The radio station wants to tell their listeners the weather for the next 10 days. Out of those 10 days, it will rain on 2 of them. The manager of the station said that the ratio of rainy days to sunny days was 1:4 . Is the manager correct? Explain.(1 point)

Question

Responses

no, because the ratio of rainy days to sunny days is 2:8 and 1:4 is not equivalent to 2:8
no, because the ratio of rainy days to sunny days is ratio of 2 to 8 and ratio of 1 to 4 is not equivalent to ratio of 2 to 8

no, because the correct ratio of rainy days to sunny days is 2:10
no, because the correct ratio of rainy days to sunny days is ratio of 2 to 10

yes, because out of 4 days it will only rain once
yes, because out of 4 days it will only rain once

yes, because the ratio of rainy days to sunny days is 2:8 and 1:4 is an equivalent ratio

Answer 1

The correct response is:

yes, because the ratio of rainy days to sunny days is 2:8 and 1:4 is an equivalent ratio.

Here's the explanation:

Out of the 10 days, if it rains on 2 days, that means there are 8 sunny days (10 total days - 2 rainy days = 8 sunny days).

The ratio of rainy days to sunny days is:

\[ \text{Rainy Days} : \text{Sunny Days} = 2 : 8 \]

This ratio can be simplified by dividing both sides by 2:

\[ 2:8 = 1:4 \]

Thus, the manager's statement that the ratio of rainy days to sunny days is 1:4 is indeed correct, as both ratios are equivalent.