CPhill

2/3 * 535 = about 357 members of Congress

If you want to factor this, remember, we need to take any common factors out, first.  So we have :

2x^2+8x+6  =

2(x^2 +4x + 3) =

2 (x + 1) (x + 3)

And that's it.....!!!

(A)  Sample Space :

HHH

HHT

HTT

TTT

TTH

THH

THT

HTH

(B)  This is a compound event.....tossing one coin is a simple event........tossing two or more is a compound event

Minimize the objective function  150x + 50y  where x is the number of packages ordered from Jungle and y is the numer of packages ordered from OHagan

And each package ordered from both companies supplies 5 mystery novels......and we must have at least 2500 of these....so, the constraint becomes :

5x + 5y >= 2500  →  x + y >= 500

And each package from Jungle supplies 10 romance novels and each package from OHagan supplies 5 romance novels.....and we need at least 3500 of these....so we have

10x + 5y >= 3500  →  2x + y >= 700

Further....at least 75% of the the packages must come from OHagan....in other words, out of every 4 ordered, at least 3 must come from OHagan......put another way, we have

3x <=  y

Look at the following graph :   https://www.desmos.com/calculator/6hdrqjgy2o

Since mins and maxes occur only at the corner point of a feasible region, the only point that "works" here occurs at (140, 420)..........

Thus.........  150(140) + 50(420) = $42000 is the minimum cost by ordering 140 packages from Jungle and 420 packages from OHagan....

100/5*4+4³      using the order of operations, we have

20 * 4 + 64   =

80 + 64  =

144

Thanks, Guest.......saseflower and  I  missed that  " - "

Very nice, saseflower.......5 points from me......

Very good, sasefower....I might add one tiny thing.....

8 = 14x    divide both sides by 14

8 / 14 =    x    = 4 / 7 

-85.8/[12+(-3-7)+4]  =

-85.8  / [ 12 + (-10) + 4 ]  =

-85.8 / [ 2 + 4 ] =

-85.8 / 6 =

- 14.3

64x+-48=-6x-22      add 6x, 48 to both sides

70x = 26      divide both sides by 70

x  = 26 / 70   =  13 / 35