Tabitha Tidbits costs $7 per bag, and Figaro Flakes is $5.50 per bag.
You need to set up a system of equations. Use "x" for Tabitha Tidbits and "y" for Figaro Flakes, and let the total cost of each trip equal c. Using the equation ax+by=c, substitute the cost of each trip in for c, and the number of bags for each food for a and b respectively. The two equations will be:
3x+4y=43
3x+6y=54
Isolate x in the first equation and you will get:
x=(43-4y)/3
Substitute the above equation for x into the other equation:
3*((43-4y)/3)+6y=54
Isolate y in this equation, and you will get 11/2, which is 5.5
So the cost of one bag of Figaro Flakes is $5.50
Now substitute this into the equation where you isolated x:
(43-4(5.5))/3
You will get x=7, so a bag of Tabitha Tidbits is $7
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.
Identify the slope, m. This can be done by calculating the slope between two known points of the line using the slope formula.
Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.
Answer:
36
Step-by-step explanation:
