CPhill

Total in sample  = [ 1017 + 46 + 649 + 22 + 2715 + 319 + 919 + 73 ] =  5760   (1)

Total unemployed   =  [ 46 + 22 + 319 + 73 ]  =  460     (2)

% Unemployed   =   (2)   /(1)   =   460 / 5760   =  7.9%    (round to 8% ) ⇒  "B" 

Let her normal time be  T

Let her normal rate be R

So

RT = D

RT = 18    ⇒   R  =   18/T     (1)

We need to convert 4 minutes to hours  =  4/60   = 1/15 hr

So....when she is slowed we have

(R - 9) ( T + 1/15)  = 18     (2)

Sub   (1)   into (2)   and we have

(18/T - 9) (T + 1/15) = 18      simplify

18 - 9T + (18)/ (15T) - 9/15 = 18     subtract 18 from both sides

 - 9T  + (6)/(5T) - 3/5 =  0       multiply through by -5T

45T^2 - 6 + 3T = 0

45T^2 + 3T - 6  = 0       divide through by 3

15T^2 + T-  2  =   0

(5T + 2) ( 3T - 1)  = 0

The first factor set to 0 and solved  for T produces a negative anser

The second factor set to 0 and solved for T produces   T  =1/3

This is in hrs

So   (1/3) hr   =  20 min   = her normal time to get to work

So....now...at the slowed rate   it takes her 4  minutes longer = 24min

And  24 minutes = 24/60 hrs  = 2/5 hrs

Check

R =  18 / (1/3) = 54mph

And   54mph * 1/3 hr = 18 miles

And at the slower rate

(54 - 9) ( 1/3 + 1/15)

(45) ( 18/ 45)   =  18 miles

Sel runs  3/8 lap in one minute

Mar runs 2/5 lap in one minute

So.... Mar runs  (2/5 - 3/8) =  [ 16 - 15] / 40    =  1/40   of a lap farther than Sel does in one minute

So....in 40 minutes....they will be even again

In this time     Sel runs (3/8)*40 = 15 laps

And Mar runs (2/5)*40 =  16 laps

So...combined.....they run 15 + 16   = 31 laps

You left out the number of times that Sel ran around the track.....

We found this equation as

f(x) = .003(2.04)^x

When x = 15, we have

.003 (2.04)^15   = 132.3 ⇒   C

No....but you are close

10500 * e^(.0375 * 9 ) = $14715.12  ⇒  "A"

In order....from top to bottom

Statement No.

3

1

5

2

4

Well......not too much to this

f(x) = 3 ( 1.023)^x

It is growth because   1.023  is > 1

I'll let you evaluate this one, NSS

We have

10500 * e^(.0375 * 9 )

See if you can do it.....I'll check your answer....if you want me to.....!!!

2x^2 - 5x - 3 = 0        factor the left side  

(2x + 1) ( x - 3)   = 0      set each factor to 0 and solve for x

2x + 1   = 0  subtract 1 from both sides          x - 3 = 0    add 3 to both sides

2x = -1     divide both sides by 2                      x = 3

x = -1/2 

Answers are in red, NSS