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

Tags

CCSS.3.MD.D.8

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

Tags

CCSS.8.EE.C.7B

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

Tags

CCSS.HSN.RN.A.2

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

Tags

CCSS.8.EE.A.4

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

• 13

• 12

• 11

• 10

Tags

CCSS.5.NBT.A.2

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

• 1212

• 121.2

• 12.12

• 12

Tags

CCSS.7.NS.A.1C

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

• 14

• 11

• 12

• 13

Tags

CCSS.5.NBT.A.2

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

• 12

• 1.2

• 0.12

• 120

Tags

CCSS.5.NBT.A.2