Nursing Elites

1. What defines a composite number?

• A. A number with only two factors
• B. A number that is a fraction
• C. A number with more than 2 factors
• D. A number with exactly two factors

Correct answer: C

Rationale: A composite number is a positive integer greater than one that has more than two factors. Choice A is incorrect because a number with only two factors is a prime number. Choice B is incorrect as being a fraction does not define a composite number. Choice D is incorrect because a number with exactly two factors is a prime number, not a composite number.

2. Which of the following is the y-intercept of the line whose equation is 7y − 42x + 7 = 0?

• A. (1/6, 0)
• B. (6, 0)
• C. (0, −1)
• D. (−1, 0)

Correct answer: C

Rationale: To find the y-intercept, set x = 0 in the equation 7y − 42x + 7 = 0. This simplifies to 7y - 42(0) + 7 = 0, which gives 7y = -7. Solving for y, we get y = -1. Therefore, the y-intercept is where x = 0, so the correct answer is (0, -1). Choice A (1/6, 0) is incorrect as it does not satisfy the given equation when x = 0. Choice B (6, 0) is incorrect as it represents the x-intercept. Choice D (-1, 0) is incorrect as it does not correspond to the y-intercept of the given equation.

3. Mom's car drove 72 miles in 90 minutes. How fast did she drive in feet per second?

• A. 0.8 feet per second
• B. 48.9 feet per second
• C. 0.009 feet per second
• D. 70.4 feet per second

Correct answer: B

Rationale: To convert miles per hour to feet per second, you need to convert miles to feet and minutes to seconds. First, convert 72 miles to feet using the conversion factor 1 mile = 5280 feet: 72 miles * 5280 feet/mile = 380160 feet. Then, convert 90 minutes to seconds: 90 minutes * 60 seconds/minute = 5400 seconds. Now, to find the speed in feet per second, divide the distance traveled in feet by the time in seconds: 380160 feet / 5400 seconds = 70.4 feet per second. Therefore, the correct answer is 70.4 feet per second. Choice A, 0.8 feet per second, is incorrect as it is a much lower speed. Choice C, 0.009 feet per second, is also incorrect as it is too low. Choice D, 70.4 feet per second, would be correct if the conversion calculations were accurate, but in this case, it's not the correct answer.

4. Apply the polynomial identity to rewrite (a + b)².

• A. a² + b²
• B. 2ab
• C. a² + 2ab + b²
• D. a² - 2ab + b²

Correct answer: C

Rationale: When you see something like (a + b)², it means you're multiplying (a + b) by itself: (a + b)² = (a + b) × (a + b) To expand this, we use the distributive property (which says you multiply each term in the first bracket by each term in the second bracket): Multiply the first term in the first bracket (a) by both terms in the second bracket: a × a = a² a × b = ab Multiply the second term in the first bracket (b) by both terms in the second bracket: b × a = ab b × b = b² Now, add up all the results from the multiplication: a² + ab + ab + b² Since ab + ab is the same as 2ab, we can simplify it to: a² + 2ab + b² So, (a + b)² = a² + 2ab + b². This is known as a basic polynomial identity, and it shows that when you square a binomial (a two-term expression like a + b), you get three terms: the square of the first term (a²), twice the product of the two terms (2ab), and the square of the second term (b²). Therefore, the correct answer is C (a² + 2ab + b²)

5. Which of the following options correctly orders the numbers below from least to greatest? 235.971, 145.884, -271.906, -193.823

• A. -271.906, -193.823, 145.884, 235.971
• B. -271.906, 235.971, -193.823, 145.884
• C. 145.884, -193.823, 235.971, -271.906
• D. -193.823, -271.906, 145.884, 235.971

Correct answer: A

Rationale: To correctly order the numbers from least to greatest, we start with the smallest number, which is -271.906, followed by -193.823, 145.884, and finally 235.971. Therefore, the correct order is -271.906, -193.823, 145.884, 235.971. Choice A is correct. Choice B is incorrect as it incorrectly places 235.971 before -193.823. Choice C is incorrect as it starts with the largest number, 145.884. Choice D is incorrect as it starts with -193.823, which is not the smallest number in the list.

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