Not necessarily.
and
may be linearly dependent, so that their span forms a subspace of
that does not contain every vector in
.
For example, we could have
and
. Any vector
of the form
, where
, is impossible to obtain as a linear combination of these
and
, since
unless
and
.
The initial value is 309.35
It means that in the year 2010 (starting year) the population was 309,350,000 people or written another way "309.35 million". The second way is more short so probably the more preferred method.
To find the value 309.35, simply look at the table under the value t = 0.
If you're talking about the second part of the question where it asks you which facts you included in your answer, you can choose any of them and it will be counted right.
Let “x” represent the cost of the dryer in dollars
The washer costs 3x dollars
3x + x = 1000
4x = 1000
x = 250
The dryer is $250
Out of 8 men, 4 can be selected and lined up in (8 x 7 x 6 x 5) = 1,680 ways.
But within that number, each group of 4 appears in (4 x 3 x 2) = 24 orders.
So there are (1,680 / 24) = 70 different groups of men.
Out of 5 women, 3 can be selected and lined up in (5 x 4 x 3) = 60 ways.
But within that number, each group of 3 appears in (3 x 2) = 6 orders.
So there are (60 / 6) = 10 different groups of women.
Each different group of 70 men can be joined by any of the 10 groups
of women. So the total number of possible subcommittees is (70 x 10) = 700 .
