Nokea
Joshua needs more than 92 points to qualify for a scholarship. Each question is worth 4 points, and there are 30 questions. What inequality determines how many questions he must answer correctly?
- A. 4x < 92
- B. 4x > 92
- C. 4x < 120
- D. 4x > 120
Correct Answer: B
Rationale: To determine the number of questions Joshua must answer correctly, we divide the total points required (92) by the points per question (4) to get 23. Since he needs more than 92 points, he must answer more than 23 questions correctly, which is represented by the inequality 4x > 92. Choices A, C, and D are incorrect because they do not accurately reflect the requirement for Joshua to answer more than 92 points' worth of questions.
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What is the least common denominator of two fractions?
- A. The smallest number that is a multiple of both denominators
- B. The smallest number that both fractions can divide into evenly
- C. The least common multiple of both denominators
- D. The greatest common factor of both denominators
Correct Answer: C
Rationale: The least common denominator of two fractions is the least common multiple of both denominators. This is because the least common denominator is the smallest number that both denominators can divide into evenly, ensuring that both fractions can be expressed with a common denominator. Choice A is incorrect as the least common denominator is a multiple of both denominators, not a number that multiplies into both. Choice B is incorrect because the common denominator needs to be a multiple of both denominators, not just a number they can divide into evenly. Choice D is incorrect as the greatest common factor is not used to find the least common denominator, but rather the least common multiple.
What is the equation that describes the relationship between x and y in the table below: x = 2, y = 6; x = 3, y = 9; x = 4, y = 12?
- A. y = 3x
- B. x = 3y
- C. y = x/3
- D. y = x + 3
Correct Answer: A
Rationale: The correct answer is y = 3x. By examining the table provided, we can see that for each increase of 1 in x, y increases by 3. This consistent pattern indicates that y is three times the value of x, leading to the equation y = 3x. Choices B, C, and D do not match the pattern observed in the table and are therefore incorrect.
When is a histogram preferred over a bar graph?
- A. Comparison between categories
- B. Frequency
- C. Percentages
- D. Proportions
Correct Answer: B
Rationale: Histograms are specifically designed to display the frequency distribution of continuous data, showing the distribution of values over intervals or bins. On the other hand, bar graphs are used to compare different categories or discrete data points. Therefore, the correct answer is B. Choices A, C, and D are incorrect because histograms are not primarily used for comparing categories, percentages, or proportions, but rather for visualizing the distribution of frequencies within data intervals.
Which is larger, feet or meters? What is the correct conversion factor between feet and meters?
- A. Feet are larger; 1 foot is 0.3048 meters
- B. Meters are larger; 1 meter is 3.28 feet
- C. Feet are smaller; 1 foot is 0.5 meters
- D. Meters are smaller; 1 meter is 2 feet
Correct Answer: A
Rationale: The correct answer is A. Feet are larger than meters. The conversion factor between feet and meters is 1 foot = 0.3048 meters. Choice B is incorrect as it states that meters are larger than feet, which is the opposite of the truth. Choice C is incorrect as it provides an incorrect conversion factor of 1 foot = 0.5 meters, which is inaccurate. Choice D is also incorrect as it suggests that meters are smaller than feet, which is not true.
How many pints are in a gallon?
- A. 2 pints
- B. 4 pints
- C. 8 pints
- D. 16 pints
Correct Answer: C
Rationale: The correct answer is C: 8 pints. In the U.S. customary system, there are 8 pints in a gallon. This conversion is essential to know for various activities like cooking, measuring liquids, or understanding container volumes. Choice A, 2 pints, is incorrect as it represents half a gallon. Choice B, 4 pints, is incorrect as it represents a half-gallon or a quart. Choice D, 16 pints, is incorrect as it represents two gallons. Therefore, the correct answer is C, 8 pints.