Alan

Some calculators, such as the TI-Nspire with CAS, will simplify this.

Just use the calculator here to find x.  x = sin^-1(3/4)   This may also be written as asin(3/4).

You should find that x = 48.59° (In the first quadrant.  It could also be 180° - 48.59° = 131.41° in the second quadrant).

$${\mathtt{x}} = \underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)} \Rightarrow {\mathtt{x}} = {\mathtt{48.590\: \!377\: \!890\: \!729^{\circ}}}$$

I think "hobo" is not just an Australian term.  Here's an extract from Wikipedia:

Nice one Melody!!

Might be simpler to factor the 20 first:

37 + 20*(log6000 + log30)

37 + 20*log(6000*30)

37 + 20*log180000

$${\mathtt{37}}{\mathtt{\,\small\textbf+\,}}{\mathtt{20}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{180\,000}}\right) = {\mathtt{142.105\: \!450\: \!102\: \!066\: \!13}}$$

Doesn't a collar have two sides?  

I know, you very clearly specified the answer for one side!

I take it this means the normal cumulative distribution function.  Here is a graph of the normal cdf for a mean of 0 and standard deviation of 1:

If you have a data set x1, x2, etc.  for which you know the mean, xav, and standard deviation, s, and want to find the cumulative probability for a particular value of x, then calculate  z = (x-xav)/s and look up the corresponding value of cumulative probability (called cnorm(z) on the graph above).  You should be able to find better graphs if you search the internet.  Alternatively, use a piece of software which will calculate it for you, given the values of xav and s (again you can almost certainly find something on the internet to do this).

Or, if you are old-fashioned, use tables of values that are printed in books!

If this is meant to be log to the base 5 of (x-2) is 3 then:

log₅(x-2)=3 means  x-2 = 5³, so x = 5³+2, or x=125+2, or x = 127.

If it is meant to be log to the base 10 of 5*(x-2) =3 then:

log₁₀(5*(x-2)) = 3 means  5*(x-2) = 10³, so x-2 = 200, so x = 202

If it is meant to be log to the base 10 of 5, all multiplied by (x-2) = 3 then:

(x-2)*log₁₀(5)=3, so x-2 = 3/log₁₀(5) so x = 3/log₁₀(5)+2 or $${\mathtt{x}} = {\frac{{\mathtt{3}}}{{log}_{10}\left({\mathtt{5}}\right)}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} \Rightarrow {\mathtt{x}} = {\mathtt{6.292\: \!029\: \!674\: \!220\: \!178\: \!6}}$$

192 = -16t²+48t+160 Subtract 192 from both sides

0 = -16t²+48t-32  Multiply through by -1

0 = 16t^2-48t+32  Divide through by 16

0 = t²-3t+2  Factor

0 = (t-1)*(t-2)

So there are two solutions:  t = 1 and t = 2

Chris beat me to it!

speed = distance/time

Adam's speed = L/4.92   if L is the distance.

Anthony's speed = L/6.3

Adam's speed/Anthony's speed = (L/4.92)/(L/6.3) = (L/4.92)*(6.3/L) = 6.3/4.92

$${\frac{{\mathtt{6.3}}}{{\mathtt{4.92}}}} = {\frac{{\mathtt{105}}}{{\mathtt{82}}}} = {\mathtt{1.280\: \!487\: \!804\: \!878\: \!048\: \!8}}$$

so Adam is approximately 1.28 times as fast as Anthony, or about 28% faster.