it represents the total area of the field, not the width.

4. 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.

5. A farmer plans to install fencing around a certain field. If each side of the hexagonal field is 320 feet long, and fencing costs $1.75 per foot, how much will the farmer need to spend on fencing material to enclose the perimeter of the field?

• A. $2,240
• B. $2,800
• C. $3,360
• D. $4,480

Correct answer: C

Rationale: To find the perimeter of a hexagonal field with 6 sides, multiply the length of one side (320 feet) by the number of sides (6): 320 x 6 = 1920 feet. The total cost of the fencing material can be calculated by multiplying the perimeter by the cost per foot: 1920 feet x $1.75 = $3360. Therefore, the farmer will need to spend $3,360 on fencing material to enclose the perimeter of the field. Choice A, B, and D are incorrect as they do not accurately calculate the total cost based on the given measurements and cost per foot.

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