In a big high school, each student can use only Math Tutorial or Chemistry Tutorial. In September 2022, a study showed that 40% of students used Math Tutorial, 35% used Chemistry Tutorial, and the rest did not use either of them The study also found that 45% of the students who used Math Tutorial do not want to use it anymore, while 35% of them prefer to use Chemistry Tutorial in the next month. Moreover, 60% of students who used Chemistry Tutorial,

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In a big high school, each student can
use only Math Tutorial or Chemistry
Tutorial. In September 2022, a study
showed that 40% of students used Math
Tutorial, 35% used Chemistry Tutorial,
and the rest did not use either of them
The study also found that 45% of the
students who used Math Tutorial do not
want to use it anymore, while 35% of
them prefer to use Chemistry Tutorial in
the next month. Moreover, 60% of
students who used Chemistry Tutorial,
want
to continue that, while only 10% of them
want to use Math Tutorial instead of
that. 30% of students who did not use
either of them want to use Math Tutorial,
and 25% want to use Chemistry Tutorial.
a) Determine the state and transition
matrices.
b) Predict the percentage of students in
each Tutorial in the second month.
c) Represent the Transition matrix using
a directed graph with weighted
edges.
d) What is the final fixed number of
students in each tutorial.
Transcribed Image Text:In a big high school, each student can use only Math Tutorial or Chemistry Tutorial. In September 2022, a study showed that 40% of students used Math Tutorial, 35% used Chemistry Tutorial, and the rest did not use either of them The study also found that 45% of the students who used Math Tutorial do not want to use it anymore, while 35% of them prefer to use Chemistry Tutorial in the next month. Moreover, 60% of students who used Chemistry Tutorial, want to continue that, while only 10% of them want to use Math Tutorial instead of that. 30% of students who did not use either of them want to use Math Tutorial, and 25% want to use Chemistry Tutorial. a) Determine the state and transition matrices. b) Predict the percentage of students in each Tutorial in the second month. c) Represent the Transition matrix using a directed graph with weighted edges. d) What is the final fixed number of students in each tutorial.
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