ElectricPavlov

1>   Area shaded is included in Fish circle and Dog circle but NOT Cat circle    so   fish AND dog but NOT cat

2>  17 are listed as taking band....of these 8 ALSO take art....the remaining ones do not take art    17-8 = 9

3>  175

       86

       52

       18+25     (18 can ALSO speak French)

       32 + 18    (Again 18 can ALSO speak French...but it didn't ask this)

Find the inverse.....solve for x

y=5^x

log y = x log 5

logy /log5 = x          now change the x's and y's

y= logx/log5 = f^-1(x)

f^-1(k) = -3 = log k/log5         k= .008

https://www.symbolab.com/solver/limit-calculator/%5Clim_%7Bx%5Cto%5Cinfty%7D%20%5Cfrac%7B%5Cleft(x%5E%7B3%7D%2B5x%5Cright)%7D%7B%5Cleft(2x%5E%7B3%7D-x%5E%7B2%7D%2B4%5Cright)%7D

Sin = opposite/hypotenuse

opposite = sqrt(40^2-32^2) = 24      sin = 24/40 = 12/20 = 6/10 = 3/5 

Since the crates are 90 kg measured to the NEAREST 10kg ...I believe to be safe you have to assume that ALL of them can weigh

 94.999...  each.

Forgot the cable part....edited:

Since cable is rated at 6400 to two significant digits......it MIGHT only support   6350 kg   (or as much as 6449.99)

For safety you will have to assume the crates are 94.99 kg each and the cable will only support 6350 kg

Then    6350/94.99 = 66.85 ~~ 66 crates max

If x1 > x2     AND  f(x1) > f(x2)     this describes a function with a  POSITIVE slope  (  f' (x)  )

So f'(x) > 0

Assumig you started the second you were born AND 365.25 days/year:

75 x 365.25 x 24 x 3600 = $2,366,820,000.00

Since we know it is an upside down parablola, the two points where it crosses the x axis (where y=0) will define the width

so

y = 0 = -0.2 x  (x-20)       means   x = 0    and x = 20   are the places where it crosses the x-axis (ground level)

distance between 0 and 20 = 20 ft

If they do not have to be grouped into what office they are running for, just listed..... there are 18 candidates

18 * 17 * 16 *15.......* 3 * 2 *1 =  18 P 18   = 18! = 6.40237370573 x 10^15  possibilities.

First digit cannot be 5 so yo have   4 * 5 * 5 possible numbers = 100

    2 out of 5 will be even as 2 and 4 are the only evens     2/5 x 100 = 40 possibilities.