To solve for [tex]\( x \)[/tex] in the given proportion:
[tex]\[
\frac{19}{40} = \frac{x}{3.6}
\][/tex]
we use the property of proportions which states that if [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], then [tex]\( a \cdot d = b \cdot c \)[/tex].
Here, [tex]\( a = 19 \)[/tex], [tex]\( b = 40 \)[/tex], [tex]\( c = x \)[/tex], and [tex]\( d = 3.6 \)[/tex]. Therefore, we can write:
[tex]\[
19 \cdot 3.6 = 40 \cdot x
\][/tex]
Next, we solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{19 \cdot 3.6}{40}
\][/tex]
Calculating the numerator [tex]\( 19 \cdot 3.6 \)[/tex]:
[tex]\[
19 \cdot 3.6 = 68.4
\][/tex]
Now, divide by the denominator 40:
[tex]\[
x = \frac{68.4}{40} = 1.71
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( 1.71 \)[/tex], and the correct answer is:
[tex]\[
\boxed{1.71}
\][/tex]
