CPhill

4000(1 + .03)^4  ≈ $4502.04

3x - 7  = 17     add 7 to both sides

3x  = 24       divide both sides by 3

x  = 8

Very nice, heureka.....!!!....while my approach isn't as "mathematical"  as heureka's, it might be more intuitive.....

Look at the following pic : 

We can let AB  be the base of our triangle......and since the area of ABD cannot exceed 12, it must be that the height of ABD cannot exceed 2.  And notice that GF  will = this maximum height....

So......any point D chosen in area  AGF [except on AG itself]  will guarantee that triangle ABD  will have an area <= to 12.

Also......any point D chosen in area  BGFD [except on BG itself]  will guarantee that triangle ABD will have an area <= 12.....because the base of such a triangle will= 12  and the height will be <= 2

So.....the probability that ABD has an area <=12  =

[ area  AGF  + area BGFD]  / [area of triangle ABC] =

[4  + 16]  /  36  =

20 / 36  =

5/9

V   = 11,140,000 (1 + .0575)^t       where V is the value after t years

Correct Answers / Total Questions x 100%  =

11 / 15  x 100%  ≈  73%   [ as found by HaHa !!!  ]

1/a  + 1/b   =   1/c       get a common denominator on the right

[b  + a]  / ab   = 1/c      and we can write

ab / [ b + a]   =  c  / 1

ab / [a + b]  =  c

3log x  = 6      divide both sides by 3

log x  = 2    expoentially we have

10^2   =  x   =   100

100 (1 + .05)^5   ≈  $127.63

109 rounds to 110

27 rounds to 30

So......  110 + 30    =  140

Sufrace Area_sphere  =  4 * pi * radius^2   = 4 * pi * 7.5^2  ≈  706.86 units^2