is this correct
i am cute busy
in ( pretty busy) place
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Question

Answer

i am "cute" busy    ..........I   think   you    wanted   to   say  :  I   am   "quite'   busy  
because   the   pronounse  of   "cute"   is   simillar   as  "quite"  
but  they   are   much   difference   in   the   meaning !!!!  "cute"   means    'hollwa"


in ( pretty busy) place   .......    that   is  ok      i  think  this   sentence  is   quite   right   !!!!

the  "pretty"  in   this   sentence  means    "very"      not   means  "beautiful"   
at   this   time   
and    you  can   use  "pretty"  to substitude    the    first   sentece   as   "quite"

                          
:D

Answer

"Cute" does not work in either sentence, but "pretty" does.

You can say, "I am pretty busy."
You can say, "...in a pretty busy place".

Answer

I am quite busy.

in a pretty busy place.

Answer

No this is not correct. 
There are words in phrases, which we can't replace with others, even though the other words will mean the same.