Nursing Elites

1. If you have a rectangle with a width of 5 inches and a length of 10 inches and scale it by a factor of 2, what will the new perimeter be?

• A. 30 inches
• B. 40 inches
• C. 60 inches
• D. 50 inches

Correct answer: C

Rationale: When a rectangle is scaled by a factor of 2, both the length and width are multiplied by 2. The new dimensions become width = 5 * 2 = 10 inches and length = 10 * 2 = 20 inches. Therefore, the new perimeter is calculated as 2 * (10 + 20) = 60 inches. Choice A, B, and D are incorrect as they do not reflect the correct calculation based on scaling the dimensions of the rectangle.

2. What is the formula for the area of a circle?

• A. A = πr²
• B. A = 2πr
• C. A = πd
• D. A = 2πd

Correct answer: A

Rationale: The correct formula for the area of a circle is A = πr², where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle. Choice B, A = 2πr, represents the circumference of a circle, not the area. Choice C, A = πd, incorrectly uses the diameter (d) instead of the radius in the formula for area. Choice D, A = 2πd, is also related to the circumference of the circle, not the area. Therefore, option A is the only correct formula for calculating the area of a circle.

3. If x represents the width of a rectangle and the length is six less than two times the width, which of the following expressions represents the length of the rectangle in terms of x?

• A. 2x-6
• B. 6-2x
• C. 6x-2
• D. 3x-4

Correct answer: A

Rationale: To find the expression representing the length of the rectangle in terms of x, we need to consider that the length is six less than two times the width. If we denote the width as x, the length can be expressed as 2x - 6. Therefore, the correct expression is 2x-6 (choice A). Choice B, 6-2x, represents the width subtracted from 6, not the length. Choice C, 6x-2, is not derived from the given information about the relationship between the width and length. Choice D, 3x-4, is not consistent with the relationship provided in the question.

4. What defines a proper fraction versus an improper fraction?

• A. Proper: numerator < denominator; Improper: numerator > denominator
• B. Proper: numerator > denominator; Improper: numerator < denominator
• C. Proper: numerator = denominator; Improper: numerator < denominator
• D. Proper: numerator < denominator; Improper: numerator = denominator

Correct answer: A

Rationale: A proper fraction is characterized by having a numerator smaller than the denominator, while an improper fraction has a numerator larger than the denominator. Therefore, choice A is correct. Choice B is incorrect because it states the opposite relationship between the numerator and denominator for proper and improper fractions. Choice C is incorrect as it describes a fraction where the numerator is equal to the denominator, which is a different concept. Choice D is incorrect as it associates a numerator being smaller than the denominator with an improper fraction, which is inaccurate.

5. Lauren must travel a distance of 1,480 miles to get to her destination. She plans to drive approximately the same number of miles per day for 5 days. Which of the following is a reasonable estimate of the number of miles she will drive per day?

• A. 240 miles
• B. 260 miles
• C. 300 miles
• D. 340 miles

Correct answer: C

Rationale: To estimate the number of miles Lauren will drive per day, the total distance can be rounded to 1,500 miles. Divide this by the number of days she plans to drive, which is 5. 1,500 miles / 5 days = 300 miles per day. Therefore, a reasonable estimate for the number of miles she will drive per day is 300. Choice A (240 miles) is too low, Choice B (260 miles) is slightly low, and Choice D (340 miles) is too high when considering the total distance and the number of days Lauren plans to drive.

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