Answer:
The number of minutes advertisement should use is found.
x ≅ 12 mins
Step-by-step explanation:
(MISSING PART OF THE QUESTION: AVERAGE WAITING TIME = 2.5 MINUTES)
<h3 /><h3>Step 1</h3>
For such problems, we can use probability density function, in which probability is found out by taking integral of a function across an interval.
Probability Density Function is given by:
![f(t)=\left \{ {{0 ,\-t](https://tex.z-dn.net/?f=f%28t%29%3D%5Cleft%20%5C%7B%20%7B%7B0%20%2C%5C-t%3C0%20%20%7D%5Catop%20%7B%5Cfrac%7Be%5E%7B-t%2F%5Cmu%7D%7D%7B%5Cmu%7D%7D%2Ct%5Cgeq0%7D%20%5Cright.%20%5C%5C)
Consider the second function:
![f(t)=\frac{e^{-t/\mu}}{\mu}\\](https://tex.z-dn.net/?f=f%28t%29%3D%5Cfrac%7Be%5E%7B-t%2F%5Cmu%7D%7D%7B%5Cmu%7D%5C%5C)
Where Average waiting time = μ = 2.5
The function f(t) becomes
![f(t)=0.4e^{-0.4t}](https://tex.z-dn.net/?f=f%28t%29%3D0.4e%5E%7B-0.4t%7D)
<h3>Step 2</h3>
The manager wants to give free hamburgers to only 1% of her costumers, which means that probability of a costumer getting a free hamburger is 0.01
The probability that a costumer has to wait for more than x minutes is:
![\int\limits^\infty_x {f(t)} \, dt= \int\limits^\infty_x {}0.4e^{-0.4t}dt](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%5Cinfty_x%20%7Bf%28t%29%7D%20%5C%2C%20dt%3D%20%5Cint%5Climits%5E%5Cinfty_x%20%7B%7D0.4e%5E%7B-0.4t%7Ddt)
which is equal to 0.01
<h3>
Step 3</h3>
Solve the equation for x
![\int\limits^{\infty}_x {0.4e^{-0.4t}} \, dt =0.01\\\\\frac{0.4e^{-0.4t}}{-0.4}=0.01\\\\-e^{-0.4t} |^\infty_x =0.01\\\\e^{-0.4x}=0.01](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D_x%20%7B0.4e%5E%7B-0.4t%7D%7D%20%5C%2C%20dt%20%3D0.01%5C%5C%5C%5C%5Cfrac%7B0.4e%5E%7B-0.4t%7D%7D%7B-0.4%7D%3D0.01%5C%5C%5C%5C-e%5E%7B-0.4t%7D%20%7C%5E%5Cinfty_x%20%3D0.01%5C%5C%5C%5Ce%5E%7B-0.4x%7D%3D0.01)
Take natural log on both sides
![ln (e^{-0.4x})=ln(0.01)\\-0.4x=ln(0.01)\\-0.4x=-4.61\\x= 11.53](https://tex.z-dn.net/?f=ln%20%28e%5E%7B-0.4x%7D%29%3Dln%280.01%29%5C%5C-0.4x%3Dln%280.01%29%5C%5C-0.4x%3D-4.61%5C%5Cx%3D%2011.53)
<h3>Results</h3>
The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger
Answer:
x = 80°
Step-by-step explanation:
Angle on a straight line = 180°
(x + 40)° + (x - 20)° = 180°
x + 40° + x - 20° = 180°
2x + 20° = 180°
2x = 180° - 20°
2x = 160°
x = 160°/2
x = 80°
Check:
(x + 40)° + (x - 20)° = 180°
(80° + 40°) + (80° - 20°) = 180°
120° + 60° = 180°
180° = 180°
Answer:
7
Step-by-step explanation:
280=40t/40
t=7