Path Counting and Exponential Operations

The video tutorial covers five math problems, each focusing on different mathematical concepts. Problem 133 involves calculating per capita expenditure using scientific notation. Problem 134 deals with finding the dimensions of a rectangular window given its perimeter. Problem 135 explores the number of possible paths a mouse can take in a diagram. Problem 136 introduces a custom operation involving square roots, and Problem 137 evaluates an expression with repeating decimals. Each problem is solved step-by-step, demonstrating various mathematical techniques and concepts.

What is the per capita expenditure if a country's total annual expenditure is 1.2 x 10^12 and its population is 2.4 x 10^8?

• $500

• $5,000

• $50,000

• $500,000

If a rectangular window is twice as long as it is wide and has a perimeter of 10 feet, what is its width?

• 2 feet

• 3 feet

• 5/3 feet

• 10/3 feet

Given a rectangular window with a perimeter of 10 feet, what is its length if it is twice as long as it is wide?

• 3 feet

• 2 feet

• 10/3 feet

• 5/3 feet

How many different paths can a mouse take from point x to point y in the given diagram?

• 4

• 8

• 12

• 16

What is the result of the operation 5 ⊙ 45 ⊙ 60, where ⊙ is defined as the square root of the product of two numbers?

• 60

• 30

• 45

• 15

If the operation ⊙ is defined as the square root of the product of two numbers, what is 5 ⊙ 45?

• 15

• 25

• 45

• 35

What is the value of 10^4 - 10^2 x 0.0012, where 0.0012 is a repeating decimal?

• 13

• 12

• 11

• 10

What is 10^4 times 0.0012, where 0.0012 is a repeating decimal?

• 1212

• 121.2

• 12.12

• 12

What is the result of subtracting 0.12 repeating from 12.12 repeating?

• 14

• 11

• 12

• 13

What is the value of 10^2 times 0.0012, where 0.0012 is a repeating decimal?

• 12

• 1.2

• 0.12

• 120