Answer:
A
Step-by-step explanation:
the formula of the slope is (y2 - y1)/(x2 - x1)
slope = (3-2)/(-1-2) = 1/(-3) = -1/3
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:
189.98
Step-by-step explanation:
50 is half of 100, so 55/100 would be greater than 1/2
Answer:
64 inches
Step-by-step explanation:
We know the following:
- A chessboard is made of 64 white and black squares.
- The 64 squares are arranged in 8 rows and 8 columns.
- Each square is 2 inches thick.
From the first point, we see that a chessboard is a square. This means its length and width are equal.
This is also why the number of rows is equal to the number of columns.
It has been established that there are 8 rows (and 8 columns). Each row is made up of 8 squares.
Therefore, the length of 8 squares (a row) is:
L = 8 * 2 = 16 inches.
Hence, each row (and column) is 16 inches long.
Therefore, Perimeter will be:
P = 4L
P = 4 * 16
P = 64 inches
The perimeter of the chessboard is 64 inches.
