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3 years ago

5x – 4y=8 -x + 2y = -4 1. 2. 44 - by = -6 4x – 4y = -8

Mathematics

1 answer:

ycow [4]3 years ago

8 0

-x + 2y = -4

-x = -2y - 4

x = 2y + 4

5(2y + 4) - 4y = 8

10y + 20 - 4y = 8

6y + 20 = 8

6y = -18

y = -3

-x + 2y = -4

-x + 2(-3) = -4

-x - 6 = -4

-x = 2

x = -2

The coordinate pair is (-2, -3) (x = -2, y = -3.)

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<u>Tony</u> has 45 dollars

<u>Milan</u> has 15 dollars

<u>Lucy</u> has 25 dollars

<em>Explanation:</em>

<u>Let </u><u><em>x</em></u><u> represent the amount of money Milan has in his wallet.</u>

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MILAN: x

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<u>Lucy, Milan, and Tony have a total of $85 in their wallets. Hence, the following equation.</u>

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3x+x+x+10=85

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The number of minutes advertisement should use is found.

x ≅ 12 mins

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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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