Let's solve the given equation step-by-step to find the correct value of [tex]\( Z \)[/tex].
Given:
[tex]\[
\frac{5.5}{288} = \frac{Z}{398}
\][/tex]
To solve for [tex]\( Z \)[/tex], we need to isolate [tex]\( Z \)[/tex] on one side of the equation. We can do this by using cross multiplication. Cross multiplication involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the products equal to each other:
[tex]\[
5.5 \times 398 = Z \times 288
\][/tex]
Now, we can solve for [tex]\( Z \)[/tex] by dividing both sides of the equation by 288:
[tex]\[
Z = \frac{5.5 \times 398}{288}
\][/tex]
By performing this calculation:
[tex]\[
Z = \frac{5.5 \cdot 398}{288}
\][/tex]
We find that:
[tex]\[
Z \approx 7.600694444444445
\][/tex]
Hence, the closest approximation to the value of [tex]\( Z \)[/tex] from the given options is:
[tex]\[
7.6
\][/tex]
