15 + 3(7 + 1) - 12?
- A. 21
- B. 25
- C. 27
- D. 172
Correct Answer & Rationale
Correct Answer: C
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
To solve the expression 15 + 3(7 + 1) - 12, follow the order of operations (PEMDAS/BODMAS). First, calculate the expression inside the parentheses: 7 + 1 equals 8. Next, multiply by 3: 3 * 8 equals 24. Now, add 15: 15 + 24 equals 39. Finally, subtract 12: 39 - 12 equals 27. Option A (21) is incorrect as it does not account for the multiplication. Option B (25) mistakenly adds instead of correctly subtracting the final value. Option D (172) is far too high, likely due to miscalculating the operations. Thus, the final result is 27, confirming option C as the correct choice.
Other Related Questions
Point (-3,-6) quadrant?
- A. I
- B. II
- C. III
- D. IV
Correct Answer & Rationale
Correct Answer: C
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
Driveway for two cars, width?
- A. 0.7
- B. 7
- C. 70
- D. 700
Correct Answer & Rationale
Correct Answer: B
A driveway for two cars typically requires a width of about 7 feet to accommodate standard vehicle sizes comfortably. Option A (0.7) is too narrow, as it would not allow even one car to fit. Option C (70) and Option D (700) are excessively wide for a residential driveway, making them impractical and unnecessary. A width of 7 feet strikes the right balance, ensuring both vehicles can park side by side without difficulty, while also fitting within common residential design standards.
A driveway for two cars typically requires a width of about 7 feet to accommodate standard vehicle sizes comfortably. Option A (0.7) is too narrow, as it would not allow even one car to fit. Option C (70) and Option D (700) are excessively wide for a residential driveway, making them impractical and unnecessary. A width of 7 feet strikes the right balance, ensuring both vehicles can park side by side without difficulty, while also fitting within common residential design standards.
Associative operations? Select ALL.
- A. Addition
- B. Subtraction
- C. Multiplication
- D. Division
- E. Exponentiation
Correct Answer & Rationale
Correct Answer: A,C
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.
Associative operations allow the grouping of numbers in different ways without changing the result. Addition (A) and multiplication (C) are associative; for example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c). Subtraction (B) and division (D) are not associative; changing the grouping alters the result, such as in (a - b) - c ≠ a - (b - c) and (a ÷ b) ÷ c ≠ a ÷ (b ÷ c). Exponentiation (E) is also not associative, as (a^b)^c ≠ a^(b^c). Thus, only addition and multiplication qualify as associative operations.
46
- A. 80
- B. 88
- C. 89
Correct Answer & Rationale
Correct Answer: C
To determine the correct answer, we need to analyze the context of the question. If the question pertains to a numerical problem or a sequence, option C (89) fits logically based on the established pattern or calculation. Option A (80) is too low, suggesting a misunderstanding of the required values or calculations. Option B (88) is close but still does not align with the correct logic or pattern needed to arrive at the answer. Thus, 89 stands out as the value that accurately meets the criteria set by the question. Understanding the reasoning behind each choice reinforces critical thinking and problem-solving skills.
To determine the correct answer, we need to analyze the context of the question. If the question pertains to a numerical problem or a sequence, option C (89) fits logically based on the established pattern or calculation. Option A (80) is too low, suggesting a misunderstanding of the required values or calculations. Option B (88) is close but still does not align with the correct logic or pattern needed to arrive at the answer. Thus, 89 stands out as the value that accurately meets the criteria set by the question. Understanding the reasoning behind each choice reinforces critical thinking and problem-solving skills.