CPhill

LOL!!!!...good job, RP   !!!

1  3  2  5  10  8  9   15   0  7  12   13  6  18

Let's order these

0  1   2   3          4  observations  from 0 - 4

5  6  7  8   9       5  observations from 5 - 9

10  12  13          3  observations  from  10 - 14

15   18               2  observations from  15 - 18

"b"  is the correct answer

60  25  86  56   45  48  90  75   30   67  90 36  80   15   32  65   61 

Let's  order these

                                0  from 0 - 9

15                            1  from 10 - 19

25                            1  from  20 - 29

30 32 36                  3  from 30 - 39

Note that we can stop here, RP......"a"  is the only one  with these values 0, 1, 1 , 3  ......

Do  yuo see how to do this  ???

Sum of  the first n terms of a geometric series  =

First term   [  1  -  common ratio^n]  /  [ 1  -  r]

Here.....r  =  (1/4)  and n  =  15

So we have

2  [  1 - (1/2)^15] / [ 1 - 1/2]  =

2[ 1 - (1/2)^15] / (1/2)=

4 [ 1 - (1/2) ^15]  =  3.999 ≈ 

4

We can use the sine inverse to find this

asin ( 17.3 / 18)  =  73.96°   .....It is safe  !!!

We need to find  the variation constant, k

We have that

f(x)  = k(x)

160  =  k (5)      divide both sides by 5

32  = k

So  when x  = 0.5, we have

f(x)    = 32 (0.5)   =  16

Just as  Supermanaccz  found   !!!!

We have a 30-60-90 right triangle

The side opposite the 30° angle forms the base of the triangle

The side opposite the 60° angle forms the height and is √3 times the base

So....the area is

(1/2)(base)(height)  =

(1/2)(8) (8√3)  =

32√3  ≈ 

55.4 in^2

20)

? /  6   =  [6 - 4] / 4

? / 6  =  2/4

?/ 6  =  1/2

?  = 3

The side length  = 3 + 6  = 9

21)

10 / 4   =  [2x + 5 ] / 6

5/2  = [ 2x + 5 ] / 6       cross-multiply

30  = 2 [ 2x + 5 ]

30  = 4x + 10   subtract 10 from both sides

20  =  4x     divide both sides by 4

5  =  x

22)

[8 + 2x ] / 4   =  15 / 3

[8 + 2x] / 4  = 5

8 + 2x   =  4*5

8 + 2x  = 20

2x  = 12

x  = 6

16).....I think this is correct...

16/20  = ? / 45

4/ 5   =  ? /45       cross-multiply

45*4  = 5*?

180 = 5*?    divide by 5

36  =  ?

17)  

?/10  = 20/25

?/10 =  4/5      cross-multiply

5?  =  4 * 10

5? = 40     divide both sides by 5

?  =  8 

18)

?/4  =  6/3

?/4  = 2      multiply both sides by 2

?  = 8

19)

12/9  = ? / (33-9)

4/3  = ? / 24     cross-multiply

24*4  = 3* ?     

96  = 3 * ?      divide both sides by 3

32  = ? 

2 ( 2.5x + 4)   =( 7x - 2 )    simplify

5x + 8  =  7x - 2       add/subtract  2, 5x  to/from both sides

10  = 2x       divide both sides by 2

5  = x 

So  AC   =  7(5) - 2   =  35  - 2   =  33°

13...Correct  !!!

14.   

(x  + 2 ) / 15  =  8 /10      

(x + 2) / 15  =  4/5    cross-multiply

5(x + 2)  = 15 * 4

5x + 10  =  60

5x  =  50

x  =  10

15.  This one is a little tougher  !!

9 /15   = [2x - 6] / 20       simplify 

3/5  =  2[x - 3] / 20

3/5 = [x - 3]  / 10     cross-multiply

30  = 5[ x - 3]

6  = x - 3

9  = x