1. **Problem 1: Average height expression** The botanist has 4 plants with an average height of 23.2 cm. A fifth plant with height $x$ cm is added. 2. **Formula for average**: $$\text{Average} = \frac{\text{Sum of all heights}}{\text{Number of plants}}$$ 3. **Calculate sum of first 4 plants**: $$\text{Sum of 4 plants} = 4 \times 23.2 = 92.8$$ 4. **Add fifth plant height**: $$\text{Total sum} = 92.8 + x$$ 5. **Calculate new average with 5 plants**: $$\text{New average} = \frac{92.8 + x}{5}$$ 6. **Simplify expression using original average**: Since $92.8 = 4 \times 23.2$, the expression can be written as: $$\frac{4 \times 23.2 + x}{5} = \frac{4 \times 23.2 + x}{5}$$ 7. **Answer for problem 1**: The correct expression is $\frac{23.2 + x}{5}$ only if $23.2$ represented the total sum, but it represents the average, so the correct choice is: $$\boxed{\frac{92.8 + x}{5}}$$ Since the options show $\frac{23.2 + x}{5}$, the closest correct expression is option D: $\frac{(23.2) + x}{5}$, but this is incorrect because it ignores the multiplication by 4. **Therefore, none of the options exactly match the correct formula, but option D is the closest in form.** --- 8. **Problem 2: Function $\otimes$ defined as $j \otimes s = 4js - s^2$** Calculate $-3 \otimes 2$: $$-3 \otimes 2 = 4 \times (-3) \times 2 - 2^2 = -24 - 4 = -28$$ Calculate $2 \otimes -3$: $$2 \otimes -3 = 4 \times 2 \times (-3) - (-3)^2 = -24 - 9 = -33$$ Correct answers: - $-3 \otimes 2 = -28$ (Option A) - $2 \otimes -3 = -33$ (Option C) --- 9. **Problem 3: Survey bias** The owner offers an optional survey at a sporting event to learn about community preferences. - Since the survey is optional, some people may choose not to answer, which can cause bias. - People at the sporting event may not represent the entire community. The best description is: **D. The data will be biased because the people at the sporting event do not represent the interest of the entire community.**