Palindromes are numbers that remain the same, when reversed.
There are 10 palindromes divisible by 9 between 1000 and 9999
To do this, we list the numbers divisible by 9 between 10 and 99.
The numbers are:
[tex]\mathbf{A = 09,\ 18,\ 27,\ 36,\ 45.\ 54,\ 63,\ 72,\ 81,\ 90,\ 99}[/tex]
Flip these numbers
[tex]\mathbf{B =90,\ 81,\ 72,\ 63,\ 54.\ 45,\ 36,\ 27,\ 18,\ 09,\ 99}[/tex]
Combine corresponding numbers
[tex]\mathbf{AB =0990,\ 1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}[/tex]
Rewrite as:
[tex]\mathbf{AB =990,\ 1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}[/tex]
990 is less than 1000.
So, we have:
[tex]\mathbf{AB =1881,\ 2772,\ 3663,\ 4554,\5445,\ 6336,\ 7227,\ 8118,\ 9009,\ 9999}[/tex]
Count the numbers
[tex]\mathbf{n(AB) =10}[/tex]
Hence, there are 10 palindromes divisible by 9 between 1000 and 9999
Read more about palindromes at:
https://brainly.com/question/14076732
