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emmasim [6.3K]
2 years ago
14

A bag contains hair ribbons for a spirit rally. The bag contains 4 black ribbons and 5 green ribbons. Lila selects a ribbon at r

andom, then Jessica selects a ribbon at random from the remaining ribbons. What is the probability that Lila selects a green ribbon and Jessica selects a black ribbon? Express your answer as a fraction in the simplest form.
A. 20/81
B. 1/20
C. 1/16
D. 5/18
Mathematics
1 answer:
ale4655 [162]2 years ago
4 0

Answer:

Total ribbons = 3 + 12 = 15So, 3/15 = black12/15 = greenTherefore the probability Lila selects the black ribbon first is 12/15Because Lila has taken one

Step-by-step explanation:

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A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and
goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}

Solve for S(t):

\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}

e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}

The left side is the derivative of a product:

\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}

Integrate both sides:

e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt

e^{t/800}S(t)=64e^{t/800}+C

S(t)=64+Ce^{-t/800}

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

0=64+C\impleis C=-64

and so (b) the amount of sugar in the tank at time t is

S(t)=64\left(1-e^{-t/800}\right)

As t\to\infty, the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
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user100 [1]

Answer:

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Step-by-step explanation:

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=(8)2+(0)2‾‾‾‾‾‾‾‾‾‾√

=64+0‾‾‾‾‾‾√

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3 years ago
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Answer:

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Step-by-step explanation:

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