From the Massachusetts Department of Agricultural Resources – produce tips.
It has advice for storing apples, advice like
Small quantities should be refrigerator-stored in a plastic bag that has a few perforated holes. These holes allow air into the bag so the apples can breathe. Store large quantities in a cool dark airy place.
Carrots
Carrots may not be stored in the refrigerator in plastic bags for several weeks without loss of nutritional value. Remove tops before storing to keep them from absorbing all of the vegetable’s moisture.
and more, they have information on beets, green beans, peaches, raspberries, and winter squash. Store them correctly and get the most from your purchases.