What is a prime number?
- A. A number divisible by only 1 and itself
- B. A number divisible by 2 and 3
- C. A number divisible by any number
- D. A number with exactly three factors
Correct Answer: A
Rationale: The correct answer is A: 'A number divisible by only 1 and itself.' A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. This definition aligns with choice A. Choice B is incorrect because not all prime numbers are divisible by 2 and 3. Choice C is incorrect as prime numbers are not divisible by any number other than 1 and themselves. Choice D is incorrect because a prime number has exactly two factors, 1 and itself, not three factors.
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Which of the following relationships represents no correlation between two variables?
- A. As a student's class attendance decreases, the student's overall grade remains the same
- B. As the number of hours a person exercises decreases, the weight of that person increases
- C. As the number of miles driven increases, the amount of gasoline in the tank decreases
- D. As the amount of water a plant receives increases, the growth rate of the plant increases
Correct Answer: A
Rationale: Choice A represents no correlation between two variables as it states that as a student's class attendance decreases, the student's overall grade remains the same. This scenario shows no relationship between class attendance and grade. In contrast, choices B, C, and D show clear correlations between the variables mentioned. Choice B indicates a negative correlation between exercise hours and weight gain, choice C indicates a negative correlation between miles driven and gasoline in the tank, and choice D indicates a positive correlation between water intake and plant growth rate, making them all examples of correlated relationships.
When the weights of the newborn babies are graphed, the distribution of weights is symmetric with the majority of weights centered around a single peak. Which of the following describes the shape of this distribution?
- A. Uniform
- B. Bimodal
- C. Bell-shaped
- D. Skewed right
Correct Answer: C
Rationale: The correct answer is C: Bell-shaped. A symmetric distribution with a single peak is characteristic of a bell-shaped distribution, also known as a normal distribution. This distribution forms a symmetrical, bell-like curve when graphed. Choice A, 'Uniform,' would describe a distribution where all values have equal probability. Choice B, 'Bimodal,' would indicate a distribution with two distinct peaks. Choice D, 'Skewed right,' suggests a distribution where the tail on the right side is longer or more pronounced, unlike the symmetrical bell-shaped distribution described in the question.
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.
How do you find the least common multiple?
- A. List all multiples of the numbers, then find the smallest common one
- B. List all factors of the numbers, then find the largest common one
- C. Divide the largest number by the smallest
- D. Multiply the two numbers together
Correct Answer: A
Rationale: The correct way to find the least common multiple is to list all the multiples of each number and then identify the smallest common multiple. Choice A is correct because it describes the correct process. Listing factors, as suggested in choice B, helps in finding the greatest common factor, not the least common multiple. Dividing the largest number by the smallest, as mentioned in choice C, does not help find the least common multiple. Multiplying the two numbers together, as stated in choice D, results in their least common multiple when the numbers have no common factors.
Which of the following expressions represents the sum of three times a number and eight times a different number?
- A. 3x + 8y
- B. 8x + 3x
- C. 3x - 8y
- D. 8x - 3y
Correct Answer: A
Rationale: The correct expression for the sum of three times a number and eight times a different number is given by 3x + 8y. This represents adding three times the variable x (3x) to eight times the variable y (8y). Choice B (8x + 3x) is incorrect as it represents adding eight times x to three times x, which is redundant. Choice C (3x - 8y) is incorrect because it represents subtracting eight times y from three times x, not their sum. Choice D (8x - 3y) is also incorrect as it represents subtracting three times y from eight times x, not their sum.