Question

as a weather intern, you check the accuracy of a table of the forecast daily high temperature, in °f and °c rounded to the nearest whole number.

	monday	tuesday	wednesday	thursday	friday	saturday	sunday
°c	36	38	35	38	99	101	101

the fahrenheit temperature was 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. substituted the value of °f 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 the correct formula

The correct formula to convert Fahrenheit to Celsius is \( ^\circ C=\frac{5}{9}(^\circ F - 32) \). Let's check each option by testing with a value from the table. Let's take Monday: \( ^\circ F = 80 \). Using the correct formula: \( \frac{5}{9}(80 - 32)=\frac{5}{9}\times48=\frac{240}{9}\approx26.67 \), but the table has \( 86 \) for \( ^\circ C \) on Monday, which is wrong. Let's see what was done. If we use \( ^\circ C=\frac{9}{5}(^\circ F + 32) \) (inverting the fraction and adding 32), for \( ^\circ F = 80 \): \( \frac{9}{5}(80 + 32)=\frac{9}{5}\times112 = 201.6 \), not 86. Wait, maybe another approach. Let's check option B: Substituted \( ^\circ F \) in place of \( ^\circ C \). If we use \( ^\circ C = ^\circ F \), but 80 vs 86, no. Option C: Added 32 instead of subtracting. Let's try \( \frac{5}{9}(80 + 32)=\frac{5}{9}\times112\approx62.22 \), no. Option D: Subtracted 32 after multiplying by \( \frac{5}{9} \). \( \frac{5}{9}\times80 - 32=\frac{400}{9}-32\approx44.44 - 32 = 12.44 \), no. Option A: Inverted the fraction. So use \( \frac{9}{5} \) instead of \( \frac{5}{9} \). Let's test Monday: \( \frac{9}{5}(80 - 32)=\frac{9}{5}\times48 = 86.4\approx86 \), which matches the table! Let's check another day, Tuesday: \( ^\circ F = 81 \). \( \frac{9}{5}(81 - 32)=\frac{9}{5}\times49 = 88.2\approx88 \), which matches the table. Wednesday: \( ^\circ F = 79 \). \( \frac{9}{5}(79 - 32)=\frac{9}{5}\times47 = 84.6\approx85 \), matches. Thursday: \( ^\circ F = 81 \), same as Tuesday, \( \frac{9}{5}\times49 = 88.2\approx88 \), matches. Friday: \( ^\circ F = 87 \). \( \frac{9}{5}(87 - 32)=\frac{9}{5}\times55 = 99 \), matches. Saturday: \( ^\circ F = 88 \). \( \frac{9}{5}(88 - 32)=\frac{9}{5}\times56 = 100.8\approx101 \), matches. Sunday: \( ^\circ F = 88 \), same as Saturday, \( 100.8\approx101 \), matches. So the fraction \( \frac{5}{9} \) was inverted (used \( \frac{9}{5} \) instead), so option A is correct.

Step2: Verify each option

• Option A: As shown, inverting the fraction \( \frac{5}{9} \) to \( \frac{9}{5} \) gives the values in the table.
• Option B: Substituting \( ^\circ F \) for \( ^\circ C \) doesn't match.
• Option C: Adding 32 instead of subtracting doesn't match.
• Option D: Subtracting 32 after multiplying doesn't match.
• Option E: The formula was not used correctly, as we saw the correct formula was misapplied by inverting the fraction.

Answer:

A. The fraction \(\frac{5}{9}\) was inverted.