KitSoundwave

for 30 dogs to 20 cats: 

a) 3/2

b) 1.5

c) for every 3 dogs there are 2 cats

for the orange leaf one: 

a) 4/7

b) 0.571428

c) for every 4 sugar cones orange leaf sells, there are 7 waffle cones

use systems of equations

the two systems are: 

f=9s

f+3=6(s+3)

steps: 

1. expand 6(s+3) to get 6s+18

2. substitute f in terms of s (and we know that f=9s, so then the second equation becomes 9s+3=6s+18

3. now we know how to solve. add -6s to both sides, add -3 to both sides, and finally divide both sides by 3. 

We get: 

f=45, s=5

so the son is 5 years old and the father is 45 years old

so you're asking 16=4^x

16=4^2 so x=2

we need to start by doing this: 1-0.4=0.6

then, 72/0.6=120

how many are not cows? 120-72=48

120+48=168

Actually, when people see titles like @Guests's, they likely won't help because it's something called "cheating" . 

in this case, the formula is the # of 3 digit palindromes / the # of 3 digit numbers. By bashing we get 90/900 and that can be simplified to 1/10
 

why does it say "blocked by moderator"?

this case is the range of numbers choose sides of a triangle. 

so 6 choose 3 = 20

and we want to choose a set of numbers that when you apply the pythagorean theorem (a^2+b^2+c^2) the result is a whole number

only 3, 4, and 5 works in this case between the range 1 to 6 (proof: 3^2+4^2=9+16=25, 25=5^2)

so 1, 2, and 6 doesn't work

so the probablility is 1/2 if no number can be used more than once. 

but if a number can be used more than once in the range 1 to 6 (still only the set 3, 4, and 5 works), then the answer is 1/6 choose 3 = 1/20

use the good ol' pythagorean theorem

a^2+b^2=c^2

11^2+17^2=410

x^2=410

sqrt410 (can't be simplified any further) 

after bashing randomly, I got x=6, y=2, z=4, and L=8. 

since x=6 and z=4, 6+4=10