The centre of this circle is at 12
1
2
and has radius 12
1
2
, so the equation is (−12)2+2=12
(
x
−
1
2
)
2
+
y
2
=
1
2
.
Record the data on the line plot. <---------------------> 1,3,1,1,2,2,3,3,4,5,4,3,1,2
igomit [66]
1 3
1 2 3
1 2 3 4
<---- 1 2 3 4 5---->
something like this.. where you put the numbers on top of one another in order creating a line plot of your data, with the numbers above the line
The best thing to do here is to put each of these into fractions, with the total (31) as the denominator.
14/31= silver
6/31= black
8/31= copper
3/31= various colours.
As you're looking for the keys that are silver or copper, you've got to add the two denominators together, which gives you 14+8= 22.
This cannot be simplified further, therefore, the probability of choosing either a silver or copper key is 22/31
Hope this helps :)