Answer:
This means that Tina has enough t-shirts for the entire trip and doesn't need to pack any more t-shirts.
Step-by-step explanation:
In total, she has five t-shirts, and she is packing for a five-day trip. Therefore, she has enough shirts to last her the entire trip.
Given:
The cost C (in dollars) to participate in a ski club is given by,

Where x is the number of ski trips we take.
To find:
The number of ski trips when a total cost of $315 and $485 is spent.
Explanation:
Substituting C = 315 in the given equation we get,

Substituting C = 485 in the given equation we get,

Thus,
If we spend a total cost of $315, we can take 3 ski trips.
If we spend a total cost of $485, we can take 5 ski trips.
Final answer:
• If we spend a total cost of $315, we can take 3 ski trips.
,
• If we spend a total cost of $485, we can take 5 ski trips.
Answer:
a) 5:3
b) 7.5:5.3
Step-by-step explanation:
150min : 90min (1 and a half hour)
10 : 6
5 : 3
150 × 10 mm : 1060 mm
1500 : 1060
750 : 530
7.5 : 5.3
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.