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4 years ago

Solving equations with rational numbers

Mathematics

1 answer:

Nonamiya [84]4 years ago

6 0

Answer:

P= 2

T=6

3) 252$

Step-by-step explanation:

1) set up your equation 3/8p=6/8 then divide 3/8 from both sides (remember when you divide fractions you would multiply by the reciprocal so 3/8 x 8/6. Also make sure you simplify)

2) Do the same here. 38/7 divided by 19/21

3) Turn the fraction into an improper fraction then multiply 126 by that amount (3/6)

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4 years ago

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liraira [26]

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1) $\frac{2}{5}$

2) 49.225

3) $\frac{7}{2}$

Step-by-step explanation:

1) To find the expected value of the dice we can use the following equation:

$E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})$

So in our problem the values x will be: 1/1, 1/2, 1/3, 1/4, 1/5 and 1/6 and the probavility for all values is 1/6 so the expected values will be: $E(x)=(\frac{1}{1} *\frac{1}{6}) +(\frac{1}{2} *\frac{1}{6}) +(\frac{1}{3} *\frac{1}{6})+(\frac{1}{4} *\frac{1}{6})+(\frac{1}{5} *\frac{1}{6})+(\frac{1}{6} *\frac{1}{6})$

$E(x)=0.167+0.083+0.056+0.042+0.033+0.028=0.409\approx \frac{2}{5}$

2) To find the variance of the expected values we can use the equation:

$Var(x)=\frac{\sum_{i=1}^{n}(x_{i}-\overline{x})^{2} }{n}$

So for our problem will be:

$Var(x)=\frac{(3-10.5)^2+(4-10.5)^2+(17-10.5)^2+(18-10.5)^2}{4}$

$Var(x)=\frac{56.25+42.25+42.25+56.25}{4}$ $Var(x)=\frac{196.9}{4}=49.225$

3) To find the expected value of the dice we can use the following equation:

$E(x)=x_{1}*P(x_{1})+x_{2}*P(x_{2})+...+x_{n}*P(x_{n})$

So in our problem the values x will be: 1, 2, 3, 4, 5 and 6 and the probavility for all values is 1/6 so the expected values will be: $E(x)=(1*\frac{1}{6}) +(2 *\frac{1}{6}) +(3 *\frac{1}{6})+(4 *\frac{1}{6})+(5 *\frac{1}{6})+(6 *\frac{1}{6})$

$E(x)=0.17+0.33+0.5+0.67+0.83+1=3.5\approx \frac{7}{2}$

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3 years ago