For calculating the mean, you want to add up all of the numbers then divide by how many numbers there are. So you'd do:
5+10+12+4+6+11+13+5 then divide that by 8
The answer to your question is: 8.25
Answer:
Step-by-step explanation:
a)
The mistaken assumption is that Apple spends "far less" on Research and Development than any of its rivals.
b)
The assumption is incorrect because it took cognizance of the percentage used, and not the actual money spent. In truth, Apple generates far more income than the other two rivals. With Apple generating over $100bn in the said time span, and Google generating $37bn. At the end of the day, Apple spends $2.1bn on Research and Development, while Google spends $5.3bn on the same. This is quite close than the quoted distance of 14% - 2%
c)
Yes, I think so. But only when the 3 companies generate almost the same revenue.
Its answer c) 6
Have a great day
I'll give you an example from topology that might help - even if you don't know topology, the distinction between the proof styles should be clear.
Proposition: Let
S
be a closed subset of a complete metric space (,)
(
E
,
d
)
. Then the metric space (,)
(
S
,
d
)
is complete.
Proof Outline: Cauchy sequences in (,)
(
S
,
d
)
converge in (,)
(
E
,
d
)
by completeness, and since (,)
(
S
,
d
)
is closed, convergent sequences of points in (,)
(
S
,
d
)
converge in (,)
(
S
,
d
)
, so any Cauchy sequence of points in (,)
(
S
,
d
)
must converge in (,)
(
S
,
d
)
.
Proof: Let ()
(
a
n
)
be a Cauchy sequence in (,)
(
S
,
d
)
. Then each ∈
a
n
∈
E
since ⊆
S
⊆
E
, so we may treat ()
(
a
n
)
as a sequence in (,)
(
E
,
d
)
. By completeness of (,)
(
E
,
d
)
, →
a
n
→
a
for some point ∈
a
∈
E
. Since
S
is closed,
S
contains all of its limit points, implying that any convergent sequence of points of
S
must converge to a point of
S
. This shows that ∈
a
∈
S
, and so we see that →∈
a
n
→
a
∈
S
. As ()
(
a
n
)
was arbitrary, we see that Cauchy sequences in (,)
(
S
,
d
)
converge in (,)
(
S
,
d
)
, which is what we wanted to show.
The main difference here is the level of detail in the proofs. In the outline, we left out most of the details that are intuitively clear, providing the main idea so that a reader could fill in the details for themselves. In the actual proof, we go through the trouble of providing the more subtle details to make the argument more rigorous - ideally, a reader of a more complete proof should not be left wondering about any gaps in logic.
(There is another type of proof called a formal proof, in which everything is derived from first principles using mathematical logic. This type of proof is entirely rigorous but almost always very lengthy, so we typically sacrifice some rigor in favor of clarity.)
As you learn more about a topic, your proofs typically begin to approach proof outlines, since things that may not have seemed obvious before become intuitive and clear. When you are first learning it is best to go through the detailed proof to make sure that you understand everything as well as you think you do, and only once you have mastered a subject do you allow yourself to omit obvious details that should be clear to someone who understands the subject on the same level as you.
