Answer:
case A. ![\sqrt{18}*\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D%2A%5Csqrt%7B6%7D)
case B. ![\sqrt{108}](https://tex.z-dn.net/?f=%5Csqrt%7B108%7D)
case E. ![\sqrt{3}*\sqrt{36}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%2A%5Csqrt%7B36%7D)
Step-by-step explanation:
we have
![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
we know that
![6\sqrt{3}=\sqrt{36*3}=\sqrt{108}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D%3D%5Csqrt%7B36%2A3%7D%3D%5Csqrt%7B108%7D)
<u>Verify each case</u>
case A) ![\sqrt{18}*\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D%2A%5Csqrt%7B6%7D)
![\sqrt{18}*\sqrt{6}=\sqrt{18*6}=\sqrt{108}](https://tex.z-dn.net/?f=%5Csqrt%7B18%7D%2A%5Csqrt%7B6%7D%3D%5Csqrt%7B18%2A6%7D%3D%5Csqrt%7B108%7D)
therefore
is equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
case B) ![\sqrt{108}](https://tex.z-dn.net/?f=%5Csqrt%7B108%7D)
so
is equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
case C) ![\sqrt{3}*\sqrt{6}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%2A%5Csqrt%7B6%7D)
![\sqrt{3}*\sqrt{6}=\sqrt{18}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%2A%5Csqrt%7B6%7D%3D%5Csqrt%7B18%7D)
therefore
is not equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
case D) ![\sqrt{54}](https://tex.z-dn.net/?f=%5Csqrt%7B54%7D)
so
is not equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
case E) ![\sqrt{3}*\sqrt{36}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%2A%5Csqrt%7B36%7D)
![\sqrt{3}*\sqrt{36}=\sqrt{108}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D%2A%5Csqrt%7B36%7D%3D%5Csqrt%7B108%7D)
therefore
is equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
case F) ![108](https://tex.z-dn.net/?f=108)
so
is not equivalent to ![6\sqrt{3}](https://tex.z-dn.net/?f=6%5Csqrt%7B3%7D)
Volume of a cube=side³
Data:;
volume=343 cm³
Therefore:
343 cm³=side³
side=∛343 cm³=7 cm.
Answer: the lenght of each side of the cube is 7 cm.
Answer:
$6,427.99
Step-by-step explanation:
-We first find the effective annual interest rate as follows:
![i_m=(1+i/m)^m-1\\\\=(1+0.0825/2)^2-1\\\\=0.084202](https://tex.z-dn.net/?f=i_m%3D%281%2Bi%2Fm%29%5Em-1%5C%5C%5C%5C%3D%281%2B0.0825%2F2%29%5E2-1%5C%5C%5C%5C%3D0.084202)
#We the use this rate to find the compounded amount after 18 years:
![A=P(1+i_m)^n\\\\=1500(1.084202)^{18}\\\\=6427.99](https://tex.z-dn.net/?f=A%3DP%281%2Bi_m%29%5En%5C%5C%5C%5C%3D1500%281.084202%29%5E%7B18%7D%5C%5C%5C%5C%3D6427.99)
Hence, the amount after 18 years is $6,427.99
Given that the total profit is <u>$2400.00</u> and he made <u>$30.00</u> in profit for each share.
Number of shares = $2400 ÷ 30 = 80
Answer: He bought 80 shares