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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.
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What is the probability of consecutively pulling two more orange blocks, without replacement, from a bag containing 3 orange blocks, 5 green blocks, and 4 purple blocks?
- A. 3/12
- B. 3/55
- C. 2/10
- D. 1/3
Correct Answer: B
Rationale: To calculate the probability of consecutively pulling two more orange blocks without replacement, we first determine the probability of pulling an orange block on the first draw, which is 3/12 (3 orange blocks out of 12 total blocks). After removing one orange block, there are only 11 blocks left, so the probability of pulling another orange block on the second draw is 2/11. To find the combined probability, we multiply the probabilities together: (3/12) * (2/11) = 6/132 = 3/55. Therefore, the correct answer is B. Choice A (3/12) incorrectly simplifies the probability before calculating the second draw. Choice C (2/10) does not consider the specific number of orange blocks in the bag. Choice D (1/3) does not account for the reduced number of blocks after the first draw.
A patient requires a 30% decrease in the dosage of their medication. Their current dosage is 340 mg. What will their dosage be after the decrease?
- A. 70 mg
- B. 238 mg
- C. 270 mg
- D. 340 mg
Correct Answer: B
Rationale: To calculate a 30% decrease in 340 mg, you multiply 340 by 0.3, which equals 102 mg. Subtracting this from the current dosage gives 340 - 102 = 238 mg. Therefore, the correct answer is 238 mg. Choice A (70 mg) is incorrect because it represents a 70% decrease, not 30%. Choice C (270 mg) is incorrect as it does not reflect the correct calculation for a 30% decrease. Choice D (340 mg) is the initial dosage and not the reduced dosage after a 30% decrease.
Robert plans to drive 1,800 miles. His car gets 30 miles per gallon, and his tank holds 12 gallons. How many tanks of gas will he need for the trip?
- A. 4 tanks
- B. 5 tanks
- C. 6 tanks
- D. 7 tanks
Correct Answer: B
Rationale: To calculate how many gallons of gas Robert needs for the 1,800-mile trip, divide the total distance by the car's mileage per gallon: 1,800 miles · 30 mpg = 60 gallons. Since his tank holds 12 gallons, Robert will need 60 gallons · 12 gallons per tank = 5 tanks of gas for the trip. Choice A (4 tanks), Choice C (6 tanks), and Choice D (7 tanks) are incorrect as they do not correctly calculate the number of tanks needed based on the car's mileage and tank capacity.
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.
Which unit of measurement is larger, inches or centimeters?
- A. Inches are larger
- B. Centimeters are larger
- C. They are the same size
- D. It depends on the measurement
Correct Answer: A
Rationale: Inches are larger than centimeters. This is because one inch is equivalent to 2.54 centimeters. Therefore, when comparing the two units, inches are greater in length than centimeters. Choice B is incorrect as centimeters are smaller than inches. Choice C is incorrect as inches and centimeters are not the same size. Choice D is incorrect as the relationship between inches and centimeters is fixed, with inches being larger in general.