12. Which of the following rafional numbers are equal to -16 ? 13. Which of the following rational numbers are equal to $$ \frac{3}{5} $$ ? $$ \frac{12}{20}, \frac{-3}{-5}, 0.3, \frac{6}{10} $$ 14. Which of the following rational numbers are equal to $$ \frac{12}{15} $$ ? $$ \frac{4}{5}, \frac{40}{50},-\frac{8}{10}, \frac{8}{10} $$ 5. The weight $$ w $$ of an object in pounds is related to its distance $$ d $$ from the

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Sure, let's address each of your questions based on the information provided.

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### **Question 12**
**Which of the following rational numbers are equal to -16?**

*It seems like the list of options for this question is missing. Could you please provide the possible rational numbers to consider?*

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### **Question 13**
**Which of the following rational numbers are equal to $$ \frac{3}{5} $$?**

Given Options:
- $$ \frac{12}{20} $$
- $$ \frac{-3}{-5} $$
- $$ 0.3 $$
- $$ \frac{6}{10} $$

**Let's evaluate each option:**

1. **$$ \frac{12}{20} $$:**
   $$
   \frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}
   $$
   **Equal to $$ \frac{3}{5} $$.**

2. **$$ \frac{-3}{-5} $$:**
   $$
   \frac{-3}{-5} = \frac{3}{5} \quad (\text{Negative signs cancel out})
   $$
   **Equal to $$ \frac{3}{5} $$.**

3. **$$ 0.3 $$:**
   $$
   0.3 = \frac{3}{10}
   $$
   **Not equal to $$ \frac{3}{5} $$.**

4. **$$ \frac{6}{10} $$:**
   $$
   \frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5}
   $$
   **Equal to $$ \frac{3}{5} $$.**

**_Conclusion:_** The rational numbers equal to $$ \frac{3}{5} $$ are:
- $$ \frac{12}{20} $$
- $$ \frac{-3}{-5} $$
- $$ \frac{6}{10} $$

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### **Question 14**
**Which of the following rational numbers are equal to $$ \frac{12}{15} $$?**

Given Options:
- $$ \frac{4}{5} $$
- $$ \frac{40}{50} $$
- $$ -\frac{8}{10} $$
- $$ \frac{8}{10} $$

First, simplify $$ \frac{12}{15} $$:
$$
\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}
$$

**Now, evaluate each option:**

1. **$$ \frac{4}{5} $$:**
   $$
   \frac{4}{5} = \frac{4}{5} \quad (\text{Already simplified})
   $$
   **Equal to $$ \frac{12}{15} $$.**

2. **$$ \frac{40}{50} $$:**
   $$
   \frac{40}{50} = \frac{40 \div 10}{50 \div 10} = \frac{4}{5}
   $$
   **Equal to $$ \frac{12}{15} $$.**

3. **$$ -\frac{8}{10} $$:**
   $$
   -\frac{8}{10} = -\frac{8 \div 2}{10 \div 2} = -\frac{4}{5}
   $$
   **Not equal to $$ \frac{12}{15} $$.**

4. **$$ \frac{8}{10} $$:**
   $$
   \frac{8}{10} = \frac{8 \div 2}{10 \div 2} = \frac{4}{5}
   $$
   **Equal to $$ \frac{12}{15} $$.**

**_Conclusion:_** The rational numbers equal to $$ \frac{12}{15} $$ are:
- $$ \frac{4}{5} $$
- $$ \frac{40}{50} $$
- $$ \frac{8}{10} $$

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### **Question 5**
**The weight $$ w $$ of an object in pounds is related to its distance $$ d $$ from the…**

*It appears that the question is incomplete. Could you please provide the full question or additional details so I can assist you effectively?*

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Feel free to provide the missing information for questions 12 and 5, and I'll be happy to help!
**Question 12:** Cannot determine which rational numbers are equal to -16 without the provided options. **Question 13:** The rational numbers equal to $$ \frac{3}{5} $$ are $$ \frac{12}{20} $$, $$ \frac{-3}{-5} $$, and $$ \frac{6}{10} $$. **Question 14:** The rational numbers equal to $$ \frac{12}{15} $$ are $$ \frac{4}{5} $$, $$ \frac{40}{50} $$, and $$ \frac{8}{10} $$. **Question 5:** Cannot answer the question as it is incomplete.

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