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2 years ago

Jack is 27 years older than Susan. In 5 years, he will be 4 times as old as she is

Mathematics

2 answers:

Ahat [919]2 years ago

6 0

Answer:

x - Jack's age

y - Susan's age

Jack is 27 years older than Susan.

In 5 years he will be 4 times as old as she is.

Jack is 31 years old and Susan is 4 years old.

timurjin [86]2 years ago

5 0

Answer:

jack is 31 and susan is 4

Step-by-step explanation:

j = s + 27

---

j + 5 = 4(s + 5)

j = 4s + 20 - 5

j = 4s + 15

---

j = s + 27

j = 4s + 15

---

4s + 15 = s + 27

3s = 12

s = 4

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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

aksik [14]

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)

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

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

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

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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2 years ago

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kirill115 [55]

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2 years ago

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3 years ago

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ivanzaharov [21]

Answer:

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3 years ago

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2 years ago