A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:

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BlackTom AI · Accepted Answer

We start by identifying the given predictive model and the value to plug in.
The model is mark = 20 + 40 × log(hours). Here, hours = 20.
Next, compute log(20). Assuming log means base-10, log10(20) ≈ 1.3010.
Multiply by 40: 40 × 1.3010 ≈ 52.04.
Add 20: 52.04 + 20 ≈ 72.04.
Rounding to the nearest whole number gives 72.
Now evaluate each answer option:
- Option a: 78. If we substitute 78, the implied log(hours) would be (78 − 20)/40 = 58/40 = 1.45, which corresponds to hours ≈ 10^1.45 ≈ 28.2. This is inconsistent with hours = 20, so this option is not correct.
- Option b: 80. Implies log(hours) = (80 − 20)/40 = 60/40 = 1.5, so hours ≈ 10^1.5 ≈ 31.6. Again not matching 20 hours.
- Option c: 72. This matches our calculation: log(20) ≈ 1.3010, 40 × 1.3010 ≈ 52.04, plus 20 ≈ 72.04, rounded to 72. This aligns with the model for 20 hours.
- Option d: 140. Would require log(hours) = (140 − 20)/40 = 120/40 = 3.0, so hours ≈ 10^3 = 1000, which is completely inconsistent with 20 hours.
In summary, only the computation with 20 hours yields approximately 72 when rounded, making option c the correct choice.

MUF0142 Fund. Mathematics Unit 2 - Semester 1, 2025 7.4 Transforming Data Quiz (Formative)

A model that describes the association between the hours spent studying for an examand the mark achieved is: mark = 20 + 40 × log (hours) From this model, we would predict that a student who studies for 20 hours would scorea mark (to the nearest whole number) of:

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