Answer:
0.3
Step-by-step explanation:
Find the number in the tenth place
3
and look one place to the right for the rounding digit
1
. Round up if this number is greater than or equal to
5
and round down if it is less than
5
.
0.3
Answer:
C. 5 × 3
Step-by-step explanation:
The order of a matrix is the number of rows and columns that a matrix has. Rows are listed first and columns are listed second. The matrix has 5 rows going across horizontally and 3 columns going down vertically.
So, the order of the matrix is 5 × 3.
Hope that helps.
Answer:
Both brothers will have the same amount of money is their saving accounts after six months.
Step-by-step explanation:
I worked this out by finding out the first 8 months of savings for both brothers:
Patrick: His brother:
200 150
225 185
250 220
275 253
300 290
325 325
375 360
400 395
I then looked across my results to see that at 6 months both brothers had $325.
Hope this helped.
Consider all options:
A.
![\left[\begin{array}{cc}5&5\\-4&-4\end{array}\right] \cdot \left[\begin{array}{cc}5&5\\-4&-4\end{array}\right] =\left[\begin{array}{cc}5\cdot 5+5\cdot (-4)&5\cdot 5+5\cdot (-4)\\-4\cdot 5+(-4)\cdot (-4)&-4\cdot 5+(-4)\cdot (-4)\end{array}\right]=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%265%5C%5C-4%26-4%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%265%5C%5C-4%26-4%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%5Ccdot%205%2B5%5Ccdot%20%28-4%29%265%5Ccdot%205%2B5%5Ccdot%20%28-4%29%5C%5C-4%5Ccdot%205%2B%28-4%29%5Ccdot%20%28-4%29%26-4%5Ccdot%205%2B%28-4%29%5Ccdot%20%28-4%29%5Cend%7Barray%7D%5Cright%5D%3D)
![=\left[\begin{array}{cc}5&5\\-4&-4\end{array}\right].](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%265%5C%5C-4%26-4%5Cend%7Barray%7D%5Cright%5D.)
This option is true.
B.
![\left[\begin{array}{cc}6&5\\5&6\end{array}\right] \cdot \left[\begin{array}{cc}6&5\\5&6\end{array}\right] =\left[\begin{array}{cc}6\cdot 6+5\cdot 5&6\cdot 5+5\cdot 6\\5\cdot 6+6\cdot 5&5\cdot 5+6\cdot 6\end{array}\right]=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%265%5C%5C5%266%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%265%5C%5C5%266%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%5Ccdot%206%2B5%5Ccdot%205%266%5Ccdot%205%2B5%5Ccdot%206%5C%5C5%5Ccdot%206%2B6%5Ccdot%205%265%5Ccdot%205%2B6%5Ccdot%206%5Cend%7Barray%7D%5Cright%5D%3D)
![=\left[\begin{array}{cc}61&60\\60&61\end{array}\right].](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D61%2660%5C%5C60%2661%5Cend%7Barray%7D%5Cright%5D.)
This option is false.
C.
![\left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right] \cdot \left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right] =\left[\begin{array}{cc}0.5\cdot 0.5+(-0.5)\cdot (-0.5)&0.5\cdot (-0.5)+(-0.5)\cdot 0.5\\-0.5\cdot 0.5+0.5\cdot (-0.5)&-0.5\cdot (-0.5)+0.5\cdot 0.5\end{array}\right]=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%26-0.5%5C%5C-0.5%260.5%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%26-0.5%5C%5C-0.5%260.5%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%5Ccdot%200.5%2B%28-0.5%29%5Ccdot%20%28-0.5%29%260.5%5Ccdot%20%28-0.5%29%2B%28-0.5%29%5Ccdot%200.5%5C%5C-0.5%5Ccdot%200.5%2B0.5%5Ccdot%20%28-0.5%29%26-0.5%5Ccdot%20%28-0.5%29%2B0.5%5Ccdot%200.5%5Cend%7Barray%7D%5Cright%5D%3D)
![=\left[\begin{array}{cc}0.5&-0.5\\-0.5&0.5\end{array}\right].](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%26-0.5%5C%5C-0.5%260.5%5Cend%7Barray%7D%5Cright%5D.)
This option is true.
D.
![\left[\begin{array}{cc}0.5&0.5\\-0.5&0.5\end{array}\right] \cdot \left[\begin{array}{cc}0.5&0.5\\-0.5&0.5\end{array}\right] =\left[\begin{array}{cc}0.5\cdot 0.5+0.5\cdot (-0.5)&0.5\cdot 0.5+0.5\cdot 0.5\\-0.5\cdot 0.5+0.5\cdot (-0.5)&-0.5\cdot 0.5+0.5\cdot 0.5\end{array}\right]=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%260.5%5C%5C-0.5%260.5%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%260.5%5C%5C-0.5%260.5%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0.5%5Ccdot%200.5%2B0.5%5Ccdot%20%28-0.5%29%260.5%5Ccdot%200.5%2B0.5%5Ccdot%200.5%5C%5C-0.5%5Ccdot%200.5%2B0.5%5Ccdot%20%28-0.5%29%26-0.5%5Ccdot%200.5%2B0.5%5Ccdot%200.5%5Cend%7Barray%7D%5Cright%5D%3D)
![=\left[\begin{array}{cc}0&0.5\\-0.5&0\end{array}\right].](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D0%260.5%5C%5C-0.5%260%5Cend%7Barray%7D%5Cright%5D.)
This option is false.
E.
![\left[\begin{array}{cc}-6&-6\\5&5\end{array}\right] \cdot \left[\begin{array}{cc}-6&-6\\5&5\end{array}\right] =\left[\begin{array}{cc}-6\cdot (-6)+(-6)\cdot 5&-6\cdot (-6)+(-6)\cdot 5\\5\cdot (-6)+5\cdot 5&5\cdot (-6)+5\cdot 5\end{array}\right]=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-6%26-6%5C%5C5%265%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-6%26-6%5C%5C5%265%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-6%5Ccdot%20%28-6%29%2B%28-6%29%5Ccdot%205%26-6%5Ccdot%20%28-6%29%2B%28-6%29%5Ccdot%205%5C%5C5%5Ccdot%20%28-6%29%2B5%5Ccdot%205%265%5Ccdot%20%28-6%29%2B5%5Ccdot%205%5Cend%7Barray%7D%5Cright%5D%3D)
![=\left[\begin{array}{cc}6&6\\-5&-5\end{array}\right].](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6%266%5C%5C-5%26-5%5Cend%7Barray%7D%5Cright%5D.)
This option is false.
Answer: correct options are A and C.
