Here's the method on the first one (36)
The ratio is
, hence if we call
the number below
, we will have
hence
I_72__I_36_I_24_I_12_I
<span>I_126_I_
63_I_42_I_21_I
</span>
say we're going to add "x" gallons of water, now how many gallons of alcohol is in pure water? well 0%, and 0% of "x" is (0/100) * x = 0.
the 3 gallons we know are 100% alcohol, how many gallons of alcohol is in it? well (100/100) * 3 = 3.
the resulting mix will have x + 3 gallons total and it's going to be 15% alcohol, how many gallons of alcohol is that? (15/100) * (x+3).
now, the amount of alcohol never increased, so the original 3 gallons of only alcohol will remain even after the water has been added, so.
![\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{gallons of }}{amount}\\ \cline{2-4}&\\ \textit{pure water}&x&0.00&0\\ \textit{pure alcohol}&3&1.00&3\\ \cline{2-4}&\\ mixture&x+3&0.15&0.15(x+3) \end{array} \begin{array}{llll} \\[3em] \leftarrow \textit{this amount}\\\\ \leftarrow \textit{must be equal to this one} \end{array} \\\\\\ 3 = 0.15(x+3)\implies 3=0.15x+0.45\implies 2.55=0.15x \\\\\\ \cfrac{2.55}{0.15}=x\implies 17=x](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Blcccl%7D%20%26%5Cstackrel%7Bsolution%7D%7Bquantity%7D%26%5Cstackrel%7B%5Ctextit%7B%5C%25%20of%20%7D%7D%7Bamount%7D%26%5Cstackrel%7B%5Ctextit%7Bgallons%20of%20%7D%7D%7Bamount%7D%5C%5C%20%5Ccline%7B2-4%7D%26%5C%5C%20%5Ctextit%7Bpure%20water%7D%26x%260.00%260%5C%5C%20%5Ctextit%7Bpure%20alcohol%7D%263%261.00%263%5C%5C%20%5Ccline%7B2-4%7D%26%5C%5C%20mixture%26x%2B3%260.15%260.15%28x%2B3%29%20%5Cend%7Barray%7D%20%5Cbegin%7Barray%7D%7Bllll%7D%20%5C%5C%5B3em%5D%20%5Cleftarrow%20%5Ctextit%7Bthis%20amount%7D%5C%5C%5C%5C%20%5Cleftarrow%20%5Ctextit%7Bmust%20be%20equal%20to%20this%20one%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5C%5C%203%20%3D%200.15%28x%2B3%29%5Cimplies%203%3D0.15x%2B0.45%5Cimplies%202.55%3D0.15x%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B2.55%7D%7B0.15%7D%3Dx%5Cimplies%2017%3Dx)
Answer:
A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y. That is, given an element x in X, there is only one element in Y that x is related to. For example, consider the following sets X and Y.
Answer:
a=4+2/x <-- 2 over x its a fraction
Step-by-step explanation:
Answer:
11/1000 is the answer let me know if you need more help
