Question 6:
To find the correct inequality for the student's situation, we need to represent the total amount of money spent on the calculator and notebooks. The cost of the calculator is $24, and each notebook costs $2. If the student buys \( n \) notebooks, the total cost of the notebooks would be \( 2n \).
The total expenditure would then be:
\[ 2n + 24 \]
Since the student cannot spend more than $37, the correct inequality is:
\[ 2n + 24 \leq 37 \]
However, looking at the options provided, the equivalent form is:
\[ 37 \geq 2n + 24 \]
So the correct response is:
37 ≥ 2n + 24.
Question 7:
To solve the equation \( A = 12(a + b) \) for \( b \), follow these steps:
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Divide both sides by 12: \[ \frac{A}{12} = a + b \]
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Subtract \( a \) from both sides: \[ b = \frac{A}{12} - a \]
However, let's look at the original options provided to see if any match.
None of the options directly match \( b = \frac{A}{12} - a \).
But if we were to manipulate the equation \( A = 12(a + b) \) after expanding that gives us:
\[ A = 12a + 12b \] And isolating \( b \):
\[ 12b = A - 12a \]
Dividing through by 12, we get:
\[ b = \frac{A}{12} - a \]
Given the choices provided, let's check which one is closest in form to our resultant equations, but it seems like none of the options reflect the correct algebraic manipulation of the given equation.
Thus, very likely, our presented options might have an error, or if you meant to give one perhaps matching \( b = 12A - a \), then that is also invalid as it translates incorrectly, but none of the options worked out.
If we are to select the best option from the given responses based on any mix-up, then we can pick: b = 12A - a, however, it doesn't compute correctly unless its framed appropriately.
Please ensure the options you're looking at are exact, or perhaps exceed those confines for an accurate choice.