Gymnast clothing manufactures expensive soccer cleats for sale to college bookstores in runs of up to 500. its cost (in dollars) for a run of x pairs of cleats is: c(x) = 2950 + 6x + 0.1x2 (0 ≤ x ≤ 500). gymnast clothing sells the cleats at $130 per pair. find the revenue and profit functions. how many should gymnast clothing manufacture to make a profit?

Manufacture more than 24 items to make a profit.

Step-by-step explanation:

Let's find the Revenue function:

Revenue () = Price per pair * Number of pairs sold

Now let's find the profit function:

Profit () = Revenue () - Cost

()  = ()  –

, Where, ()

The requirement to make a profit:

⇒

   or    x=1215.735

Therefore, they should manufacture more than 24 items to make a profit.

answer:   35 % is the probability of a late departure or an early arrival.

step-by-step explanation:

let l represents the late departure and e represents the early departure.

then, according to the question,

p(l) = 12 %,   p(e) = 27 % and = 4 %

and, we have to find out,

but, we know that,

which is the required equation that will use to find the probability of a late departure or an early departure.

therefore,   the probability of a late departure or an early arrival =   35 %