Answer: The fraction of the pets that are dogs with long hairs is [tex]\dfrac{1}{4}.[/tex]
Step-by-step explanation: Given that [tex]\dfrac{3}{8}[/tex] of the pets in the pet show are dogs and [tex]\dfrac{2}{3}[/tex] of the dogs have long hair.
We are to find the fraction of the pets that are dogs with long hairs.
Let x represents the total number of pets in the pet show.
So, the number of dogs in the pet show is
[tex]n_d=\dfrac{3}{8}\times x=\dfrac{3x}{8}.[/tex]
Therefore, the number of dogs with long hairs in the pet show is
[tex]n_{dh}=\dfrac{2}{3}\times\dfrac{3x}{8}=\dfrac{1}{4}x.[/tex]
Thus, the fraction of the pets that are dogs with long hairs is [tex]\dfrac{1}{4}.[/tex]
