Final answer:
Ben's hand is the only one that contains all rational numbers, as the cards in his hand can be expressed as fractions or whole numbers, including sqrt(25) which equals 5, a rational number.
Step-by-step explanation:
The student's question asks which person's hand contains all rational numbers. Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, where q is not zero. Looking at the hands of all players, we can analyze their cards:
- Lisa: 2, √2, 5, 1/2 - The presence of √2, which is an irrational number, means Lisa's hand does not contain all rational numbers.
- Ben: 0.435, 0.5, √25, 0 - Since √25 is equal to 5, all of these numbers are rational. Ben's hand contains all rational numbers.
- Kari: π, 2, 6, -2 - π (pi) is an irrational number, so Kari's hand does not contain all rational numbers.
- Terri: 200, π, 50, 1.43256744376665... - The presence of π and the non-repeating, non-terminating decimal means Terri's hand also does not contain all rational numbers.
Therefore, the person whose hand contains all rational numbers is Ben.