I would say the answer is B. Best of luck
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:
Radius AC=12
Step-by-step explanation:
AB is a tangent to circle c so the tangent AB is perpendicular to the radius at A.
Then triangle ABC is right triangle at A.
So by Pythagoras theorem,
CB^2=AB^2 + AC^2
37^2= 35^2 + AC ^2
1369=1225 + AC^2
AC^2= 1369-1225= 144
AC=radical AC^2 =radical 144=12
Hope this helps...
(Note: ^ means power)
Answer: 463.96 mm² or 46.4 cm²
Step-by-step explanation:
Quarters are circular in shape so the surface area of one side will be the area of a circle.
Area of a circle = π * r²
Radius = Diameter / 2
= 24.3 / 2
= 12.15 mm
Area = 22/7 * 12.15²
= 463.96 mm²
Patrick's gross pay (GP) is the product of his hourly wage (W) and the number of hours (h) he worked. Expressed mathematically,
GP = W x h = ($15 / hour) x (28 hours) = $420
Thus, Patrick's gross pay for last week's work is $420.
