To analyze the statements regarding Liz and Sara's cookie baking, let's consider the details provided.
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Sara had baked more cookies at the start of the 5 hours than Liz.
- To determine this, we check the number of cookies each girl baked at the start (x = 0).
- From the information given, when x = 0, the equation for Sara is: \[ y = 45(0) + 38 = 38 \]
- For Liz, the graph indicates that at x = 0, y = 19.
- Since 38 > 19, this statement is true.
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Sara bakes 45 cookies each hour.
- The equation for Sara's cookie baking is \(y = 45x + 38\). The slope (45) indicates the number of cookies baked per hour. Therefore, this statement is also true.
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Liz bakes 19 cookies each hour.
- To find Liz's baking rate, we note that the graph shows she starts at 19 cookies and moves to 179 cookies over 4 hours (the change is 179 - 19 = 160 cookies over a span of 4 hours).
- Therefore, her rate is: \[ \text{Rate} = \frac{160 \text{ cookies}}{4 \text{ hours}} = 40 \text{ cookies per hour}. \]
- Since she bakes 40 cookies per hour, this statement is false.
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Liz bakes more cookies each hour than Sara.
- From our previous calculations, Liz bakes 40 cookies per hour, while Sara bakes 45 cookies per hour.
- Since 40 < 45, this statement is false.
In summary, the correct true statements are:
- Sara had baked more cookies at the start of the 5 hours than Liz.
- Sara bakes 45 cookies each hour.