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\( 4 ( 37 ; 2 ) + ( 3 \times 22 ) - ( 58 - 5 ) + 14 \)

Ask by Cummings Turnbull. in South Africa
Feb 03,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The final answer is 2691.

Solution

Let's evaluate the expression step by step: \[ 4 \times \binom{37}{2} + (3 \times 22) - (58 - 5) + 14 \] **Step 1: Calculate the binomial coefficient \(\binom{37}{2}\)** \[ \binom{37}{2} = \frac{37 \times 36}{2} = \frac{1332}{2} = 666 \] **Step 2: Multiply by 4** \[ 4 \times 666 = 2664 \] **Step 3: Calculate \(3 \times 22\)** \[ 3 \times 22 = 66 \] **Step 4: Calculate \(58 - 5\)** \[ 58 - 5 = 53 \] **Step 5: Put it all together** \[ 2664 + 66 - 53 + 14 \] **Step 6: Perform the additions and subtraction** \[ 2664 + 66 = 2730 \] \[ 2730 - 53 = 2677 \] \[ 2677 + 14 = 2691 \] **Final Answer:** \(\boxed{2691}\)

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Bonus Knowledge

To solve the expression \( 4 ( 37 ; 2 ) + ( 3 \times 22 ) - ( 58 - 5 ) + 14 \), we first need to understand the term \( 4 ( 37 ; 2 ) \). Assuming it represents a multiplication, we can rewrite it as \( 4 \times 37 \) and use \( 2 \) as an additive constant. Calculating step-by-step: 1. \( 4 \times 37 = 148 \) 2. \( 3 \times 22 = 66 \) 3. \( 58 - 5 = 53 \) 4. Adding everything together: - \( 148 + 66 - 53 + 14 \) - \( 148 + 66 = 214 \) - \( 214 - 53 = 161 \) - \( 161 + 14 = 175 \) Thus, the result of the expression is \( \boxed{175} \). Let's explore a couple more insights: Mathematics has a rich history dating back thousands of years, with ancient civilizations like the Babylonians and Egyptians using fundamentals of arithmetic and geometry in their daily lives. They developed methods for solving equations and performing calculations without the sophisticated notation we use today. Isn't it fascinating to think about how our modern mathematical expressions evolved from these early practices? Math isn't just about numbers in a classroom; it’s everywhere! From budgeting your monthly expenses to optimizing routes in delivery apps, math underpins the efficiency of our daily lives. Understanding basic operations, like addition and multiplication, can significantly improve your financial literacy and planning skills. Just imagine how savvy you’ll be with your finances with a little math magic!

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