Question

The relationship between temperature in degrees Fahrenheit, \(F,\) and temperature in degrees Celsius, \(C\) , is expressed by the formula \(F=\frac{9}{5} C+32 .\) Calvin reads a temperature of \(38^{\circ}\) on a Celsius thermometer. To the nearest degree, what is the equivalent temperature on a Fahrenheit thermometer? \(\mathbf{F} . \quad 36^{\circ}\) G. \(53^{\circ}\) H. \(68^{\circ}\) J. K. \(100^{\circ}\)

Short answer

Answer: K. \(100^{\circ}\) Fahrenheit

Step-by-step solution

Identify the given temperature in Celsius

Calvin reads a temperature of \(38^{\circ}\) Celsius. So, \(C = 38\).

Use the conversion formula

We need to convert \(38^{\circ}\) Celsius to Fahrenheit using the formula: \(F=\frac{9}{5} C+32\).

Substitute the Celsius value into the formula

Replace C with 38 in the conversion formula, \(F=\frac{9}{5} C+32\): $$ F = \frac{9}{5} 38 + 32 $$

Calculate the Fahrenheit value

Calculate the value for \(F\): $$ F = \frac{9}{5} 38 + 32 = 68 + 32 = 100 $$

Match the result with answer choices

We find out that the equivalent temperature in Fahrenheit is \(100^{\circ}\). Comparing it with the answer choices, we can see that our result matches answer choice \(\boxed{\text{K. } 100^{\circ}}\).

Key concepts

Fahrenheit to Celsius

Temperature conversion is a practical skill that comes in handy in various real-world scenarios, like reading weather reports or cooking. Converting from Fahrenheit to Celsius is straightforward once you understand the formula and the relationship between these two scales. The standard formula used for conversion is:
\[ C = \frac{5}{9}(F - 32) \]
Where \(C\) represents degrees Celsius and \(F\) represents degrees Fahrenheit. This formula is derived from the freezing and boiling points of water on both scales—32°F for freezing and 212°F for boiling, which correspond to 0°C and 100°C, respectively. To convert Celsius to Fahrenheit, which was needed in the given exercise, the formula rearranges to:
\[ F = \frac{9}{5}C + 32 \]
This calculation shows how each degree Celsius is equivalent to 1.8 degrees Fahrenheit, plus the offset of 32 degrees to account for the different starting points of the two scales.
When applying these conversions to real-world measurements, remember to use precise calculations for accurate results, and round to the desired level of precision.

Mathematical Formulas

Mathematical formulas are like tools in a toolkit for solving various types of problems, ranging from simple arithmetic to complex calculus. Formulas provide a systematic way to approach and solve mathematical problems efficiently.
A critical aspect of using mathematical formulas is plugging in the values correctly and performing the operations in the right order. This requires a solid understanding of algebra and arithmetic rules, such as the order of operations. Remembering the simple acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) can be helpful to remember this sequence.
In temperature conversion, the formula \(F = \frac{9}{5}C + 32\) is critical, as it provides a direct method to convert Celsius to Fahrenheit. When working with such formulas, it's vital to maintain unit consistency and carefully manage the arithmetic to get an accurate result.

Arithmetic Precision

It's always important to carry out calculations precisely and round only at the final step to avoid compounding rounding errors. This will ensure the most accurate outcome and is especially important in scientific and technical fields where small differences can have significant effects.

ACT Math Problems

The ACT is a standardized test widely used for college admissions in the United States. It includes a math section that evaluates a student's mathematical skills typically learned in high school courses. Temperature conversion problems, like the one provided in the exercise, are examples of the practical math applications that can appear on the ACT.
To excel in ACT math problems:

• Understand and memorize key mathematical formulas.
• Practice applying these formulas to solve a variety of problems.
• Develop strong problem-solving strategies, such as breaking down complex problems into simpler parts.
• Enhance your time management skills, as timed tests require quick thinking and efficiency.

In the case of the temperature conversion problem, quick recognition of the formula, correct substitution of values, and accurate calculation are essential. These skills are transferable to a wide range of math questions, underscoring the importance of a robust mathematical foundation.
By consistently practicing these types of problems, students can improve their speed and accuracy, which are paramount in achieving a high score on the ACT math section. Remember, understanding the concepts behind the questions can make a significant difference in performance.