Select all the ratios that are equivalent to each other. 4:7, 8:15, 16:28, 2:3, 20:35

Haruka hiked several kilometers in the morning. she hiked only 66 kilometers in the afternoon, which was 25% less than she had hiked in the morning. how many kilometers did haruka hike in all?

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Agroup of randomly selected members of the foodies food club were asked to pick their favorite type of food. the bar graph below shows the results of the survey. there are 244 members in the foodies.