2 gallons were left at the end of the day
First you find how many prizes were dolls. Then you subtract that number from 64.
Answer:
![\displaystyle \frac{2}{7}+\sqrt{121}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2%7D%7B7%7D%2B%5Csqrt%7B121%7D)
Step-by-step explanation:
<u>Rational Numbers</u>
A rational number is any number that can be expressed as a fraction
![\displaystyle \frac{a}{b}, \ b\neq 0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Ba%7D%7Bb%7D%2C%20%5C%20b%5Cneq%200)
for a and b any integer and b different from 0.
As a consequence, any number that cannot be expressed as a fraction or rational number is defined as an Irrational number.
Let's analyze each one of the given options
![\displaystyle \frac{5}{9}+\sqrt{18}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B5%7D%7B9%7D%2B%5Csqrt%7B18%7D)
The first part of the number is indeed a rational number, but the second part is a square root whose result cannot be expressed as a rational, thus the number is not rational
![\pi + \sqrt{16}](https://tex.z-dn.net/?f=%5Cpi%20%2B%20%5Csqrt%7B16%7D)
The second part is an exact square root (resulting 4) but the first part is a known irrational number called pi. It's not possible to express pi as a fraction, thus the number is irrational
![\displaystyle \frac{2}{7}+\sqrt{121}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B2%7D%7B7%7D%2B%5Csqrt%7B121%7D)
The square root of 121 is 11. It makes the whole number a sum of a rational number plus an integer, thus the given number is rational
![\displaystyle \frac{3}{10}+\sqrt{11}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B3%7D%7B10%7D%2B%5Csqrt%7B11%7D)
As with the first number, the square root is not exact. The sum of a rational number plus an irrational number gives an irrational number.
Correct option:
![\boxed{\displaystyle \frac{2}{7}+\sqrt{121}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Cdisplaystyle%20%5Cfrac%7B2%7D%7B7%7D%2B%5Csqrt%7B121%7D%7D)