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:
I think the answer would be C
Answer: (4/5)^7 x 1/5
Step-by-step explanation: This is a geometric probability distribution. The probability of a success is 20% = 1/5 and the probability of a failure is therefore 4/5.
We want to know the probability that Ben is successful on the eight attempt. This means he has failed the first 7 times but succeeds on the 8th try.
So probability is (4/5)^7 x 1/5
Answer:
Graph A
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Since we are dealing with a slope of zero, we replace m with 0:
y = 0x + b
y = b
Here, we see that we would have a horizontal line. Therefore, graph A would be our answer.
13) First, take the constant (number that is not a variable. In this case -59) and use arithmatic to bring it to the other side. So we have n^2 + 14n = 51
Then to complete the square, we have to do a quick computation. Take the coefficient with the single variable, not the squared variable (in this case 14) and divide it by 2, (getting seven). Now, square that answer, seven, leaving us with 49. Add that to the end of the equation as the coefficient, but remember to add it to the other side of the equation too, following the math rules. So now we have n^2 + 14n + 49 = 100. Now, we can factor the left side to be (n+7) * (n+7), or (n+7)^2. Now our equation is (n+7)^2 = 100. We can take the square root of both sides, giving us: n + 7 = -10 and n +7 = 10 (because when you take the square root of a number, it could be positive or negative. Now solve those two equations for n and you have your answer: n = -17 and n=3
Sorry this was such a long, confsing answer. It's really not as hard as it seems, I just wanted to kind of explain how to do it.
