Nursing Elites

1. Bob decides to go into business selling lemonade. He buys a wooden stand for $45 and sets it up outside his house. He figures that the cost of lemons, sugar, and paper cups for each glass of lemonade sold will be 10¢. Which of these expressions describes his cost for making g glasses of lemonade?

• A. $45 + $0.1 × g
• B. $44.90 × g
• C. $44.90 × g + 10¢
• D. $90

Correct answer: A

Rationale: The cost for making g glasses of lemonade includes the initial cost of the stand ($45) plus 10¢ for each glass of lemonade sold. Therefore, the expression that represents the cost for making g glasses of lemonade is $45 + $0.1 × g, which matches option A. Choice B, $44.90 × g, is incorrect as it does not account for the initial stand cost of $45. Choice C, $44.90 × g + 10¢, is incorrect because it does not include the initial stand cost and incorrectly adds an extra 10¢ for every glass. Choice D, $90, is incorrect as it does not consider the variable cost of 10¢ per glass and only represents the initial stand cost.

2. What is a direct proportion? What is an inverse proportion?

• A. Direct: Both quantities increase or decrease together; Inverse: When one quantity increases, the other decreases by the same factor
• B. Direct: Both quantities decrease together; Inverse: When one quantity increases, the other increases
• C. Direct: One quantity stays the same while the other increases; Inverse: Both quantities increase together
• D. Direct: One quantity increases while the other decreases; Inverse: Both quantities decrease together

Correct answer: A

Rationale: In a direct proportion, both quantities increase or decrease together. This means that as one quantity goes up, the other also goes up, and vice versa. On the other hand, in an inverse proportion, when one quantity increases, the other decreases by the same factor. Therefore, choice A is correct as it accurately defines direct and inverse proportions. Choices B, C, and D are incorrect because they do not accurately describe the relationship between quantities in direct and inverse proportions.

3. How do you convert pounds to kg and kg to pounds?

• A. Multiply by 2.2 for pounds; divide by 2.2 for kg
• B. Multiply by 2 for pounds; divide by 2 for kg
• C. Multiply by 1.8 for pounds; divide by 1.8 for kg
• D. Multiply by 1.5 for pounds; divide by 1.5 for kg

Correct answer: A

Rationale: To convert pounds to kg, you need to divide by 2.2, not multiply. Similarly, to convert kg to pounds, you should multiply by 2.2. Therefore, choice A is correct. Choices B, C, and D are incorrect because they provide incorrect conversion factors for pounds and kg, leading to inaccurate results.

4. Melissa is ordering fencing to enclose a square area of 5625 square feet. How many feet of fencing does she need?

• A. 75 feet
• B. 150 feet
• C. 300 feet
• D. 5,625 feet

Correct answer: C

Rationale: To find the side length of the square, we take the square root of the area: √5625 ft² = 75 ft. The perimeter of a square is 4 times its side length, so the fencing needed is 4 × 75 ft = 300 ft. Therefore, Melissa needs 300 feet of fencing to enclose the square area of 5625 square feet. Option A (75 feet) is the side length of the square, not the fencing needed. Option B (150 feet) is half of the correct answer and does not account for all sides of the square. Option D (5,625 feet) is the total area, not the length of fencing required.

5. 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: The circumference of a circle is given by the formula Circumference = 2 x π x radius. Given that the radius of the picture frame is 3 inches, the estimated circumference can be calculated as 2 x π x 3 = 18.84 inches, which is closest to 18 inches among the given options. Choice A (12 inches) is too small, choice B (16 inches) is also underestimated, and choice D (24 inches) is too large based on the calculated value using the formula.

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