CPhill

3 / 3^3  =   [3] / [ 3 * 3 * 3]   =  one 3 cancels on top/bottom  =   1 / [ 3 * 3]    = 1 / 9

21parts / 4 hrs = ? parts / 7 hrs      cross-multiply

7 * 21  = 4 * ?      divide both sides by 4

[ 7 * 21] / 4 = ?   = 36.75 parts in 7 hrs

15%  = .15        and  "of" means "multiply"......so we have

.15 * 70  =

10.5

8 cos(x) − 4 = 0   add 4 to both sides

8cos(x)  = 4      divide both sides by 8

cos(x) = 4/8

cos(x)  = 1/2     and this happens at   pi/3 and 5pi/3   on the requested interval

48 / 18 = 

[ 8 * 6 ] / [3 * 6] =       the 6s cancel on top/bottom

8 / 3

-1x > 15     divide both sides by -1 and reverse the inequality sign

x < -15

Assuming 150  is supposed to  be 150m^2.....we have

45* 82 / 150  =  24.6   [or, 25 tins]

5^-4 = 1/5⁴  = 1/ [5² * 5²]  = 1 / [25 * 25]   = 1/ 625

See the graph  of the constraints, here : https://www.desmos.com/calculator/laixdb2hd8

There is only one corner point [vertex] at (400,500)

The max profit will be :

P = 14(400) + 22(500)  - 900  = $15700

96,97,98,99,100,101,102,103,and 104  =

Each of the first 4 terms written in reverse order and paired with the last 4 terms will produce a sum of 4(200)

Adding the middle term - 100 - produces   4(200) + 100  = 800 + 100   = 900