Question

last week, it rained g inches. this week, the amount of rain decreased by 5%. which expressions represent the amount of rain that fell this week? select all that apply. a. g - 0.05 b. g - 0.05g c. 0.95g d. 0.05g e. (1 - 0.05)g

Explanation:

Step1: Analyze the decrease amount

The decrease in rain is 5% of \( g \), which is \( 0.05g \) (since 5% = 0.05).

Step2: Find this week's rain (method 1)

Subtract the decrease from last week's rain: \( g - 0.05g \), so option B is valid.

Step3: Simplify the expression (method 2)

Factor \( g \) from \( g - 0.05g \): \( g(1 - 0.05)=0.95g \), so options C and E (since \( (1 - 0.05)g = 0.95g \)) are valid.

Step4: Evaluate other options

Option A subtracts 0.05 (a constant) instead of 5% of \( g \), so it's invalid. Option D is just the decrease amount, not the remaining rain, so it's invalid.

Answer:

B. \( g - 0.05g \), C. \( 0.95g \), E. \( (1 - 0.05)g \)