No shady characters are honest. Some shady characters are highly respected people. Therefore, some highly respected people are honest. By looking at the diagram it is clear that conclusion is not necessarily supported by the premises. You might say that you know from everyday experience that the conclusion to this syllogism is true, but the structure of this syllogism is such that it does not establish a necessary connection between the premises and the conclusion.
All millionaires are rich people.
Some Americans are rich people. Therefore, some Americans are millionaires. Beginning with the A- claim, diagram both premises. In this situation we are forced to put the X on the line between areas 4 and 5, which immediately indicates the syllogism is invalid. Anytime you must place an X on a line you can immediately conclude that the particular syllogism is invalid.