Answer:
A sample size of 1380 should be obtained.
Step-by-step explanation:
Minimum sample size:
The minimum sample size is of:
In which z is the critical value, related to the confidence level, E is the desired margin of error, 
and 
are the proportions.
99% confidence level
So 
, z is the value of Z that has a pvalue of 
, so 
.
Estimates of 22.6% male and 18.1% female from a previous year
This means that 
.
Within 3 percentage points, minimum sample size:
This is n for which 
. So
Rounding up:
A sample size of 1380 should be obtained.
To answer the question above, determine the velocity of the car at time zero. To do such, determine the increase in velocity every hour (acceleration).
a = (62 - 53) / (6 -3) = 3 km/ h^2
Calculate for the initial velocity (v) by using either of the velocities paired with the corresponding time,
v = 53 km/h - (3 km/h^2) x 3 h = 44 km/h
The equation is <em>y = 44 + 3x</em>. Where x is the time in hours, y is the velocity in km/h.
Answer:
The solution of the system of equations is, (1,-1,2)
Step-by-step explanation:
Given system equation;
x + 5y - 3z = -10
-5x + 6y – 5z = -21
-x + 8y - 8z = -25
Matrix form is written as;
![\left[\begin{array}{ccc}1&5&-3\\-5&6&-5\\-1&8&-8\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-10\\-21\\-25\end{array}\right] \\\\\\det. = 1\left[\begin{array}{cc}\\6&-5\\8&-8\end{array}\right] -5\left[\begin{array}{cc}\\-5&-5\\-1&-8\end{array}\right] -3\left[\begin{array}{cc}\\-5&6\\-1&8\end{array}\right] \\\\\\det. = 1(-8) -5(35)-3(-34)= -8 - 175+ 102 = -81](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%265%26-3%5C%5C-5%266%26-5%5C%5C-1%268%26-8%5Cend%7Barray%7D%5Cright%5D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C6%26-5%5C%5C8%26-8%5Cend%7Barray%7D%5Cright%5D%20-5%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%5D%20-3%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5Cdet.%20%3D%201%28-8%29%20-5%2835%29-3%28-34%29%3D%20-8%20-%20175%2B%20102%20%3D%20-81)
Cofactor;
![First \ row \left[\begin{array}{cc}+\\ 6&-5\\\ 8&-8\end{array}\right \left\begin{array}{cc}-\\ -5&-5\\-1&-8\end{array}\right \left\begin{array}{cc}+\\-5&6\\-1&8\end{array}\right] = [-8 \ \ -35 \ \ -34]\\\\\\\ Second \ row \left[\begin{array}{cc}-\\ 5&-3\\\ 8&-8\end{array}\right \left\begin{array}{cc}+\\ 1&-3\\-1&-8\end{array}\right \left\begin{array}{cc}-\\1&5\\-1&8\end{array}\right] = [16\ \ -11 \ \ -13]\\\\\\](https://tex.z-dn.net/?f=First%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%206%26-5%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%20-5%26-5%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C-5%266%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5B-8%20%20%5C%20%5C%20-35%20%5C%20%5C%20-34%5D%5C%5C%5C%5C%5C%5C%5C%20Second%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%205%26-3%5C%5C%5C%208%26-8%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%201%26-3%5C%5C-1%26-8%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C1%265%5C%5C-1%268%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5B16%5C%20%5C%20-11%20%5C%20%5C%20-13%5D%5C%5C%5C%5C%5C%5C)
![Third \ row \left[\begin{array}{cc}+\\ 5&-3\\\ 6&-5\end{array}\right \left\begin{array}{cc}-\\ 1&-3\\-5&-5\end{array}\right \left\begin{array}{cc}+\\1&5\\-5&6\end{array}\right]= [-7 \ \ 20\ \ 31]](https://tex.z-dn.net/?f=Third%20%5C%20row%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C%205%26-3%5C%5C%5C%206%26-5%5Cend%7Barray%7D%5Cright%20%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D-%5C%5C%201%26-3%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%20%5Cleft%5Cbegin%7Barray%7D%7Bcc%7D%2B%5C%5C1%265%5C%5C-5%266%5Cend%7Barray%7D%5Cright%5D%3D%20%5B-7%20%5C%20%20%5C%2020%5C%20%5C%2031%5D)
![\left[\begin{array}{ccc}-8&-35&-34\\16&-11&-13\\-7&20&31\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%26-35%26-34%5C%5C16%26-11%26-13%5C%5C-7%2620%2631%5Cend%7Barray%7D%5Cright%5D)
![inverse \ matrix =-\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] \\\\\\](https://tex.z-dn.net/?f=inverse%20%5C%20matrix%20%3D-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C%5C)
Solution of the matrix:
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = -\frac{1}{81} \left[\begin{array}{ccc}-8&16&-7\\-35&-11&20\\-34&-13&31\end{array}\right] X \left[\begin{array}{c}-10\\-21\\-25\end{array}\right] = \left[\begin{array}{c}\frac{-8*-10 }{-81 } +\frac{16*-21 }{-81 } + \frac{-7*-25 }{-81 }\\\\\frac{-35*-10 }{-81 } +\frac{-11*-21 }{-81 }+ \frac{20*-25 }{-81 }\\\\\frac{-34*-10 }{-81 }+ \frac{-13*-21 }{-81 }+ \frac{31*-25 }{-81 }\end{array}\right] \\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20-%5Cfrac%7B1%7D%7B81%7D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-8%2616%26-7%5C%5C-35%26-11%2620%5C%5C-34%26-13%2631%5Cend%7Barray%7D%5Cright%5D%20%20X%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-10%5C%5C-21%5C%5C-25%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-8%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B16%2A-21%20%7D%7B-81%20%7D%20%2B%20%5Cfrac%7B-7%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-35%2A-10%20%7D%7B-81%20%7D%20%2B%5Cfrac%7B-11%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B20%2A-25%20%7D%7B-81%20%7D%5C%5C%5C%5C%5Cfrac%7B-34%2A-10%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B-13%2A-21%20%7D%7B-81%20%7D%2B%20%5Cfrac%7B31%2A-25%20%7D%7B-81%20%7D%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5C)
![\left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}\frac{-81}{-81} \\\\\frac{81}{-81} \\\\\frac{-162}{-81} \end{array}\right] = \left[\begin{array}{c}1\\-1\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Dx%5C%5Cy%5C%5Cz%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D%5Cfrac%7B-81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B81%7D%7B-81%7D%20%5C%5C%5C%5C%5Cfrac%7B-162%7D%7B-81%7D%20%5Cend%7Barray%7D%5Cright%5D%20%3D%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%5C%5C-1%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Therefore, the correct option is (1,-1,2)
Answer:
It means two lines intersected.
C is correct
Hope this helps!
:)
