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Technically, alright is just a shortened, "incorrect" usage of all right. However, over time it has began to have a new meaning. It technically is just a one word spelling of the phrase "all right."
Typically we use "all right" when it is for sure correct or permissiable. When we use alright, in todays language, we are saying it is "satisfactory" or "okay."
In the samples you gave, the only real "appropriate" one in both cases would be "all right." Alright, by itself, is not technically an appropriate usage of the word.
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