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.
Answer:
y= -2/5x-13/5
Step-by-step explanation:
Answer:
answer is here
Step-by-step explanation:
https://www.mathpapa.com/algebra-calculator.html
Their distance would be 50 feet in 2.5 minutes, if the speeds remain constant.
The equation of a circle is
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center
and r is the radius
(-4, 2) being the center
and r = 5
means that
h = -4
k = 2
r = 5
so
(x - (-4))^2 + (y - 2)^2 = (5)^2
simplified
(x + 4)^2 + (y - 2)^2 = 25
Therefore your answer is C.
