Introduction:
In chemistry, the law of multiple proportions states that when two elements combine to form multiple compounds, the ratio of the masses of one element that combine with a fixed mass of the other element can be expressed in small whole numbers. In this case, we are examining the compounds formed by carbon and oxygen.

Data:
1. Carbon content in one compound: 42.9%
2. Carbon content in the other compound: 27.3%

Explanation:
To determine whether the data is in agreement with the law of multiple proportions, we need to compare the ratios of carbon to oxygen in the two compounds.

Step 1: Determine the ratio of carbon to oxygen in the first compound:
Since the carbon content in the first compound is 42.9%, the oxygen content can be calculated by subtracting the carbon percentage from 100%:

Oxygen content = 100% - 42.9% = 57.1%

Therefore, the ratio of carbon to oxygen in the first compound is 42.9% : 57.1%.

Step 2: Determine the ratio of carbon to oxygen in the second compound:
Similarly, since the carbon content in the second compound is 27.3%, the oxygen content can be calculated:

Oxygen content = 100% - 27.3% = 72.7%

Therefore, the ratio of carbon to oxygen in the second compound is 27.3% : 72.7%.

Step 3: Compare the ratios:
To determine whether the data follows the law of multiple proportions, we need to check if the ratio of carbon to oxygen in the two compounds can be expressed in small whole numbers.

The ratio in the first compound is approximately 0.75 : 1, while the ratio in the second compound is approximately 0.375 : 1.

Conclusion:
The data shows that the ratio of carbon to oxygen in the two compounds cannot be expressed in small whole numbers. Therefore, the data is not in agreement with the law of multiple proportions. This suggests that there may be another compound or factors influencing the composition of the compounds formed by carbon and oxygen. Further investigation and analysis are required to understand the exact nature of these compounds and their ratios.