Final answer:
To identify Donte's mistake in the given expression, one must follow the order of operations and check each step systematically. Without seeing Donte's work, it's impossible to determine exactly which mistake he made. The potential mistakes listed in the question require an examination of Donte's work to provide a definitive answer.
Step-by-step explanation:
To identify Donte's mistake in simplifying the expression [4(1+3^2) - (8 - \(\frac{5}{4}\) \times (3 \times 2)) + 4 + 3 - 8 + 5 - 4 + 8], we must follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
First, calculate any operations inside parentheses:
- (1 + 3^2) = 1 + 9 = 10
- (8 - \(\frac{5}{4}\) \times (3 \times 2)) = (8 - \(\frac{5}{4}\) \times 6) = 8 - \(\frac{30}{4}\) = 8 - 7.5 = 0.5
Next, multiply and divide from left to right:
- 4 \times 10 = 40
- We already calculated \(\frac{5}{4}\) \times 6 in the previous step
Finally, add and subtract from left to right:
- 40 - 0.5 + 4 + 3 - 8 + 5 - 4 + 8
- Combine like terms to simplify: 40 + 4 + 3 + 5 + 8 - 0.5 - 8 - 4 = 48 + 18 - 0.5 = 66 - 0.5 = 65.5
If Donte made a mistake in one of these steps, it could be one of several potential mistakes listed in the question. Without seeing Donte’s work, we cannot definitively select the correct option (a, b, c, or d). Therefore, it's necessary to see how Donte processed each step to determine which specific mistake was made.
If any step in this sequence is done incorrectly, it could result in an error in the order of operations or another type of mistake, depending on what exactly was done incorrectly.