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Ilia_Sergeevich [38]
2 years ago
10

What is the range of the function represented by these ordered pairs? {(–2, 1), (0, 0), (3, –1), (–1, 7), (5, 7)}

Mathematics
1 answer:
qaws [65]2 years ago
5 0
The range is the set of y coordinates (or outputs). For any point (x,y) the y coordinate is the second number listed. For example, with (8,7) the y coordinate is 7.

So we simply list all of the y coordinates of each ordered pair. Those values are: 1, 0, -1, 7, 7

Let's order them as you would see on a number line

-1, 0, 1, 7, 7

then let's toss out the extra 7 to get

-1, 0, 1, 7

So the range is the set {-1, 0, 1, 7}
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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

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

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Step-by-step explanation:

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