Final answer:
After calculating both expressions 3.2^2-1 and 10-0.33x2 and comparing their values 9.24 and 9.34 respectively, we conclude that the correct symbol to join them is a not equals sign (≠), since the values are not equal.
Step-by-step explanation:
The student's question revolves around the decision on what mathematical symbol should connect two expressions: 3.22-1 and 10-0.33x2. To determine which symbol is appropriate, we must evaluate both expressions. Performing the calculations, we square 3.2 to get 10.24, subtract 1 to obtain 9.24 for the first expression. For the second expression, we multiply 0.33 by 2 to get 0.66 and subtract that from 10 to get 9.34.
The two results are close, but since they are not identical, an equal sign is not suitable. The two expressions could be connected using a not equals sign (≠), as they are not equal in value. However, in the absence of additional context such as an applied rounding or approximation, none of the other options (inequality, equation) are directly applicable to the expressions as presented. If this were a case of approximation, we might use ≈ (approximately equal to), but this option is not provided.
Therefore, the correct symbol to connect the two expressions in this context is a not equals sign, indicating that 3.22-1 ≠ 10-0.33x2.