To solve the problem [tex]\(0.2 \, kg \times (-150 \, g)\)[/tex], let's break it down step-by-step:
1. First, convert 150 grams to kilograms:
[tex]\[ 150 \, g = \frac{150}{1000} \, kg \][/tex]
[tex]\[ 150 \, g = 0.15 \, kg \][/tex]
2. Next, we need to take into account that the problem requires multiplication by [tex]\(-150 \, g\)[/tex]. Thus, we introduce the negative sign:
[tex]\[ -150 \, g = -0.15 \, kg \][/tex]
3. Now, multiply 0.2 kilograms by -0.15 kilograms:
[tex]\[ 0.2 \, kg \times (-0.15 \, kg) = -0.03 \, kg^2 \][/tex]
4. Since the problem involves mass, let's also convert -0.03 kilograms back to grams:
[tex]\[ -0.03 \, kg = -0.03 \times 1000 \, g \][/tex]
[tex]\[ -0.03 \, kg = -30 \, g \][/tex]
Thus, the result of [tex]\(0.2 \, kg \times (-150 \, g)\)[/tex] is [tex]\(-0.03 \, kg\)[/tex] or [tex]\(-30 \, g\)[/tex].
Given the choices in the table:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|}
\hline
\text{\(0.2 \, kg \cdot -150 \, g = ?\)} &
\text{\(0.0050 \, kg\)} &
\text{50 \, gramos} &
\text{0.50 \, kg} &
\text{1850 \, gramos} &
\text{Ninguna de las anteriores, es la verdadera} \\
\hline
\end{array}
\][/tex]
The correct answer is:
[tex]\[ \text{Ninguna de las anteriores, es la verdadera} \][/tex]
as [tex]\(-0.03 \, kg\)[/tex] or [tex]\(-30 \, g\)[/tex] does not match any given option except "Ninguna de las anteriores, es la verdadera".
