Answer:
24
Step-by-step explanation:
You don't really need to do a permutation here. We know that there are 4 options for digits and three places so therefore we have 4 choices for the first digit, 3 for the second and 2 for the last so the answer is 4 * 3 * 2 = 24.
Here are my answers!
the only one i’m not completely sure of is #4 but i’m assuming it’s where the function is above and below the x-axis
Answer:
Yes, double cosets partition G.
Step-by-step explanation:
We are going to define a <em>relation</em> over the elements of G.
Let
. We say that
if, and only if,
, or, equivalently, if
, for some
.
This defines an <em>equivalence relation over </em><em>G</em>, that is, this relation is <em>reflexive, symmetric and transitive:</em>
- Reflexivity: (
for all
.) Note that we can write
, where
is the <em>identity element</em>, so
and then
. Therefore,
. - Symmetry: (If
then
.) If
then
for some
and
. Multiplying by the inverses of h and k we get that
and is known that
and
. This means that
or, equivalently,
.
- Transitivity: (If
and
, then
.) If
and
, then there exists
and
such that
and
. Then,
where
and
. Consequently,
.
Now that we prove that the relation "
" is an equivalence over G, we use the fact that the <em>different equivalence classes partition </em><em>G.</em><em> </em>Since the equivalence classes are defined by
, then we're done.
Answer:
$0.41
Step-by-step explanation:
"per pound" tells you the the pounds should go on the bottom of a fraction (ratio, division)
see image. Divide to find the answer.
The median may stay the same.
The range will always change.
I dont think the last 2 will always change.