Final answer:
After calculating the expression 94/9 x (1.75 - 2/14 + 1/4), none of the provided options are equivalent. The correct calculation yields approximately 19.2698, and each option was evaluated and found not to match this result.
Therefore, none of the options are equivalent to the original expression.
Step-by-step explanation:
To find which expressions are equivalent to 94/9 x (1.75 - 2/14 + 1/4), we must first calculate the value inside the parenthesis and then multiply by 94/9.
Calculating inside the parenthesis:
- Convert 1.75 to fraction: 1.75 = 7/4.
- Find a common denominator for 2/14 and 1/4: The common denominator is 28.
- Convert fractions: 2/14 = 4/28 and 1/4 = 7/28.
- Combine fractions: (7/4 - 4/28 + 7/28) = (7/4 + 3/28)
- Convert 7/4 to twenty-eighths: 7/4 = 49/28.
- Add fractions: (49/28 + 3/28) = (52/28) which simplifies to 13/7 or approximately 1.8571.
Multiply this by 94/9:
- 94/9 * 13/7 = 1214/63.
- Converting to a decimal: 1214/63 ≈ 19.2698.
None of the options provided exactly match this result. However, let's evaluate them:
- A is just a sum of two fractions, not equivalent.
- B, 1.6875, is not equal to approximately 19.2698.
- C represents a sum of two fractions, not equivalent.
- D, -98/8 which is -12.25, is not equivalent.
- E, -1.125, also does not match.
- F, 74/4, simplifies to 18.5, which is also not equivalent.