Answer:
1) ![\frac{2}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D)
2) 49.225
3) ![\frac{7}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D)
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})](https://tex.z-dn.net/?f=E%28x%29%3Dx_%7B1%7D%2AP%28x_%7B1%7D%29%2Bx_%7B2%7D%2AP%28x_%7B2%7D%29%2B...%2Bx_%7Bn%7D%2AP%28x_%7Bn%7D%29)
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})](https://tex.z-dn.net/?f=E%28x%29%3D%28%5Cfrac%7B1%7D%7B1%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29%20%2B%28%5Cfrac%7B1%7D%7B2%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29%20%2B%28%5Cfrac%7B1%7D%7B3%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%28%5Cfrac%7B1%7D%7B4%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%28%5Cfrac%7B1%7D%7B5%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%28%5Cfrac%7B1%7D%7B6%7D%20%2A%5Cfrac%7B1%7D%7B6%7D%29)
![E(x)=0.167+0.083+0.056+0.042+0.033+0.028=0.409\approx \frac{2}{5}](https://tex.z-dn.net/?f=E%28x%29%3D0.167%2B0.083%2B0.056%2B0.042%2B0.033%2B0.028%3D0.409%5Capprox%20%5Cfrac%7B2%7D%7B5%7D)
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}](https://tex.z-dn.net/?f=Var%28x%29%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%28x_%7Bi%7D-%5Coverline%7Bx%7D%29%5E%7B2%7D%20%7D%7Bn%7D)
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}](https://tex.z-dn.net/?f=Var%28x%29%3D%5Cfrac%7B%283-10.5%29%5E2%2B%284-10.5%29%5E2%2B%2817-10.5%29%5E2%2B%2818-10.5%29%5E2%7D%7B4%7D)
![Var(x)=\frac{56.25+42.25+42.25+56.25}{4}](https://tex.z-dn.net/?f=Var%28x%29%3D%5Cfrac%7B56.25%2B42.25%2B42.25%2B56.25%7D%7B4%7D)
![Var(x)=\frac{196.9}{4}=49.225](https://tex.z-dn.net/?f=Var%28x%29%3D%5Cfrac%7B196.9%7D%7B4%7D%3D49.225)
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})](https://tex.z-dn.net/?f=E%28x%29%3Dx_%7B1%7D%2AP%28x_%7B1%7D%29%2Bx_%7B2%7D%2AP%28x_%7B2%7D%29%2B...%2Bx_%7Bn%7D%2AP%28x_%7Bn%7D%29)
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})](https://tex.z-dn.net/?f=E%28x%29%3D%281%2A%5Cfrac%7B1%7D%7B6%7D%29%20%2B%282%20%2A%5Cfrac%7B1%7D%7B6%7D%29%20%2B%283%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%284%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%285%20%2A%5Cfrac%7B1%7D%7B6%7D%29%2B%286%20%2A%5Cfrac%7B1%7D%7B6%7D%29)
![E(x)=0.17+0.33+0.5+0.67+0.83+1=3.5\approx \frac{7}{2}](https://tex.z-dn.net/?f=E%28x%29%3D0.17%2B0.33%2B0.5%2B0.67%2B0.83%2B1%3D3.5%5Capprox%20%5Cfrac%7B7%7D%7B2%7D)
Just go to another website to do it
10 lbs of apples will cost $55
How? Well...
First, you would need to find the unit rate, which is 5.5
You find the unit rate by simply dividing 33 by 6. Next, after you found your unit rate, you're going to multiply that by 10. We now know that 10 x 5.5= 55. Therefore, you will need $55 for 10 lbs of apples.
Answer:
Option B.
Step-by-step explanation:
The given expression is
We need an expression Which represents the same solution as the given expression.
It can be written as
Since
is equivalent to given equation, therefore this equation represents the same solution as the given expression.
Hence, option B is correct.
Answer:
![\frac{7}{x+7}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bx%2B7%7D)
Step-by-step explanation:
<u>Step 1: Pull a 7 from the top</u>
<u />![\frac{7x + 42}{x^2 + 13x + 42}](https://tex.z-dn.net/?f=%5Cfrac%7B7x%20%2B%2042%7D%7Bx%5E2%20%2B%2013x%20%2B%2042%7D)
![\frac{7(x + 6)}{x^2 + 13x + 42}](https://tex.z-dn.net/?f=%5Cfrac%7B7%28x%20%2B%206%29%7D%7Bx%5E2%20%2B%2013x%20%2B%2042%7D)
<u>Step 2: Factor the bottom</u>
<u />![\frac{7(x + 6)}{(x + 7)(x + 6)}](https://tex.z-dn.net/?f=%5Cfrac%7B7%28x%20%2B%206%29%7D%7B%28x%20%2B%207%29%28x%20%2B%206%29%7D)
<u>Step 3: Cancel the top (x+6) and the bottom (x+6)</u>
<u />![\frac{7}{x+7}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bx%2B7%7D)
Answer: ![\frac{7}{x+7}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7Bx%2B7%7D)