CPhill

B = 38°

c  =  18

So...C   = 90  - 38  =   52°

Using the Law of Sines

b/ sin B  = c / sin C

b /sin (38)  = 18 / sin (52 )  

b  =   18*sin(38)  / sin( 52 )   = 14.06 

sin^-1  = .2945   ≈  17.127557612801°

minutes  = .127557612801* 60  = 7.65345676806

seconds = .65345676806  * 60 =  39.21" 

So

17 ° 7'  39.21"

tan (50°)  ≈  1.1918

cos (134°) ≈ -0.6947

If x + 1/x = 7, then what is the value of x^2 + 1/(x^2) + 1?

Note that

(x + 1/x)^2   = 7^2

x^2  + 2 (x * 1/x)  + (1/x)^2  = 49

x^2  + 2(1)  + 1/x^2  =  49

x^2  +  2  +  1/x^2   =  49      subtract 2 from both sides

x^2  + 1/x^2   =  47   ......so.....

x^2 + 1/x^2  + 1   =  47  + 1

x^2 + 1/x^2 +  1   = 48

Well...don't know about the "cool"  part...but....here goes nothing......

                       Algebra      Not in Algebra     Total

Chemistry             5               6                        11

Not in Chemistry  14            15                        29

Total                     29            21                        40

A)  N(Algebra  or Chemistry)  =  N (Algebra)  + N (Chemistry) - N (In Both) =

                                                      29          +         11             -           5            =     35   

B)   Ratio of those in just Chemistry to total  =   6 / 40   =  3/20

So.....we would expect the same ratio  in  2000  =  3/20 * 2000  =  (2000/20) * 3 =  600    

I'll let you write the "complete sentences" part based on  my answers...... 

If j, k, and l are positive with jk = 24, jl = 48, and kl = 18, find j + k + l.

jk  = 24 ⇒  24/j  = k

jl = 48  ⇒  48/j  = l

kl = 18   

So

kl  = 18

(24/j) (48/j)  = 18

1152 / j^2  = 18

j^2  = 1152/18

j^2  = 64   take the positive root

j =  8

So.....24 / j = k   ⇒    24 / 8  = k ......  3  = k

And  48 / j  = l ⇒   48 / 8  = l    ......  6  = l

So

j + k + l    = 8 + 3  +  6  =   17

Sorry, Manuel...I got distracted...I meant to write:

"Keep  the degrees....divide the minutes by 60   and the seconds  by 3600"

See my corrected answer!!

Here's the second one

39  +  50/60  + 35/ 3600   =  39.8431°

                       O     A       B     AB         Total
Male (M)    210    174      74   42          500
Female (F) 315    261    111   63          750
Total           525    435   185   105       1250

P (A / M)   =  "probability that the student has blood type A  given a male"  =   174 / 500   =  87 / 250

P(A ∩ M)  = P(A)  * P(M)  = 

174/1250     =      (435/1250) *  ( 500/ 1250 ) 

87/625   =  87/625

"C"  must be correct.......

r^2  + s^2  =  1

r^4  + s^4  = 7/8

s^2  =  1  - r^2

s^4  = (1-r^2)^2   =  r^4 - 2r^2  + 1

So

r^4  +  s^4  = 1

r^4  + r^4 - 2r^2  + 1  = 7/8

2r^4 - 2r^2  + 1/8  = 0            divide through by 2

r^4 - r^2 + 1/16  = 0

r^4 - r^2  = - 1/16      complete the square on r

r^4  - r^2  +1/4  =  -1/16  + 1/4

(r^2 -1/2)^2  =  3/16         take the positive root of both sides

r^2  - 1/2  = √3/4

r^2  =  √3/4  + 1/2

r^2  = [ 2 + √3] / 4      take the positive root

r  =√[ 2 + √3 ] / 2

So.....

s^2  = 1  - r^2

s^2   =  1  - [ 2 + √3] / 4

s^2  = [ 4 - 2 - √3] / 4

s^2  = [ 2 - √3 ] / 4

s  = √[ 2 - √3 ] / 2

So  rs  = √[ 2 + √3 ] / 2  * √[ 2 - √3 ] / 2   =   √ [ (2 + √3) (2 - √3) ]  / 4  = √ [ 4 - 3]  / 4  =   1/4

C  = 50  + 2N

Where C  is the toal cost and  N  is the number of gigabytes used