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k0ka [10]
2 years ago
15

3 gallons of paint cover 900 square feet. How many gallons will cover 300 square feet?

Mathematics
2 answers:
SVEN [57.7K]2 years ago
4 0

Answer:

1 gallon

Step-by-step explanation:

Since the relationship is direct, meaning as the number of square feet decreases, the number of gallons also decreases.

3:900 = x:300

solution:

3(300) = 900x

900=900x

x=1

Liono4ka [1.6K]2 years ago
4 0

Answer:

1

Step-by-step explanation:

3 gallons for 900 sqft

1 gallon for 300 sqft

900/300=3

3/3=1

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In a casino game, gamblers are allowed to roll n fair, 6-sided dice. If a 6 shows up on any of them, the gambler gets nothing. I
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Answer:

a) \bf \boxed{W(n) = 3*n*\left( \frac{5}{6} \right)^n\;dollars}

the smallest n that maximizes the expected payoff is n=5.

b) 4

Step-by-step explanation:

a)

The expected amount of $ won for each die would be the average of 1, 2, 3, 4 and 5 which is $3.

Let W(n) the expected money won when rolling n dice.  

n =1

If the gambler rolls only one die, the expected money won would be $3 times the probability of not getting a 6, which is 5/6.

So  

\bf W(1) = 3*1*\frac{5}{6}

n=2

If the gambler rolls 2 dice, the expected money won would be $3 times the probability of not getting a 6 in any of the dice. Since the outcome of the rolling does not depend on the previous rollings, the probability is  

\bf \frac{5}{6}\times\frac{5}{6}=\left( \frac{5}{6} \right)^2

and

\bf W(2) = 3*2*\left( \frac{5}{6} \right)^2

n=3

Similarly, since the probability of not getting a 6 in 3 dice equals

\bf \left( \frac{5}{6} \right)^3

\bf W(3) = 3*3*\left( \frac{5}{6} \right)^3

and the formula for the expected money won with n dice would be

\bf \boxed{W(n) = 3*n*\left( \frac{5}{6} \right)^n\;dollars}

In the picture attached there is a plot of the values of the expected money won for n=1 to 20 (See picture)

For n=5 and n=6 we get the maximum profit expected of $6.02816=$6 rounded to the nearest integer.

Hence, the smallest n that maximizes the expected payoff is n=5.

b)

The probability that face k (k=1,2,...or 6) shows up is 1/6,

as this face can be in any of the 10 positions of the arrangement, there are 10 ways that face k can show up.

The probability that face k (k=1,2,...or 6) shows up twice is \bf \left( \frac{1}{6} \right)^2

as this face can be in any of the \bf C(10;2)=\binom{10}{2} (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;2) ways that face k can show up twice.

The probability that face k (k=1,2,...or 6) shows up three times is \bf \left( \frac{1}{6} \right)^3

as this face can be in any of the \bf C(10;3)=\binom{10}{2} (combinations of 10 taken 2 at a time) positions of the arrangement, there are C(10;3) ways that face k can show up twice.

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The distance between given points is 3.6 units.

Step-by-step explanation:

Given points are;

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Distance between two points is calculated by;

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The distance between given points is 3.6 units.

Keywords: distance, points

Learn more about distance at:

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Answer:

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