Depending on what type of fittings you're using, you either push the hose into a push in fitting or you wrench them on. Which air line and which dryer yours has would be helpful to know here, as there are several different types of air dryers, and more than one hose connected to them.
Attached to the back of the dryer.
Clean filter hose.
Tumble dryer hoses can be purchased on a variety of websites. One option is to purchase the hose from the dryer brand’s website. Wal-Mart, Home Depot, Ace Hardware, and many other stores have dryer hoses available for purchase online as well.
There is no transmission vacuum hose. That is a vent hose.
This is usually the result of a clogged exhaust hose.
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The vacuum hose should connect to the back of the intake manifold.
The purpose of a clothes dryer lint brush is help clean lint out of the dryer system. Lint gets stuck inside a dryer and the dryer hose and becomes a fire hazard. The lint brush pulls the lint out of hard to reach places in the dryer.
You will have to get that from the dealer.
Connect a hose to your faucet and turn it on, put the hose in the water.
A hose bibb may be known as a spigot or faucet in your area. In any case, it is the valve to which you connect a garden hose.
A hose nipple is a push-on fitting that allows you to connect the hose to a threaded fitting. See related link below for a picture of a hose nipple.