See explanation below.
Explanation:
The 'difference between roots and factors of an equation' is not a straightforward question. Let's define both to establish the link between the two..
Assume we have some function of a single variable
x
;
we'll call this
f
(
x
)
Then we can form an equation:
f
(
x
)
=
0
Then the "roots" of this equation are all the values of
x
that satisfy that equation. Remember that these values may be real and/or imaginary.
Now, up to this point we have not assumed anything about
f
x
)
. To consider factors, we now need to assume that
f
(
x
)
=
g
(
x
)
⋅
h
(
x
)
.
That is that
f
(
x
)
factorises into some functions
g
(
x
)
×
h
(
x
)
If we recall our equation:
f
(
x
)
=
0
Then we can now say that either
g
(
x
)
=
0
or
h
(
x
)
=
0
.. and thus show the link between the roots and factors of an equation.
[NB: A simple example of these general principles would be where
f
(
x
)
is a quadratic function that factorises into two linear factors.
Answer:
Step-by-step explanation:
The total number of students is 350 + 50 + 225 + 375 = 1000.
There are 225 students in band only, as well as 50 students in both band and choir. So there are 275 students in band out of the total of 1000, or 27.5%.
There are 350 students in choir only, as well as 50 students in both choir and band. So there are 400 students in choir, 50 of whom are also in band. So the probability is 50/400, or 12.5%.
The probabilities are not the same.
Since the probabilities are not the same, the probability of being in band is affected by whether or not the student is in choir. So the events are not independent.
