Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7*x-4-(21)=0
Solve : 7x-25 = 0
Add 25 to both sides of the equation :
7x = 25
Divide both sides of the equation by 7:
x = 25/7 = 3.571
Answer:
![\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%26%5Cdfrac%7B75%7D%7B2%7D%26-%5Cdfrac%7B25%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
In the first equality
![5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],](https://tex.z-dn.net/?f=5%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5C4%268%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cdfrac%7B2%7D%7B5%7Dm%5Ctimes%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%262%5C%5C4%268%5Cend%7Barray%7D%5Cright%5D%2C)
the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so
![5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}](https://tex.z-dn.net/?f=5%3D%5Cdfrac%7B2%7D%7B5%7Dm%5CRightarrow%20m%3D5%5Ctimes%20%5Cdfrac%7B5%7D%7B2%7D%3D%5Cdfrac%7B25%7D%7B2%7D)
For the second equality
![(H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),](https://tex.z-dn.net/?f=%28H%2B%5B1%5C%204%5C%20-2%5D%29%2B%5B3%5C%202%5C%20-6%5D%3D%5B-2%5C%203%5C%20-1%5D%2B%28%5B1%5C%204%5C%20-2%5D%2B%5B3%5C%202%5C%20-6%5D%29%2C)
if
, then this equality represents the assotiative property of matrix addition.
Hence,
![m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right]](https://tex.z-dn.net/?f=m%5Ctimes%20H%3D%5Cdfrac%7B25%7D%7B2%7D%5Ctimes%20%5B-2%5C%203%5C%20-1%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-25%26%5Cdfrac%7B75%7D%7B2%7D%26-%5Cdfrac%7B25%7D%7B2%7D%5Cend%7Barray%7D%5Cright%5D)
A map of the area and tools that would help him do it.
Answer:23 mm
Step-by-step explanation:
add both 15 and 8 because they are as long as the one on the bottom
Answer:
![69.7 -2.58 \frac{2.8}{\sqrt{772}}=69.44](https://tex.z-dn.net/?f=%2069.7%20-2.58%20%5Cfrac%7B2.8%7D%7B%5Csqrt%7B772%7D%7D%3D69.44)
![69.7 +2.58 \frac{2.8}{\sqrt{772}}=69.96](https://tex.z-dn.net/?f=%2069.7%20%2B2.58%20%5Cfrac%7B2.8%7D%7B%5Csqrt%7B772%7D%7D%3D69.96)
And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.
Step-by-step explanation:
For this case we have the following sample size n =772 from men recruits between the ages of 18 to 24
represent the sample mean for the heigth
represent the population standard deviation
We want to construct a confidence interval for the true mean and we can use the following formula:
![\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20X%20%5Cpm%20z_%7B%5Calpha%2F2%7D%20%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
The confidence level is 0.99 or 99%o then the significance level is
and
and if we find for a critical value in the normal tandar ddistirbution who accumulates 0.005 of the area on each tail we got:
![z_{\alpha/2}= 2.58](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D%202.58)
And replacing we got:
![69.7 -2.58 \frac{2.8}{\sqrt{772}}=69.44](https://tex.z-dn.net/?f=%2069.7%20-2.58%20%5Cfrac%7B2.8%7D%7B%5Csqrt%7B772%7D%7D%3D69.44)
![69.7 +2.58 \frac{2.8}{\sqrt{772}}=69.96](https://tex.z-dn.net/?f=%2069.7%20%2B2.58%20%5Cfrac%7B2.8%7D%7B%5Csqrt%7B772%7D%7D%3D69.96)
And we can conclude that the true mean for the heights of mens between the ages of 18 to 24 is between 69.44 and 69.7 inches.