Move everything to the left hand side:   x2 -9x -36 = 0  and factor the quadratic portion   (x-12)(x+3)=0   x = 12 or x = -3

The prob of the first being red is 2/6.  Once one is removed the odds of the second are 1/5.  Multiply them together to get the total probability:   2/6 x 1/5 = 2/30 = 1/15

6.4/9.3 = 68.8%

Set up a system of 2 equations in 2 variables:   x + y = 19   x - y = 1  and solve by adding the equations together   2x = 20   x = 10, y = 9

Work is defined as motion (force) over a distance.  If 2 people pull on something and it does not move, then force was exerted, but not work.  If something physically moves then work is being done on it.  Therefore, if the nail moves then work has been done on it.

1/5 + 1/7 + x = 1   where x is the fraction of money that the third child gets   x = 1 - 1/5 - 1/7  (35 is the common denominator)   x = 35/35 - 7/35 - 5/35   x = 23/35

Let L = length (L)   Then width (W) = (L+2)   The diagonal (D) = (L+4)   We know that D2 = L2 + W2  and substitute from above for W and D   (L+4)2 = L2 + (L+2)2   L2 + 8L + 16 = L2...

Let x = # of 2 hr classes, then (3030-x) = # of 4 hr classes   x(2)(4343) + (3030-x)(4)(4343) = 35263526   8686x + 52637160 - 17372x =- 35263526   -8686x = -17373634   x = 2000

With a mean of 70 and SD of 5, you have 3 standard deviations from the mean between 55 and 80.  So, in theory, you should have 99.7% of the data in that area.

Since the yield is 85%, we need to start with 45g/.85 = 52.9 g aspirin   (52.9 g C9H8O4)(1 mole C9H8O4 / 180 g C9H8O4)(1 mole C7H6O3 / 1 mole C9H8O4)(138.1 g C7H6O3 / 1 mole C7H6O3)   = 40.59

Area = 40" x 26" = 1040 sq in = 1040/144 sq ft  (144 sq in in a sq ft)= 7.22 sq ft   7.22 x 1.69 = \$12.20

(150 g Mg(OH)2)(1 mole Mg(OH)2 /58.3 g Mg(OH)2)(6 mole H2O / 3 mole Mg(OH)2)(18 g H2O / 1 mole H2O) = 92.6

62.5 / 5 = 12.5 m/s

(24-7)/24 = 17/24

First find the prime factors:   210 = 7 x 5 x 3 x 2 x 1   Odd factors are 1, 3, 5, 7, 35, 21, 15, 105

Let w = width of the rectangle, then l = 3w-4   Area = l x w   55 = (3w-4)(w)   55 = 3w2 -4w   0 = 3w2 - 4w - 55   0 = (3w + 11)(w - 5)   w = 5 or -11/3 (the width cannot be a negative number)   so w=5,...

p = mn + b   59 = 3000n + b 64 = 2000n + b   and solve by either substitution or elimination

A = 30000(1+.12/12)(12 x 10)  = 99011.61

C = D + 300   Total length:  D + (D+300) = 5530   2D = 5230   D = 2615