CPhill

-0.23    -0.123   -0.112233    0.123 (twice)   0.223    0.25    

Sum of 2nd and 6th  =   -0.123 + 0.223  =  0.1

(9.8) (7.6)  = 74.48

(9.7) (8.6)  = 83.42

Here's what I get

In  a 10 day period....the  company produces  2 pipes per day

In a 12 day period before the fuel increase, the company would produce  2 (10/12)  = 2 (5/6)  =10/6  = 5/3 pipes per day

Note  that 12 days * ( 5/3) pipes per day    = 60 / 3 =  20 pipes

So now, after the fuel increase the number of pipes produced per day =  (5/3)([700 + 500 ] /700) =

(5/3)(1200/ 700)  = (5/3)(12/7)=  60/21 = 20 / 7   pipes per day

So in  12 days, the company now produces   12 (60/21) =  (3/7)(60)=  180 / 7 =  25.7 pipes = 25 pipes

sin 4A  = sin 5A

4A =  180  - 5A

9A   =180

A  =  20°

24x^3  - 121x^2 +  87  - 8  =  0

The product of the roots =  -(-8) / 24  =  1/3

log ₃  1/3  =   log ₃  3 ^-1  =   -1* log ₃ 3 =   -1 (1) =  -1

If   -5 -8i  is a  root so is    -5 + 8i

The sum of the roots =  -(a - 4i)  =  -a + 4i

So

-10  =  -a + 4i

a =  10 + 4i

The product of the  roots =  29 + bi

So

(-5 - 8i) (-5 + 8i)  = 29 + bi

25 - 64i^2  =  29 + bi

25 + 64  =  29 + bi

89  = 29 + bi

60  = bi

Get the bases the same on  each side

9^y =  (3^5) * (9)  * (27^3)

(3^2)^y  =  (3^5) * (3^2) * (3^3)^3

3^(2y)  = (3^7) * ( 3^9)

3^(2y)  = (3)^16      now...... solve for  the exponents

2y = 16

y   =16  /  2   =    8

When you finish your side, your brother will  still have two hours left.

In one hour you can  finish  1/2  of a side and your  brother can  fininsh 1/4 of aside

So...in one hour   working together  you  both  can  finish  1/2 + 1/4  = 3/4  of a side

Take the reciprocal of this =  4/3 

So....it will  take  4/3 of an hour  =  1hr 20 min =  80  min to finish once you start helping him

n /  (2010 * 7 * 11)  =

n / (2 *5 *  3 * 7 * 11 * 67)

A fraction will  have a terminal decimal representation  when the  denominator is only  a power of  2 or  5  or both

So....the smallest  n  that makes this a  terminating decimal  =  3 * 7 * 11 * 67  = 15477

The resulting fraction is   1/ (2  * 5)  =   1   / 10

We can choose any  4 of the 9  and  each of these can hold any of the  4 offices

So

C(9,4)  * 4!   = 3024   ways