CPhill

The sum will be given by :

100  [ 1  - (1.02)^8  ]  /  [ 1  - 1.02 ]  =

$ 858.30

11.

The points of discontinuity  will be where the denominator   =  0

So...we want to  solve this

x^2 +  5x   - 6   =   0

factor

( x + 6) ( x -1)   = 0

Setting each factor to 0  and solving for  x  produces

x + 6  = 0            x  - 1   =  0

x  = -6                x  =  1    ⇒  third answer

Note that  24  - 10  =  14  don't have black  fur

And suppose  that these 14 are part of the 17 that don't catch mice

Then.....3 that catch mice  must also have black fur....and this is the smallest number that do not catch mice but have black fur

f(8)  = sqrt (8)

g (f(8)) =  [ sqrt(8) ] ^2   =   8

f (g ( f (8) )  =  f (8)  = sqrt (8)

g ( f (g ( f (8) ) )  = g (sqrt (8))  = [ sqrt (8) ]^2  =  8

f (g ( f ( g (f (8)) ) )  =  f (8)  =  sqrt (8)

7.  This relationship is neither

9. 

The correct equation  is

y =      4

        ____   +     6

         x - 7

Here's a graph to  show this  :  https://www.desmos.com/calculator/mjcdi4to3c

4.    5^(3x)  = 900      take the log of both sides

log 5^(3x)   = log 900

3x * log (5)  = log (900)

x =  log (900)  / [ 3 * log (5) ]  ≈  1.41

5.  f  =x^2 + 5        g  =   [ x + 5 ] / x          f ° g  (-3)  =  f [ g(-3) ]

g(-3)  =  [ -3 + 5 ] / -3  =   -2/3

f (-2/3)  =   (-2/3)^2  + 5  =   5 + 4/9  =  49 / 9

2.  We  can represent this as

3^(1/3)  / 4^(1/3)      multiply top/bottom  by   4^(2/3)

[3^(1/3) * 4^(2/3)  / [ 4^(1/3) * 4^(2/3)  ]  =

[ 3^1  * 4^2 ] ^(1/3)  /  4   =

[ 48]^(1/3)  / 4  =

[ 8 * 6 ]^(1/3)  / 4  =

2 * [ 6] ^(1/3)  / 4  =

6^(1/3)  / 2   ⇒  second answer

3.   27^(1/3)   = cube root of 27   = 3

⁴ √ [2401  x¹²  y ¹⁶  ]   =

7 l x³ l  y⁴

[ We need the absolute value bars to denote that  x³  is a positive quantity]

16

20th  term of 

-2   4  -8    16

This is a geometric series where the nth term can be represented as

(-2)^n

So....the 20 th   term is

(-2)^20  =

1048576