Answer:
\frac{15a+20b}{6} 15a+20b/6
Step-by-step explanation:
\mathrm{Apply\:the\:fraction\:rule}:\quad \:a\cdot \frac{b}{c}=\frac{a\cdot \:b}{c}
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.
First you have to find a common denominator which is 8.
1/2 =4/8
7/8 - 4/8 = 3/8
So the answer is 3/8.
21 full tables because if you divide the amount of plates you have by the amount of plates needed for each table you’ll get 21.5 but they asked for full tables so that would be 21
4a+9=(-9+30-25). 4a+9=30-34. 4a+9=-4. 4a=-13. A=-3.25 :)
