To find the total time Whitney spends listening to her favorite podcast over a five-day period, we need to multiply the daily listening time by the number of days. Since Whitney listens to her podcast for \( \frac{7}{9} \) of an hour each day, we can express her five-day listening time in several ways.
Here are the options you provided:
- 5 + \( \frac{7}{9} \): This represents adding the total time to the number of days, which is not correct.
- 5 × \( \frac{7}{9} \): This represents the correct multiplication of the number of days by the daily time, which gives the total time listened over five days.
- 359: This is not a valid expression for the time spent since it's just a number.
- \( 79 + 79 + 79 + 79 + 79 \): This is correct because it represents adding \( \frac{7}{9} \) for each of the five days, and each \( 79 \) is effectively the same as \( \frac{7}{9} \).
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \): This also accurately adds \( \frac{7}{9} \) for five days, which is correct.
- 129: Not a valid expression for the time.
Thus, the three expressions that correctly represent the time Whitney spends listening to the podcast over a five-day period are:
- 5 × \( \frac{7}{9} \)
- \( 79 + 79 + 79 + 79 + 79 \)
- \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
So the correct answers are the second, fourth, and fifth options you provided.