Question

analla is a school district manager. here are some details about two schools in her district for the last school year: chart with details of school a and school b, including number of students, number of teachers, graduation rate, budget per student, % of students in sports clubs, number of sports medals won, sat average, sat range (min - max) analla wants to know which school has higher academic achievements relative to the budget per student. 1) analla thought of two different ways to define this quantity. identify these two definitions among the following options. choose 2 answers: a sat average divided by budget per student b graduation rate divided by budget per student c number of sports medals won divided by budget per student d graduation rate divided by number of sports medals won 2) determine which school has higher academic achievements relative to the budget per student, according to the two definitions. did you get the same result for both definitions? choose 1 answer: a yes. according to both definitions, school a has higher academic achievements relative to the budget per student. b yes. according to both definitions, school b has higher academic achievements relative to the budget per student. c no. the definitions have opposite results.

Explanation:

1)

To determine academic achievements relative to budget per student, we need measures of academic achievement (like SAT average, graduation rate) divided by budget per student. Option A uses SAT average (academic) over budget. Option B uses graduation rate (academic) over budget. Option C uses sports medals (not academic) and D is graduation rate over sports medals (not related to budget). So A and B are correct.

For SAT average / budget: School A (≈0.1143) > School B (0.1). For graduation rate / budget: School B (9e - 5) > School A (≈7.619e - 5). Thus, definitions give opposite results.

Answer:

A. SAT average divided by budget per student, B. Graduation rate divided by budget per student

2)

First, calculate for School A and School B using both definitions.

Definition 1: SAT average / Budget per student

• School A: \( \frac{1200}{10500} \approx 0.1143 \)
• School B: \( \frac{1000}{10000} = 0.1 \)

School A is higher here.

Definition 2: Graduation rate / Budget per student (convert rates to decimals: 80% = 0.8, 90% = 0.9)

• School A: \( \frac{0.8}{10500} \approx 7.619\times10^{-5} \)
• School B: \( \frac{0.9}{10000} = 9\times10^{-5} \)

School B is higher here.

So the results are opposite.