Answer :
To determine which statements apply to the ratio of rice and water, let's analyze the given table of data:
| Rice (cups) | Water (cups) |
|-------------|--------------|
| 2 | 5 |
| 3 | 7.5 |
| 5 | 12.5 |
| 8 | 20 |
First, observe the relation between the amounts of rice and water. As the amount of rice increases, the amount of water also increases. Specifically, we can see that the amount of water needed is directly proportional to the amount of rice. This implies a direct relationship between the two quantities.
We need to decide which values are dependent and which are independent:
1. An independent value is one that determines the value of another quantity, while a dependent value is one that is determined by the independent value.
2. In this context, the amount of water required is based on the amount of rice, making the amount of water the dependent value and the amount of rice the independent value.
Next, let's verify the ratio of water to rice to see if it supports our understanding of the relationship. Calculating the ratio for each given pair:
- For 2 cups of rice: [tex]\( \frac{5}{2} = 2.5 \)[/tex]
- For 3 cups of rice: [tex]\( \frac{7.5}{3} = 2.5 \)[/tex]
- For 5 cups of rice: [tex]\( \frac{12.5}{5} = 2.5 \)[/tex]
- For 8 cups of rice: [tex]\( \frac{20}{8} = 2.5 \)[/tex]
Each ratio [tex]\( \frac{\text{water}}{\text{rice}} \)[/tex] equals 2.5, which confirms that there is a constant proportional relationship.
Therefore, based on the analysis, the following statements apply:
- The amount of water is the dependent value.
- The amount of rice is the independent value.
Thus, the correct options are:
1. The amount of water is the dependent value.
2. The amount of rice is the independent value.
| Rice (cups) | Water (cups) |
|-------------|--------------|
| 2 | 5 |
| 3 | 7.5 |
| 5 | 12.5 |
| 8 | 20 |
First, observe the relation between the amounts of rice and water. As the amount of rice increases, the amount of water also increases. Specifically, we can see that the amount of water needed is directly proportional to the amount of rice. This implies a direct relationship between the two quantities.
We need to decide which values are dependent and which are independent:
1. An independent value is one that determines the value of another quantity, while a dependent value is one that is determined by the independent value.
2. In this context, the amount of water required is based on the amount of rice, making the amount of water the dependent value and the amount of rice the independent value.
Next, let's verify the ratio of water to rice to see if it supports our understanding of the relationship. Calculating the ratio for each given pair:
- For 2 cups of rice: [tex]\( \frac{5}{2} = 2.5 \)[/tex]
- For 3 cups of rice: [tex]\( \frac{7.5}{3} = 2.5 \)[/tex]
- For 5 cups of rice: [tex]\( \frac{12.5}{5} = 2.5 \)[/tex]
- For 8 cups of rice: [tex]\( \frac{20}{8} = 2.5 \)[/tex]
Each ratio [tex]\( \frac{\text{water}}{\text{rice}} \)[/tex] equals 2.5, which confirms that there is a constant proportional relationship.
Therefore, based on the analysis, the following statements apply:
- The amount of water is the dependent value.
- The amount of rice is the independent value.
Thus, the correct options are:
1. The amount of water is the dependent value.
2. The amount of rice is the independent value.
