Question

310[6+2(22+8)−10]÷205[100−2(25+25)+20]
a. 4
b. 8
c. 16
d. 32

Answer 1

The question involves simplifying a complex expression with multiple operations, including parentheses, multiplication, subtraction, and division. Using standard mathematics procedures and maintaining the correct significant figures are crucial to solving the problem and arriving at the correct answer.

Step-by-step explanation:

The question requires us to simplify the given mathematical expression and select the correct answer from the provided options. Let's break down the problem step by step:

1. Simplify the expression inside the brackets 6+2(22+8)10, which becomes 6 + 2 x 30 = 6 + 60 = 66.
2. Then multiply it by 310, which gives us 310 x 66.
3. Subtract 10 from the result of the multiplication, which gives us (310 x 66) - 10.
4. Now let's handle the denominator. We have 205 x (100 - 2(25 + 25) + 20), which simplifies to 205 x (100 - 2 x 50 + 20) = 205 x 70.
5. Finally, we divide the numerator by the denominator to get the result: ((310 x 66) - 10) / (205 x 70).

We use the properties of numbers and operations to simplify the expression, paying particular attention to maintain the correct number of significant figures. This exercise resembles the mathematical practices often found in higher-level high school or AP courses, where complex expressions require careful manipulation.