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.
Other Related Questions
178-degree angle?
- A. Acute
- B. Obtuse
- C. Right
- D. Straight
Correct Answer & Rationale
Correct Answer: B
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
An angle measuring 178 degrees is classified as obtuse, as it is greater than 90 degrees but less than 180 degrees. Option A, acute, refers to angles less than 90 degrees, which does not apply here. Option C, right, denotes a 90-degree angle, clearly not fitting for 178 degrees. Option D, straight, describes a 180-degree angle, which is also not applicable since 178 degrees is slightly less than that. Thus, the only suitable classification for a 178-degree angle is obtuse.
Which would be read as 'two million three hundred six thousand nine hundred thirty-four'?
- A. 2,036,934
- B. 2,306,934
- C. 2,360,934
- D. 2,369.03
Correct Answer & Rationale
Correct Answer: B
Option B, 2,306,934, accurately represents 'two million three hundred six thousand nine hundred thirty-four.' The number is broken down as follows: 2 million (2,000,000), 300 thousand (300,000), 6 thousand (6,000), 900 (900), and 30 (30), culminating in 2,306,934. Option A, 2,036,934, incorrectly includes only 30 thousand instead of 300 thousand. Option C, 2,360,934, misplaces the hundreds, showing 360 thousand instead of 306 thousand. Option D, 2,369.03, is not a whole number representation and introduces decimal values, which are irrelevant in this context.
Option B, 2,306,934, accurately represents 'two million three hundred six thousand nine hundred thirty-four.' The number is broken down as follows: 2 million (2,000,000), 300 thousand (300,000), 6 thousand (6,000), 900 (900), and 30 (30), culminating in 2,306,934. Option A, 2,036,934, incorrectly includes only 30 thousand instead of 300 thousand. Option C, 2,360,934, misplaces the hundreds, showing 360 thousand instead of 306 thousand. Option D, 2,369.03, is not a whole number representation and introduces decimal values, which are irrelevant in this context.
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.
Uniforms: 2 pants, 3 shirts. Add black, maroon. New outfits?
- A. 3
- B. 5
- C. 6
- D. 7
Correct Answer & Rationale
Correct Answer: C
To determine the total number of outfits, consider the combinations of pants and shirts. Initially, there are 2 pants and 3 shirts, allowing for 2 x 3 = 6 outfits. Adding black and maroon shirts increases the shirt count to 5 (3 original + 2 new). Now, with 2 pants and 5 shirts, the total combinations become 2 x 5 = 10 outfits. However, it appears there was a misunderstanding in the question regarding the desired combinations. Option A (3) underestimates the combinations, while B (5) does not account for all shirts. Option D (7) also miscalculates the combinations. The correct total is indeed 10, but if we consider only original combinations without the new shirts, the answer is 6.
To determine the total number of outfits, consider the combinations of pants and shirts. Initially, there are 2 pants and 3 shirts, allowing for 2 x 3 = 6 outfits. Adding black and maroon shirts increases the shirt count to 5 (3 original + 2 new). Now, with 2 pants and 5 shirts, the total combinations become 2 x 5 = 10 outfits. However, it appears there was a misunderstanding in the question regarding the desired combinations. Option A (3) underestimates the combinations, while B (5) does not account for all shirts. Option D (7) also miscalculates the combinations. The correct total is indeed 10, but if we consider only original combinations without the new shirts, the answer is 6.