Let's analyze each statement one by one:
a. [tex]\( h + 15 = E \)[/tex] is the equation that represents how much Caroline earns after [tex]\( h \)[/tex] hours.
This statement suggests that you add 15 to the number of hours to get the earnings. This is incorrect because Caroline charges [tex]$15 per hour, so you should multiply the number of hours by 15 to get the earnings, not add 15. The correct equation should be \( 15h = E \). Therefore, this statement is False.
b. If Caroline babysits for 5 hours, she earns $[/tex]20.
This statement says that babysitting for 5 hours results in earnings of [tex]$20. To check this, we calculate the earnings for 5 hours:
\[ 15 \text{ (dollars per hour)} \times 5 \text{ (hours)} = 75 \text{ (dollars)} \]
Thus, Caroline actually earns $[/tex]75 for 5 hours of babysitting, not [tex]$20. Therefore, this statement is False.
c. \( 15h = E \) is the equation that represents how much Caroline earns after \( h \) hours.
This statement correctly represents the relationship between hours and earnings. Caroline charges $[/tex]15 per hour, so multiplying the hours [tex]\( h \)[/tex] by 15 gives the total earnings [tex]\( E \)[/tex]. Therefore, this statement is True.
d. If Caroline earns [tex]$52.50, then she babysat for 3.5 hours.
To check this, we divide the earnings by the rate per hour:
\[ \frac{52.50 \text{ (dollars)}}{15 \text{ (dollars per hour)}} = 3.5 \text{ (hours)} \]
Therefore, Caroline babysat for exactly 3.5 hours to earn $[/tex]52.50. This statement is True.
In summary, the statements that are true are:
c. [tex]\( 15h = E \)[/tex] is the equation that represents how much Caroline earns after [tex]\( h \)[/tex] hours.
d. If Caroline earns $52.50, then she babysat for 3.5 hours.
