Question

the number of hate crime convictions in a particular region was 26 convictions in 2006 and has declined by about 4 convictions each year since then. let n be the number of hate crime convictions in the year that is t years since 2006. complete parts (a) through (e).

3	26 - 4·3
4	26 - 4·4

n = 26 - 4t

(b) perform a unit analysis of the equation found in part (a).
choose the correct answer.

a. in the equation, the units on both sides are the number of convictions, so the equation is correct.

b. in the equation, the units on one side are the number of convictions and the units on the other side are years, so the equation is correct.

c. in the equation, the units on both sides are years, so the equation is correct.

Explanation:

To analyze the units of the equation \( n = 26 - 4t \):

• The variable \( n \) represents the number of hate crime convictions, so its unit is "number of convictions".
• The constant 26 is also the number of convictions (from 2006), so its unit is "number of convictions".
• The term \( 4t \): The rate 4 has units of "convictions per year" (since 4 convictions decline per year), and \( t \) has units of "years". When we multiply \( 4 \) (convictions/year) by \( t \) (years), the "years" cancel out, leaving units of "convictions" for \( 4t \).
• Subtracting two quantities with units of "convictions" (26 convictions - 4t convictions) gives a result with units of "convictions", which matches the unit of \( n \).

So both sides of the equation have units of "number of convictions", making the equation consistent in terms of units. Option A correctly describes this.

Answer:

A. In the equation, the units on both sides are the number of convictions, so the equation is correct.