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Complete the following equation: 2 + (2)(2) - 2 · 2 = ?
- A. 5
- B. 3
- C. 2
- D. 1
Correct Answer: A
Rationale: To solve the equation, follow the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
1. Calculate inside the parentheses first: (2)(2) = 4.
2. Then, perform multiplication and division: 2 + 4 - 1 = 6 - 1 = 5.
Therefore, the correct answer is 5.
Choice B (3) is incorrect because multiplication is done before subtraction. Choices C (2) and D (1) are incorrect as they do not follow the correct order of operations to solve the equation.
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If Hannah spends at least $16 on 4 packages of coffee, which of the following inequalities represents the possible costs?
- A. 16 ≥ 4p
- B. 16 < 4p
- C. 16 > 4p
- D. 16 ≤ 4p
Correct Answer: D
Rationale: To represent the relationship between the number of packages of coffee and the minimum cost, the inequality can be written as 4p ≥ 16 (cost is at least $16). This inequality can also be expressed as 16 ≤ 4p, which reads as the cost being less than or equal to $16. Therefore, the correct answer is D. Choice A (16 ≥ 4p) implies that the cost can be greater than or equal to $16, which does not align with the statement that Hannah spends at least $16. Choice B (16 < 4p) suggests that the cost is less than $16, which contradicts the given information. Choice C (16 > 4p) indicates that the cost is greater than $16, which is not accurate based on the scenario provided.
The cost of renting a bicycle is $3.60 per hour. Which equation shows the best relationship between the total cost (C) and the number of hours (h) rented?
- A. C = 3.60h
- B. C = h + 3.60
- C. C = 3.60h + 10.80
- D. C = 10.80h
Correct Answer: A
Rationale: The best relationship is C = 3.60h because the cost increases by $3.60 for each hour of rental. This equation represents a linear relationship where the total cost (C) is directly proportional to the number of hours rented (h). Choice B (C = h + 3.60) is incorrect because it wrongly assumes a fixed additional cost of $3.60 regardless of the number of hours rented. Choice C (C = 3.60h + 10.80) is incorrect as it overestimates the initial cost. Choice D (C = 10.80h) is incorrect as it implies a constant rate of $10.80 per hour, which is not the case.
Joshua has to earn more than 92 points on a state test to qualify for a scholarship. Each question is worth 4 points, and the test has 30 questions. Which inequality can be solved to determine the number of questions Joshua must answer correctly?
- A. 4x < 30
- B. 4x < 92
- C. 4x > 30
- D. 4x > 92
Correct Answer: D
Rationale: Joshua must answer more than 92 points' worth of questions. Since each question is worth 4 points, the inequality is 4x > 92. Choice A (4x < 30) is incorrect as it represents that Joshua must answer less than 30 questions correctly, not earning more than 92 points. Choice B (4x < 92) is incorrect as it signifies that Joshua must earn less than 92 points, which contradicts the requirement. Choice C (4x > 30) is incorrect as it implies that Joshua must answer more than 30 questions correctly, but the threshold is 92 points, not 30 points.
Simplify the following expression:
3 (1/6) - 1 (5/6)
- A. 2 (1/3)
- B. 1 (1/3)
- C. 2 (1/9)
- D. 5/6
Correct Answer: B
Rationale: To simplify:
First, subtract the whole numbers: 3 - 1 = 2.
Then, subtract the fractions: (1/6) - (5/6) = - (4/6) = - (2/3).
Now, subtract (2 - 2/3) = 1 (1/3).
If Stella's current weight is 56 kilograms, which of the following is her approximate weight in pounds? (Note: 1 kilogram is approximately equal to 2.2 pounds.)
- A. 123 pounds
- B. 110 pounds
- C. 156 pounds
- D. 137 pounds
Correct Answer: A
Rationale: To convert Stella's weight from kilograms to pounds, you multiply her weight in kilograms (56) by the conversion factor (2.2): 56 2.2 = 123.2 pounds. Since we need to find the approximate weight in pounds, the closest option is 123 pounds, making choice A the correct answer. Choices B, C, and D are incorrect because they do not reflect the accurate conversion of Stella's weight from kilograms to pounds.