90x^2+15x-30 (hope this helps)
He would want to charge $0.85 per glass of lemonade to cover his expenses and have $10.00 profit. But in reality he would'nt make $17.00 because people don't carry freaking nickels and dimes.
Answer: 0.87400mg of caffeine.
Step-by-step explanation:
You have
N(t)=N0(e^−rt)(1)
as a general Exponential decay equation where N0 is the amount at t=0, N(t) is the amount remaining at time t and r is the exponential decay constant. You're specifically given that after 10 hours, the decay factor is 0.2601, i.e.,
N(10)/N(0)=N0(e^−10r)/N0(e^0)= e^−10r=0.2601 . .(2)
Taking the last 2 parts of (2) to the power of 0.1t gives
e^−rt=0.2601^.1t . .(3)
This means that
N(t)=N0(e^−rt)=N0(0.2601^.1t). .(4)
Also,
N(2.56)N(1.56)=N0(0.2601.1(2.56))N0(0.2601.1(1.56))=0.2601.1(2.56−1.56)=0.2601^.1
= 0.87400mg of caffeine.
Well, the keyword here is One of the performers insist on being the last.
So, the amount of performers that we can arrange freely is 7 performers.
Different ways we can schedule their appearance is :
7 ! = 7 x 6 x 5 x 4 x 3 x 2 x 1
= 5040
hope this helps
