Question

consider the following hypothetical basketball records for college a and college b. answer parts a through c.

	college a	college b
away games	12 wins, 4 losses	56 wins, 20 losses

a. give numerical evidence to support the claim that college a has a better team than college b. choose the correct answer below.
a. college a lost only 23 games, whereas college b lost 39 games.
b. college a won 10 of their home games, whereas college b won 9 of their home games.
c. college a won about 34.5% of their home games and about 75% of their away games, whereas college b only won about 32.1% of their home games and about 73.7% of their away games.

b. give numerical evidence to support the claim that college b has a better team than college a. choose the correct answer below.
a. college b won 65 games, whereas college a only won 22 games.

Explanation:

Step1: Calculate total games for College A

Home games: 10 wins + 19 losses = 29 games. Away games: 12 wins + 4 losses = 16 games. Total games for A: \(29 + 16 = 45\) games. Losses for A: \(19 + 4 = 23\) losses.

Step2: Calculate total games for College B

Home games: 9 wins + 19 losses = 28 games. Away games: 56 wins + 20 losses = 76 games. Total games for B: \(28 + 76 = 104\) games. Losses for B: \(19 + 20 = 39\) losses.

Step3: Analyze option A

College A lost 23 games, College B lost 39 games. Since A has fewer losses, this supports A being better.

Step4: Analyze option B

College A home wins: 10, College B home wins: 9. A has 1 more home win, but this is a small factor.

Step5: Analyze option C

Calculate win percentages:

• College A home win %: \(\frac{10}{29} \approx 34.5\%\), away win %: \(\frac{12}{16} = 75\%\)
• College B home win %: \(\frac{9}{28} \approx 32.1\%\), away win %: \(\frac{56}{76} \approx 73.7\%\)

A has higher home and away win percentages, supporting A is better.

For part a, option C also supports, but option A (fewer losses) and C (higher win percentages) are strong. But let's check the first part's options:

Wait, the first part (a) is to support A is better. Let's re - evaluate:

Option A: A lost 23, B lost 39. Correct, as fewer losses mean better.

Option B: A home wins 10, B home wins 9. A has 1 more, but total games differ.

Option C: A's home and away win % higher. Correct.

But let's check the numbers again.

For part a, the correct option is C? Wait, no:

Wait, the question is "Give numerical evidence to support the claim that college A has a better team than college B".

Let's recalculate win percentages:

College A:

Home games: 10 wins, 19 losses. Total home: 29. Win %: \(10/29\approx34.5\%\)

Away games: 12 wins, 4 losses. Total away: 16. Win %: \(12/16 = 75\%\)

College B:

Home games: 9 wins, 19 losses. Total home: 28. Win %: \(9/28\approx32.1\%\)

Away games: 56 wins, 20 losses. Total away: 76. Win %: \(56/76\approx73.7\%\)

So A has higher home and away win percentages, which is option C.

For part b, to support B is better:

Option A: B won 9 + 56 = 65 games, A won 10 + 12 = 22 games. B has more total wins, so this supports B is better.

Answer:

a. The correct answer is C (College A won about 34.5% of their home games, and about 75% of their away games, whereas college B only won about 32.1% of their home games and about 73.7% of their away games) and A (College A lost only 23 games, whereas college B lost 39 games). But among the options given (A, B, C), let's check the options again:

Option A: College A lost only 23 games, whereas college B lost 39 games. Correct.

Option B: College A won 10 of their home games, whereas college B won 9 of their home games. A has 1 more home win, but B has more total games.

Option C: College A won about 34.5% of their home games, and about 75% of their away games, whereas college B only won about 32.1% of their home games and about 73.7% of their away games. Correct.

But the options are A, B, C. Let's see the problem's options:

The options are:

A. College A lost only 23 games, whereas college B lost 39 games.

B. College A won 10 of their home games, whereas college B won 9 of their home games.

C. College A won about 34.5% of their home games, and about 75% of their away games, whereas college B only won about 32.1% of their home games and about 73.7% of their away games.

All three options have some merit, but the most comprehensive is C, as it looks at win percentages (which account for the number of games) rather than just raw wins or losses.

For part b, to support B is better:

Option A: College B won 65 games (9 + 56), College A won 22 games (10 + 12). B has more total wins, so this supports B is better.