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For all numbers x[x] denotes the value o...

For all numbers x[x] denotes the value of `x^3` rounded to the nearest multiple of ten.
`{:("Column A"," ","Column B"),([x + 1],,[x] + 1):}`

A

If column A is larger

B

If column B is larger

C

If the columns are equal

D

If there is not enough information to decide

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the two columns based on the function defined as the value of \( x^3 \) rounded to the nearest multiple of ten. We will evaluate both columns for different values of \( x \) to determine which column is larger or if there is not enough information to decide. ### Step-by-Step Solution 1. **Understanding the Columns**: - **Column A**: \( [x + 1] \) - **Column B**: \( [x] + 1 \) - Here, \( [x] \) denotes the value of \( x^3 \) rounded to the nearest multiple of ten. 2. **Evaluate for \( x = 0 \)**: - **Column A**: \[ [0 + 1] = [1] \] Calculate \( 1^3 = 1 \) and round to the nearest multiple of ten: \[ [1] = 0 \] - **Column B**: \[ [0] + 1 = [0] + 1 \] Calculate \( 0^3 = 0 \) and round to the nearest multiple of ten: \[ [0] = 0 \quad \Rightarrow \quad 0 + 1 = 1 \] - **Comparison**: Column A = 0, Column B = 1. Thus, Column B is larger. 3. **Evaluate for \( x = 1 \)**: - **Column A**: \[ [1 + 1] = [2] \] Calculate \( 2^3 = 8 \) and round to the nearest multiple of ten: \[ [2] = 10 \] - **Column B**: \[ [1] + 1 = [1] + 1 \] Calculate \( 1^3 = 1 \) and round to the nearest multiple of ten: \[ [1] = 0 \quad \Rightarrow \quad 0 + 1 = 1 \] - **Comparison**: Column A = 10, Column B = 1. Thus, Column A is larger. 4. **Conclusion**: - For \( x = 0 \), Column B is larger. - For \( x = 1 \), Column A is larger. - Since the results vary depending on the value of \( x \), we conclude that there is not enough information to decide which column is consistently larger. ### Final Answer There is not enough information to decide which column is larger.
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