Write regular expressions for each of the following:

A string of at least $3$ a$\text{'}$s followed by one$-$or$-$more b$\text{'}$s $($you may not use the $\{\}$ count regex operators$).$

A string of exactly n a$\text{'}$s followed by exactly n$+4$ b$\text{'}$s for n$>0.$

A string of characters starting with a $<$ and ending with a $>.$ The string between the angle brackets may not be empty and may not contain a $>$ characters unless escaped by being preceded by a $\backslash .$ Any $\backslash$ character within the string must also be escaped by being preceded by a $\backslash .$

A decimal number possibly having a decimal point. Specifically, the regex should allow decimal integers without a decimal point. If there is a decimal point, it must be preceded by at least one decimal digit but need not be followed by any decimal digit.

An ISO$-8601$ date of the form YYYYMMDD or YYYY$-$MM$-$DD$.$ The regex must be precise enough to restrict MM to be in $01...12$ and DD in $01...31$ but can permit invalid dates like $2024-09-31.$