Question

as a weather - watcher, you check the accuracy of a table of the forecasted daily high temperature, in degrees fahrenheit (°f) and degrees celsius (°c), rounded to the nearest whole number.

monday	tuesday	wednesday	thursday	friday	saturday	sunday
°c	27	27	26	27	31	31	31

the fahrenheit temperature is supposed to be converted to celsius using the formula °c = \\(\frac{5}{9}(°f - 32)\\). one of the following statements about how the formula was used to obtain the °c values in the table is true. which one?
a. the fraction \\(\frac{5}{9}\\) was inverted.
b. the value of °f was substituted in place of °c in the formula.
c. thirty - two was added instead of subtracted.
d. thirty - two was subtracted after °f was multiplied by \\(\frac{5}{9}\\).
e. the formula was used correctly.

Explanation:

Step1: Recall conversion formula

The correct formula for converting Fahrenheit ($^{\circ}F$) to Celsius ($^{\circ}C$) is $^{\circ}C=\frac{5}{9}(^{\circ}F - 32)$.

Step2: Analyze option A

There is no indication that $\frac{5}{9}$ was inverted as there are no values in the table that would suggest such an error.

Step3: Analyze option B

If the value of $^{\circ}F$ was substituted in place of $^{\circ}C$ in the formula, incorrect calculations would result. But we need to check further.

Step4: Analyze option C

If 32 was added instead of subtracted, the formula would be $^{\circ}C=\frac{5}{9}(^{\circ}F + 32)$ and the values in the table do not match this incorrect - application.

Step5: Analyze option D

If 32 was subtracted after $^{\circ}F$ was multiplied by $\frac{5}{9}$, the formula would be $^{\circ}C=\frac{5}{9}^{\circ}F-32$, which is not the correct formula and does not match the table values.

Step6: Analyze option E

Let's take an example, say $^{\circ}F = 80$. Using the correct formula $^{\circ}C=\frac{5}{9}(80 - 32)=\frac{5}{9}\times48=\frac{240}{9}\approx26.67
eq62$. So the formula was not used correctly.

Let's assume an error in substitution. If we substitute values wrongly as in option B, we can see that the values in the table are wrong in a way that would be consistent with substituting $^{\circ}F$ values in place of $^{\circ}C$ values in the formula.

Answer:

B. The value of $^{\circ}F$ was substituted in place of $^{\circ}C$ in the formula.