Questions Open Mic #$1-8$: An open mic night at a local caf$$ is popular on Wednesday nights. Between $8-10$ p$.$m$.$ a performer arrives on average every $3\mathrm{.}5$ minutes. The performers sign up on a first come, first serve basis and each performer is asked to keep their songs short. Most performers abide by this and the average performance time is $3$ minutes.

$1.$ The caf$$ usually has one barista making coffee drinks. Caf$$ customers during the Wednesday open mic nights order $2$ drinks$/$minute on average. The barista$$s average time to make a drink is $28$ seconds. How long $($in minutes$)$ does a customer wait until they have their drink?$$

Do not round off your intermediate calculations. This will result in the wrong answer.

$2.$ The caf$$ has been seeing an increase in business on open mic nights and the barista is getting orders every $20$ seconds. The caf$$ decides to hire a backup for the barista to speed up the drink making. Now the barista can make a drink in an average of $15$ seconds. How many drinks orders are waiting to be made? Round your answer to $2$ decimals.

$3.$ On average how many performers are in the caf$?$

$4.$ What is the value of $,$ the service rate? Round to $4$ decimals.

$5.$ What is the value of $?$ Round to $4$ decimals.