Answer:
Step-by-step explanation:
Write a list of all possible outcomes
1-2
1-3
1-4
2-1
2-3
2-4
3-1
3-2
3-4
4-1
4-2
4-3
There are 12 possible outcomes. How many of them have totals of 6 or 7
I count 4
So the probability is 4/12 = 1/3, just as you said.
Is there an easier way?
You might be able to get the 12 easier.
You have 4 choices for the first number and 3 for the second.
P(12) = 4*3 = 12
Getting 6 or 7 might be somewhat trickier.
4 and 3 make seven. That gives two ways 4-3 and 3-4
4 and 2 make six. That gives 2 more ways 4-2 and 2-4
That's all that's possible.
answer: 4 ways make success. The total number of ways is 12.
Answer:




Step-by-step explanation:
Given
I will answer this question using the attached triangle
Solving (a): Sine and Cosine A
In trigonometry:
and

So:

Substitute values for BC and BA




Substitute values for AC and BA



Solving (b): Sine and Cosine B
In trigonometry:
and

So:

Substitute values for AC and BA




Substitute values for BC and BA



Using a calculator:

So:

-- approximated

-- approximated

So:

--- approximated

--- approximated
Answer:
C) a positive correlation
Step-by-step explanation:
<em>More people ⇒ Longer time</em> is a positive correlation between those variables. However, <em>longer time</em> is not the desired outcome.
Rather, <em>shorter time</em> is the desired outcome. The correlation between <em>more people</em> and <em>shorter time</em> is negative. In order to compute that correlation numerically, one would have to define a function that would give a numerical value for "shorter time" that would model the goodness of outcome as time gets shorter.
Given:
A triangle ABC.
The given expression for b is:

To find:
The expression that is equivalent to b.
Solution:
According to the Law of Cosines,

It can be written as:
...(i)
We have,
...(ii)
On comparing (i) and (ii), we get




Therefore, the required values are
.