Answer: 15/32
Step-by-step explanation:
The data that we have is:
5/8 of the vegetable sold where green.
of theses 5/8, 3/4 were string beans.
Then the 3/4 is applied to the 5/8 of green vegetables.
Then the fraction (of the total number of vegetables) that were string beans was:
F = (3/4)*(5/8) = (3*5)/(4*8) = 15/32
The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars 
(not all zero) such that
which leads to the system of linear equations,
From the third equation, we have 
, and substituting this into the second equation gives
and in turn, 
. Substituting these into the first equation gives
which tells us that any value of 
will work. If 
, then 
and 
. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.
Answer:
16
Step-by-step explanation:
We can use the Pythagorean theorem to find the height
a^2 + b^2 = c^2 with a and b legs and c the hypotenuse
The triangle is a right triangle with legs GH and FG and hypotenuse FH
FG^2 + GH^2 = FH^2
FG ^2 + 12^2 = 20^2
FG^2 +144 = 400
Subtract 144 from each side
FG^2 +144-144 = 400-144
FG^2 =256
Take the square root of each side
sqrt(FG^2) =sqrt(256)
FG = 16
We have that
the volume of a right square pyramid ---------- > (1/3)b²h
Let
V1------------ > initial volume
V1=(1/3)b²h
<span>if its height is multiplied by 8
</span>
V2=(1/3)b²(8h)-------------- > V2=V1*8
therefore
the answer is the option D
the factor is is 8
