Answer:
about 105
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
6 / (2/5) = 15
It should take the nail 15 minutes to crawl 6 meters.
Answer:
u=0.375
Step-by-step explanation:
First we can write the equation down, -6(-4u+4)-6u=2(u-5)-8. First what you want to do is distribute -6 to (4u+4) and 2 to (u-5). This would result in 24u-24-6u=2u-10-8. Next add up all like terms and you will get 18u-24=2u-18. Next you would want to add 24 on both sides so that you get 18u=2u+6 then subtract 2u from both sides to get 16u=6. You the divide 16 on both sides to get u=0.375.
Here is dependence between scores and x-values:
![Z_i=\dfrac{X_i-\mu}{\sigma},](https://tex.z-dn.net/?f=Z_i%3D%5Cdfrac%7BX_i-%5Cmu%7D%7B%5Csigma%7D%2C)
where
is the mean,
is standard deviation and i changes from 1 to 2.
1. When i=1,
then
![-0.25=\dfrac{57-\mu}{\sigma}.](https://tex.z-dn.net/?f=-0.25%3D%5Cdfrac%7B57-%5Cmu%7D%7B%5Csigma%7D.)
2. When i=2,
then
![1.25=\dfrac{87-\mu}{\sigma}.](https://tex.z-dn.net/?f=1.25%3D%5Cdfrac%7B87-%5Cmu%7D%7B%5Csigma%7D.)
Now solve the system of equations:
![\left\{\begin{array}{l}-0.25=\dfrac{57-\mu}{\sigma}\\ \\1.25=\dfrac{87-\mu}{\sigma}.\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D-0.25%3D%5Cdfrac%7B57-%5Cmu%7D%7B%5Csigma%7D%5C%5C%20%5C%5C1.25%3D%5Cdfrac%7B87-%5Cmu%7D%7B%5Csigma%7D.%5Cend%7Barray%7D%5Cright.)
![\left\{\begin{array}{l}-0.25\sigma=57-\mu\\ \\1.25\sigma=87-\mu.\end{array}\right.](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D-0.25%5Csigma%3D57-%5Cmu%5C%5C%20%5C%5C1.25%5Csigma%3D87-%5Cmu.%5Cend%7Barray%7D%5Cright.)
Subtract first equation from the second:
![1.25\sigma-(-0.25\sigma)=87-57,\\ \\1.5\sigma=30,\\ \\\sigma=20.](https://tex.z-dn.net/?f=1.25%5Csigma-%28-0.25%5Csigma%29%3D87-57%2C%5C%5C%20%5C%5C1.5%5Csigma%3D30%2C%5C%5C%20%5C%5C%5Csigma%3D20.)
Then
![1.25=\dfrac{87-\mu}{20},\\ \\87-\mu=25,\\ \\\mu=87-25=62.](https://tex.z-dn.net/?f=1.25%3D%5Cdfrac%7B87-%5Cmu%7D%7B20%7D%2C%5C%5C%20%5C%5C87-%5Cmu%3D25%2C%5C%5C%20%5C%5C%5Cmu%3D87-25%3D62.)
Answer: the mean is 62, the standard deviation is 20.