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Mathematics

1 answer:

ipn [44]3 years ago

6 0

Answer:

Question #3: Answer = 31

Step-by-step explanation

• Plug in 3 for x

• Plug in -4 for y

| -3(3)² + 2(-4) | -(3)(-4)

From here, simplify. Don't forget to use PEMDAS!

| -27 +8 | + 12

| -19 | + 12

19 + 12

Use this same method to solve for Question #2!

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1) A traditional die is a cube with each of its six sides representing the numbers from 1 to 6. Mr. Dicey customized a die by re

liraira [26]

Answer:

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: $E(x)=(1*\frac{1}{6}) +(2 *\frac{1}{6}) +(3 *\frac{1}{6})+(4 *\frac{1}{6})+(5 *\frac{1}{6})+(6 *\frac{1}{6})$