Let's break down and solve the problem step by step. ### **Problem Summary** You are given a formula to calculate calories burned: \[ Calories = (Age \times 0.2757 + Weight \times 0.03295 + HeartRate \times 1.0781 - 75.4991) \times Time / 8.368 \] With inputs: - **Age** = 25 years - **Weight** = 70 kg - **HeartRate** = 150 beats/min - **Time** = 30 minutes ### **Step 1: Plug Values Into the Formula** \[ Calories = (25 \times 0.2757 + 70 \times 0.03295 + 150 \times 1.0781 - 75.4991) \times 30 / 8.368 \] ### **Step 2: Calculate Each Term** - \( 25 \times 0.2757 = 6.8925 \) - \( 70 \times 0.03295 = 2.3065 \) - \( 150 \times 1.0781 = 161.715 \) ### **Step 3: Add/Subtract the Values** \[ = (6.8925 + 2.3065 + 161.715 - 75.4991) \] \[ = (6.8925 + 2.3065) = 9.199 \] \[ = (9.199 + 161.715) = 170.914 \] \[ = (170.914 - 75.4991) = 95.4149 \] ### **Step 4: Multiply by Time** \[ 95.4149 \times 30 = 2,862.447 \] ### **Step 5: Divide by 8.368** \[ Calories = \frac{2,862.447}{8.368} \approx 342.18 \] --- ## **Final Answer** **Calories burned = 342.18 calories** (rounded to two decimal places) --- **Summary Table:** | Step | Value | |---------------------|------------| | Age term | 6.8925 | | Weight term | 2.3065 | | HeartRate term | 161.715 | | Subtotal | 170.914 | | Subtract constant | 95.4149 | | Multiply by Time | 2,862.447 | | Divide by 8.368 | 342.18 | --- ### **Explanation** - Plugged each value into the formula. - Calculated each term separately. - Summed and subtracted as per the equation. - Multiplied by the duration (Time). - Divided by the constant (8.368). **Calories burned is approximately 342.18 calories.**

Let's analyze and solve the problem step-by-step with detailed calculations and explanations. --- ### **Given Data:** - Age = **25 years** - Weight = **70 kg** - Heart Rate = **150 beats/min** - Time = **30 minutes** ### **Step 1: Write down the formula** \[ \text{Calories} = \frac{( \text{Age} \times 0.2757 + \text{Weight} \times 0.03295 + \text{Heart Rate} \times 1.0781 - 75.4991) \times \text{Time}}{8.368} \] --- ### **Step 2: Calculate each component inside the parentheses** #### a) Age term: \[ 25 \times 0.2757 = 6.8925 \] #### b) Weight term: \[ 70 \times 0.03295 = 2.3065 \] #### c) Heart rate term: \[ 150 \times 1.0781 = 161.715 \] --- ### **Step 3: Sum the terms inside the parentheses** \[ 6.8925 + 2.3065 + 161.715 = 170.914 \] Now subtract 75.4991: \[ 170.914 - 75.4991 = 95.4149 \] --- ### **Step 4: Multiply by Time** Time = 30 minutes \[ 95.4149 \times 30 = 2,862.447 \] --- ### **Step 5: Divide by 8.368 to get calories burned** \[ \frac{2,862.447}{8.368} \approx 342.18 \] --- ### **Final Calculation:** \[ \boxed{ \text{Calories} \approx 342.18 } \] --- ### **Final Answer:** **The person burns approximately _342.18 calories_ during 30 minutes of activity with the given parameters.** --- ### **Summary:** | Step | Calculation | Result | |--------|-----------------------------|----------------| | 1 | Age term: \(25 \times 0.2757\) | 6.8925 | | 2 | Weight term: \(70 \times 0.03295\) | 2.3065 | | 3 | Heart rate term: \(150 \times 1.0781\) | 161.715 | | 4 | Sum inside parentheses: | 170.914 | | 5 | Subtract constant: | 95.4149 | | 6 | Multiply by Time (30 min): | 2,862.447 | | 7 | Divide by 8.368: | **342.18 calories** | --- **Note:** All calculations are rounded to four decimal places for precision.

The formula provided estimates calories burned based on physiological parameters such as age, weight, heart rate, and activity duration. It accounts for the metabolic rate influenced by these factors, adjusting for individual differences. By substituting specific values into the formula, we can accurately determine the energy expenditure during physical activity. This method is commonly used in exercise physiology to quantify workout intensity and caloric consumption.

Sure! Here's a simple Python code to calculate the calories burned based on the given formula and inputs: ```python # Input parameters age = 25 # in years weight = 70 # in kg heart_rate = 150 # in beats per minute time = 30 # in minutes # Calculate each component age_term = age * 0.2757 weight_term = weight * 0.03295 heart_rate_term = heart_rate * 1.0781 # Sum the components inside the parentheses total = age_term + weight_term + heart_rate_term - 75.4991 # Calculate total calories burned calories_burned = (total * time) / 8.368 # Output the result print(f"Calories burned: {calories_burned:.2f}") ``` **Explanation:** - The code initializes variables for each parameter. - It computes each term as per the formula. - It sums these, subtracts the constant, multiplies by the activity duration. - Finally, it divides by 8.368 to get the total calories burned. - The `print` statement displays the result rounded to two decimal places. You can change the input values as needed to calculate for different scenarios.

Sure! Here's the complete Python code to calculate the calories burned based on the provided formula and input values. The code will also display the output: ```python # Input parameters age = 25 # in years weight = 70 # in kg heart_rate = 150 # in beats per minute time = 30 # in minutes # Calculate each component age_term = age * 0.2757 weight_term = weight * 0.03295 heart_rate_term = heart_rate * 1.0781 # Sum the components inside the parentheses total = age_term + weight_term + heart_rate_term - 75.4991 # Calculate total calories burned calories_burned = (total * time) / 8.368 # Output the result print(f"Calories burned: {calories_burned:.2f}") ``` **Expected Output:** ``` Calories burned: 342.18 ``` **Explanation:** - The code assigns the input values to variables. - It performs each calculation step-by-step. - It sums the components, subtracts the constant, multiplies by the activity time. - Divides by 8.368 to get the total calories burned. - Finally, it prints the result rounded to two decimal places. You can run this code in any Python environment to get the calories burned for the given parameters.