Question

Mateo is studying a human hair with a diameter of 6.5 x 10^-4 inches and a horse hair with a diameter of 1.3 x 10^-3 inches. Which statement is true?

A.The horse hair is 2 times as thick as the human hair.

B.The horse hair is 5 times as thick as the human hair

C.The human hair is 2 times as thick as the horse hair

D.The human hair is 5 times as thick as the horse hair

Answer 1

$\cfrac{1.3*10^{-3}}{6.5*10^{-4}}= 0.2*10^1=2$

A.The horse hair is 2 times as thick as the human hair. 

Answer 2

Answer:

A.The horse hair is 2 times as thick as the human hair.

Step-by-step explanation:

We have been given that Mateo is studying a human hair with a diameter of $6.5\times 10^{-4}$ inches and a horse hair with a diameter of $1.3\times 10^{-3}$ inches.

Since proportions states that two fractions are equal, So we will use proportions to solve our given problem.

$\frac{\text{Diameter of horse hair}}{\text{Diameter of human hair}}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}$

$\text{Diameter of horse hair}=\frac{1.3\times 10^{-3}}{6.5\times 10^{-4}}\times \text{Diameter of human hair}$

Now we will quotient rule of exponents to simplify our given problem.

$\text{Diameter of horse hair}=\frac{1.3\times 10^{-3--4}}{6.5}\times \text{Diameter of human hair}$

$\text{Diameter of horse hair}=\frac{1.3\times 10^{-3+4}}{6.5}\times \text{Diameter of human hair}$

$\text{Diameter of horse hair}=\frac{1.3\times 10^{1}}{6.5}\times \text{Diameter of human hair}$

$\text{Diameter of horse hair}=\frac{13}{6.5}\times \text{Diameter of human hair}$

$\text{Diameter of horse hair}=2\times \text{Diameter of human hair}$

We can see that the diameter of horse hair is 2 times the diameter of human hair. Therefore, the horse hair is 2 times as thick as the human hair and option A is the correct choice.