Nadia built a robot to filter air and water efficiently. She expects the robot to filter more than

Question

Nadia built a robot to filter air and water efficiently. She expects the robot to filter more than

\[343\] liters of air and water while using less than
\[49\] Joules of energy.
\[12A+8W > 343\] represents the number of minutes the robot filters air
\[A\] and water
\[W\] to filter more than
\[343\] liters of air and water.
\[3A+4W < 49\] represents the number of minutes the robot filters air and water while using less than
\[49\] Joules of energy.
Does the robot meet both of Nadia's expectations by filtering air for
\[20\] minutes and filtering water for
\[15\] minutes?
Choose 1 answer:
Choose 1 answer:
(Choice A) The robot meets both of Nadia's expectations.
A
The robot meets both of Nadia's expectations.
(Choice B) The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.
B
The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.
(Choice C) The robot uses the expected amount of energy, but it doesn't filter the expected amount of air and water.
C
The robot uses the expected amount of energy, but it doesn't filter the expected amount of air and water.
(Choice D) The robot doesn't meet either of Nadia's expectations.
D
The robot doesn't meet either of Nadia's expectations.

Answer 1

Bot GPT 4-o mini answered
3 days ago

To determine if the robot meets both of Nadia's expectations, we need to evaluate the inequalities based on the given values for \( A \) (air) and \( W \) (water).

Nadia's expectations are expressed in two inequalities:

\( 12A + 8W > 343 \) (to filter more than 343 liters)
\( 3A + 4W < 49 \) (to use less than 49 Joules of energy)

We will substitute \( A = 20 \) minutes and \( W = 15 \) minutes into the inequalities.

First Inequality: \[ 12A + 8W > 343 \] Substituting \( A = 20 \) and \( W = 15 \): \[ 12(20) + 8(15) > 343 \] \[ 240 + 120 > 343 \] \[ 360 > 343 \quad \text{(True)} \]

The first inequality is satisfied.

Second Inequality: \[ 3A + 4W < 49 \] Substituting \( A = 20 \) and \( W = 15 \): \[ 3(20) + 4(15) < 49 \] \[ 60 + 60 < 49 \] \[ 120 < 49 \quad \text{(False)} \]

The second inequality is not satisfied.

Based on this evaluation, the robot meets the first expectation (amount of air and water filtered), but it doesn't meet the second expectation (energy used).

Thus, the correct answer is:

(Choice B) The robot filters the expected amount of air and water, but it doesn't use the expected amount of energy.