Final answer:
The fractional part 't' of the total participants that the Hispanic participants account for in Josue's survey is calculated as 1/8 of the remaining participants, which is expressed as 't' = 1/8 * (1 - ('a' + 'b' + 1/2)), where 'a' is the fraction of African participants and 'b' is the fraction of Asian participants.
Step-by-step explanation:
To determine the fractional part 't' that Hispanic participants account for in Josue's survey, we need to account for the given fractions of the other groups first. We know that half of the participants are American, but the fraction of African and Asian participants is not specified. Let's denote the fraction of African participants as 'a' and the fraction of Asian participants as 'b'.
Since the Hispanic participants account for 1/8 of the remaining participants, we have to first calculate the remaining participants after accounting for American, African, and Asian participants.
The equation representing all participants is: a + b + 1/2 + (remaining participants) = 1. The remaining participants can be represented as: 1 - (a + b + 1/2).
The Hispanic fraction 't' of the total is 1/8 of the remaining, so 't' = 1/8 * (1 - (a + b + 1/2)). Without knowing the values of 'a' and 'b', we cannot simplify this further. Should the fractions for African and Asian participants be given, we could substitute these into the equation and calculate 't' explicitly.