Pregunta
A survey shows that
of the Americans like cheese whereas
like apples. If
of the Americans like both cheese and
apples, then
apples, then
Ask by Jimenez Jimenez. in Nigeria
Dec 28,2024
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The percentage of Americans who like both cheese and apples is between 39% and 63%.
Solución

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Respondido por UpStudy AI y revisado por un tutor profesional
Como
Mind Expander
To solve this problem, we can use the principle of inclusion-exclusion from set theory. Given that
is the set of Americans who like cheese and
is the set of Americans who like apples, we have:
We want to find the percentage
of Americans who like both cheese and apples, which can be represented as
.
Using the inclusion-exclusion principle:
This means that the percentage of people who like either cheese or apples (or both) cannot exceed 100%. Therefore, we have:
Substituting the known values:
Simplifying this gives:
On the other hand, since
represents the percentage of people who like cheese and apples, it cannot exceed the percentage of those who like cheese:
Combining these inequalities, we find:
Thus, the answer is
.

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