ImageMagick

From the terminal...

sudo yum install freetype freetype-devel libjpeg libjpeg-devel libpng libpng-devel libtiff libtiff-devel ImageMagick ImageMagick-devel ghostscript ghostscript-devel ghostscript-fonts libwmf libexif

This will install ImageMagick and all the development libraries to get it working.

And for the ruby gem...

sudo gem install rmagick

MySQL

First MySQL...

sudo yum install ruby-devel mysql mysql-devel mysql-server

Then the Ruby gem...

sudo gem install mysql -- --with-mysql-config=/usr/bin/mysql_config

Starting MySQL

Now in Terminal do...

/sbin/chkconfig mysqld on
/sbin/service mysqld start

That should enable the mysql services on your Fedora machine.

Services Running on Startup?

Do this to see what is actually running when you power up...

/usr/sbin/ntsysv

And finally to cleanup your System...

sudo yum clean all