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3 years ago

12

What is the probability that 6 rolls of a fair die will show four exactly 5 times?

1 answer:

storchak [24]3 years ago

6 0

Answer:

very less

Step-by-step explanation:

When rolling a fair 6 sided die 5 times there are 6^5 possible combinations.

Of those, there are 5 ways to roll exactly four sixes, and each of those ways have 5 possible results on the die which has not rolled a six, plus there is 1 way to roll five sixes. 5*5+1=26 combinations with at least four sixes.

Now, take the number of results which fit your conditions, divide by the number of possible results and you get your answer: 26/7776 which can be reduced to 13/3338, a bit less than 0.4%

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Answer:

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Step-by-step explanation:

Lines A and B are parallel lines. Find the measures of angles 1,2, and 3.

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3 years ago

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Answer:

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A 100 gallon tank initially contains 100 gallons of sugar water at a concentration of 0.25 pounds of sugar per gallon suppose th

Vsevolod [243]

At the start, the tank contains

(0.25 lb/gal) * (100 gal) = 25 lb

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$\dfrac{\mathrm dS}{\mathrm dt}=P-\dfrac S{100}$

Separate variables, integrate, and solve for <em>S</em>.

$\dfrac{\mathrm dS}{P-\frac S{100}}=\mathrm dt$

$\displaystyle\int\dfrac{\mathrm dS}{P-\frac S{100}}=\int\mathrm dt$

$-100\ln\left|P-\dfrac S{100}\right|=t+C$

$\ln\left|P-\dfrac S{100}\right|=-100t-100C=C-100t$

$P-\dfrac S{100}=e^{C-100t}=e^Ce^{-100t}=Ce^{-100t}$

$\dfrac S{100}=P-Ce^{-100t}$

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The solution is being drained at a constant rate of 1 gal/min; there will be 5 gal of solution remaining after time

$1000\,\mathrm{gal}+\left(-1\dfrac{\rm gal}{\rm min}\right)t=5\,\mathrm{gal}\implies t=995\,\mathrm{min}$

has passed. At this time, we want the tank to contain

(0.5 lb/gal) * (5 gal) = 2.5 lb

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$S(995)=100P-(100P-25)e^{-99,500}=2.5\implies\boxed{P\approx0.025}$

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ludmilkaskok [199]

Answer:

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