Sasha is measuring the rate of heat energy given off by an incandescent light bulb. The theoretical value is 55.4 watts. Her measurement has a 2.17 error. Which of the following values may have been Sasha's measurement? (Choose all that apply)

54.2 watts
1.20 watts
56.6 watts
57.57 watts
53.23 watts

1 answer

To determine which values may have been Sasha's measurement, we need to consider the theoretical value of 55.4 watts and the error of 2.17 watts. This means Sasha's measurement could be within the range:

\[ \text{Theoretical Value} - \text{Error} \quad \text{to} \quad \text{Theoretical Value} + \text{Error} \]

Calculating the range:

\[ 55.4 - 2.17 = 53.23 \text{ watts} \] \[ 55.4 + 2.17 = 57.57 \text{ watts} \]

So, the range of possible values for Sasha's measurement is:

\[ 53.23 \text{ watts} \quad \text{to} \quad 57.57 \text{ watts} \]

Now let's evaluate the given options:

  • 54.2 watts: Within the range \(53.23 , \text{to} , 57.57\) (valid)
  • 1.20 watts: Outside the range (not valid)
  • 56.6 watts: Within the range \(53.23 , \text{to} , 57.57\) (valid)
  • 57.57 watts: Exactly at the upper limit of the range (valid)
  • 53.23 watts: Exactly at the lower limit of the range (valid)

Thus, the values that may have been Sasha's measurement are:

  • 54.2 watts
  • 56.6 watts
  • 57.57 watts
  • 53.23 watts