Bot GPT 4-o mini We need to find the value of \( a \) such that:
\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]
First, we simplify the right-hand side:
\[ 40 \times (a \times 10^2) = 40a \times 10^2 \]
Now equate both sides of the equation:
\[ 8 \times 10^3 = 40a \times 10^2 \]
To simplify the equation, we can divide both sides by \( 10^2 \):
\[ \frac{8 \times 10^3}{10^2} = \frac{40a \times 10^2}{10^2} \]
This simplifies to:
\[ 8 \times 10^{3-2} = 40a \] \[ 8 \times 10^1 = 40a \] \[ 8 \times 10 = 40a \] \[ 80 = 40a \]
Now, solving for \( a \):
\[ a = \frac{80}{40} = 2 \]
Thus, the value of \( a \) is \( \boxed{2} \).
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