1) Put all the numbers in numerical order :
15, 23, 24, 25, 25, 25, 27
The median is the middle of the numbers : 25
Mode is the value that occurs more often : 25
2) Put all the numbers in numerical order :
2, 3, 3, 3, 3, 4, 4, 5
The middle of the numbers is 3 and 3
so, 3 + 3 = 6
6 : 2 = 3
Median = 3
Mode = 3
3) Put all the numbers in numerical order :
5, 7, 8, 9, 9, 10, 10, 10, 12
Median = 9
Mode = 10
4) Put all the numbers in numerical order :
0, 1, 1, 2, 2, 3, 3, 3, 4, 4
Median
2 + 3 = 5 : 2 = 2,5
Mode = 3
5) Put all the numbers in numerical order :
12, 13, 15, 18, 25
Median = 15
Mode = 0 (None)
6) Put all the numbers in numerical order :
1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 5
Median = 3
Mode = 3 and 4
7) Put all the numbers in numerical order :
6, 8, 9, 10, 10, 12
Median
9 + 10 = 19 : 2 = 8
Mode = 10
8) Put all the numbers in numerical order :
28, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31
Median
31 + 31 = 62 : 2 = 31
Mode = 31
Answer:
![\frac{-4+2i}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-4%2B2i%7D%7B5%7D)
Step-by-step explanation:
We are given the expression, ![\frac{\sqrt{-4}}{(3+i)-(2+3i)}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B-4%7D%7D%7B%283%2Bi%29-%282%2B3i%29%7D)
On simplifying, we have,
![\frac{2i}{3+i-2-3i}](https://tex.z-dn.net/?f=%5Cfrac%7B2i%7D%7B3%2Bi-2-3i%7D)
i.e. ![\frac{2i}{1-2i}](https://tex.z-dn.net/?f=%5Cfrac%7B2i%7D%7B1-2i%7D)
Now, we will rationalize the expression,
i.e. ![\frac{2i}{1-2i}\times \frac{1+2i}{1+2i}](https://tex.z-dn.net/?f=%5Cfrac%7B2i%7D%7B1-2i%7D%5Ctimes%20%5Cfrac%7B1%2B2i%7D%7B1%2B2i%7D)
i.e. ![\frac{(2i)\times (1+2i)}{(1-2i)\times (1+2i)}](https://tex.z-dn.net/?f=%5Cfrac%7B%282i%29%5Ctimes%20%281%2B2i%29%7D%7B%281-2i%29%5Ctimes%20%281%2B2i%29%7D)
i.e. ![\frac{2i+4i^{2}}{1-4i^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B2i%2B4i%5E%7B2%7D%7D%7B1-4i%5E%7B2%7D%7D)
Since,
, we get,
i.e. ![\frac{2i-4}{1+4}](https://tex.z-dn.net/?f=%5Cfrac%7B2i-4%7D%7B1%2B4%7D)
i.e. ![\frac{-4+2i}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B-4%2B2i%7D%7B5%7D)
So, the simplified expression is
.