CPhill

I would also like to echo ND's thoughts....thanks to Melody for all she does on here.....

I'm still getting "phantom messages," as well.......maybe they're from a "ghost" poster.....!!!  Who knows ???

I like ND's idea about classifying the posts according to grade level or topic......I don't know if the site mods would be responsible for "moving" the topics to appropriate areas (yuck, another "task"), or whether the site could include a "menu" for the questioners in which they could choose to post where they thought most appropriate. (Maybe we could include a "miscellaneous" category if a questioner were uncertain!!).

Those are my thoughts......but, I might have more as they occur to me !!!

Very impressive graphics, ND.......amazing, really  !!!

99% = .99    

"of" means  "multiply"   

So we have

.99 * 50  =  $49.50

cot(sin^-1(2/3))

First, let's evaluate sin^-1 (2/3) = 41.810314895779°

So..........cot(41.810314895779) = 1.118033988749441

Notice that if this angle could also lie in the second quadrant..... there, the cotangent would be........ (-1.118033988749441)

The sample space is just a listing of the possible outcomes......so we have....

{14, 16, 18, 20 }

For the first one, we can use the tangent to solve. We know an angle and an adjacent side to the angle. We are looking for the opposite side. So......

tan(50) = opposite/100       multiply both sides by 100

100tan(50) = opposite  ≈ 119.18 m

For the second one, we are looking for the ladder length (the hypoteneuse). We know an angle and the opposite side. The thing that relates all three of these is the sine. So we have..

sin(60) = 15/x   where x is the hypoteneuse (the ladder length).....rearranging, we have...

x = 15/sin(60) ≈ 17.32 m

And that's it  !!!

Thanx for that link, reinout.....!!!

This one is similar to this one that I just worked  →  -1/2(b)-3=>9......look at that answer and see if you can work through this one......you won't learn anything just by looking at our work.......

Remember the rule of exponents here......  aⁿ / a^m   =   a^n-m

So ...if I had......  5⁶/5²   ...it would equal........  5^6-2  =  5⁴

Now...see if you can do yours, based on this....if not.....let me know.....

(-1/2)(b)-3 ≥ 9       Add 3 to both sides

(-1/2)b ≥ 12          Multiply both sides by -2 and reverse the inequality sign (we must always do this when multiplying or dividing an inequality by a negative).....so we have....

b ≤ -24     Let's check this in the original problem by choosing some number less than or equal to -24 ...... -30 should work, if we're correct !!

(-1/2)(-30) - 3  ≥ 9

15 - 3  ≥  9

12 ≥  9

Yep....it looks OK !!!