Answer:
hello, This can be solved using your standard rise over run slope calculation. Think of the number of years after 1990 as your input variable. 2007 would be 17 years after 1990, so the "y" variable would be 17. This is your "run", and it goes in the denominator of your slope calculation. Then the difference between the 2007 population and the 1990 population would be the "p" variable difference, the "rise", which is 92500. Dividing, you will get 5441.17. Since we're talking about humans, we can't have a decimal, so let's round up to 5442.
Using the slope-intercept form of a linear equation (y = ax + b), we will say that p = 5442y + 123000. Do you know why we add the 123000? It's because that's the starting value, which is equivalent to the "intercept" in the slope-intercept form.
Hope this helps.
Step-by-step explanation:
Part (a)
There are 7 red out of 7+3 = 10 total
<h3>Answer: 7/10</h3>
==========================================================
Part (b)
We have 3 green out of 10 total
<h3>Answer: 3/10</h3>
==========================================================
Part (c)
3/10 is the probability of getting green on any selection. This is because we put the first selection back (or it is replaced with an identical copy)
So (3/10)*(3/10) = 9/100 is the probability of getting two green in a row.
<h3>Answer: 9/100</h3>
==========================================================
Part (d)
Similar to part (c) we have 7/10 as the probability of getting red on each independent selection.
(7/10)*(7/10) = 49/100
<h3>Answer: 49/100</h3>
==========================================================
Part (e)
7/10 is the probability of getting red and 3/10 is the probability of getting green. Each selection is independent of any others.
(7/10)*(3/10) = 21/100
<h3>Answer: 21/100</h3>
==========================================================
Part (f)
We have the exact same set up as part (e). Notice how (7/10)*(3/10) is the same as (3/10)*(7/10).
<h3>Answer: 21/100</h3>
We are choosing 2
2
r
shoes. How many ways are there to avoid a pair? The pairs represented in our sample can be chosen in (2)
(
n
2
r
)
ways. From each chosen pair, we can choose the left shoe or the right shoe. There are 22
2
2
r
ways to do this. So of the (22)
(
2
n
2
r
)
equally likely ways to choose 2
2
r
shoes, (2)22
(
n
2
r
)
2
2
r
are "favourable."
Another way: A perhaps more natural way to attack the problem is to imagine choosing the shoes one at a time. The probability that the second shoe chosen does not match the first is 2−22−1
2
n
−
2
2
n
−
1
. Given that this has happened, the probability the next shoe does not match either of the first two is 2−42−2
2
n
−
4
2
n
−
2
. Given that there is no match so far, the probability the next shoe does not match any of the first three is 2−62−3
2
n
−
6
2
n
−
3
. Continue. We get a product, which looks a little nicer if we start it with the term 22
2
n
2
n
. So an answer is
22⋅2−22−1⋅2−42−2⋅2−62−3⋯2−4+22−2+1.
2
n
2
n
⋅
2
n
−
2
2
n
−
1
⋅
2
n
−
4
2
n
−
2
⋅
2
n
−
6
2
n
−
3
⋯
2
n
−
4
r
+
2
2
n
−
2
r
+
1
.
This can be expressed more compactly in various ways.
1. Let A(a,b) be a point in the coordinate axis. The reflection of A with respect to the x-axis is the point A'(a, -b).
2. So the reflection of C(6, 4) is C'(6, -4)
3. Remark, a picture is always helpful when dealing with reflections.
