Question

Whitney listens to her favorite podcast for 79
of an hour each day. Which expressions represent the time Whitney spends listening to the podcast over a five-day period? Check the THREE that apply.(3 points)
Responses

79+79+79+79+79
7 ninths plus 7 ninths plus 7 ninths plus 7 ninths plus 7 ninths

5+79
5 plus 7 ninths

359
35 ninths

5×79
5 times 7 ninths

129
12 ninths

Answer 1

To determine the expressions that represent the time Whitney spends listening to her podcast over a five-day period, we need to calculate the total time. Whitney listens for \( \frac{7}{9} \) of an hour each day, and over five days, that time can be expressed in several ways.

Let's break it down:

1. **Daily Time**: \(\frac{7}{9}\) of an hour for one day.
2. **Five-Day Total**: Over five days, this can be represented as:
\[
5 \times \frac{7}{9}
\]

Now let's examine the provided responses:

1. **\(79 + 79 + 79 + 79 + 79\)**: This expression calculates the total time in hours but uses the incorrect representation since each 79 is meant to be \( \frac{7}{9} \). Hence, this response is incorrect.

2. **\( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)**: Correctly adds \( \frac{7}{9} \) five times, which equals \( 5 \times \frac{7}{9} \). This is correct.

3. **\(5 + \frac{7}{9}\)**: This expression adds a full 5 hours to \(\frac{7}{9}\) of an hour, which does not represent the total time correctly. Hence, this response is incorrect.

4. **\(359\)**: This is not a valid representation of the time Whitney spends. It's simply a number. This response is incorrect.

5. **\(\frac{35}{9}\)**: This expression is \(5 \times \frac{7}{9}\), which correctly represents the total time in hours. This response is correct.

6. **\(5 \times \frac{7}{9}\)**: This correctly represents the total time Whitney spends listening to her podcast over five days. This response is correct.

7. **\(129\)**: This is also not a valid representation of time spent across the five days. This response is incorrect.

Based on the analysis, the expressions that represent the time Whitney spends listening to the podcast over a five-day period are:

1. \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
2. \( \frac{35}{9} \)
3. \( 5 \times \frac{7}{9} \)

Thus, the three correct expressions are:
1. \( \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} + \frac{7}{9} \)
2. \( \frac{35}{9} \)
3. \( 5 \times \frac{7}{9} \)