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Lubov Fominskaja [6]
3 years ago
8

Which equation can be used to solve for the rate, r, for Sam to change all the light bulbs in the office building by himself?

Mathematics
2 answers:
Bad White [126]3 years ago
8 0

Answer:

\frac{3}{r}+\frac{3}{8}=1

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Working together, Sam and Charlie can change all light bulbs in the office building in 3 hours. It would have taken Charlie 8 hours to do the job alone. Which equation can be be used to solve for the rate 'r', for Sam to change all the light bulbs in the office building by himself.

Let Sam can change the bulbs in the office alone in 'r' hours  

Per hour work done by Sam alone = \frac{1}{r}

Let Sam takes he time to change the same bulbs in the office alone = 8 hours

Per hour work done by Sam = \frac{1}{8}

Since, Sam and Charlie complete the work together in time = 3 hours

Therefore, per hour work done by both = \frac{1}{3}

Equation for per work done by both will be,

Per hour work done by both = Per hour  work done by Sam alone + Per hour work done by Charlie

\frac{1}{r}+\frac{1}{8}=\frac{1}{3}

Therefore, equation for the rate 'r' will be,

\frac{1}{r}+\frac{1}{8}=\frac{1}{3}

\frac{3}{r}+\frac{3}{8}=1

Gala2k [10]3 years ago
7 0

Answer:

B.) 3r + 3/8 = 1

Step-by-step explanation:

just did assignment

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The manager wants to advertise that anybody who isn't served within a certain number of minutes gets a free hamburger. But she d
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Answer:

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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

Consider the second function:

f(t)=\frac{e^{-t/\mu}}{\mu}\\

Where Average waiting time = μ = 2.5

The function f(t) becomes

f(t)=0.4e^{-0.4t}

<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

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

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

<h3>Results</h3>

The costumer has to wait x = 11.53 mins ≅ 12 mins to get a free hamburger

3 0
3 years ago
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