Fractional Areas and Algebraic Concepts

The video tutorial covers various math problems, including calculating the shaded area of a circle using fractions, simplifying exponent division, determining seed germination percentages, finding possible side lengths of a triangle, solving integer inequalities, expressing car sales relationships with equations, and calculating remaining amounts after deposits. Each problem is explained step-by-step, demonstrating mathematical concepts and problem-solving techniques.

What is the fractional part of the shaded area in a circle if the unshaded parts are 3/7 and 1/3 of the total area?

• 6/21

• 4/21

• 7/21

• 5/21

What is the least common multiple used to subtract the fractions 3/7 and 1/3?

• 35

• 21

• 28

• 14

How do you simplify 0.3 to the 5th power divided by 0.3 to the 3rd power?

• 0.3

• 0.09

• 0.9

• 0.03

What is the result of multiplying 0.3 by itself?

• 0.09

• 0.3

• 0.03

• 0.9

In a horticultural experiment, if 57% of 200 seeds in plot 1 and 42% of 300 seeds in plot 2 germinate, what percentage of the total seeds germinated?

• 52%

• 45%

• 50%

• 48%

Which of the following can be the length of the third side of a triangle with sides 3 and 8?

• 10

• 5

• 12

• 11

How many integers n satisfy the inequality 1 < 5n + 5 < 25?

• 4

• 5

• 6

• 3

If a car dealer sold x used cars and y new cars, and x is 10 more than y, which equation represents this relationship?

• x = y + 10

• x = y

• x = 10y

• x = y - 10

If a 10% deposit of $110 has been paid on a product, what is the remaining amount to be paid?

• $1000

• $1100

• $900

• $990

What is the original price of a product if a 10% deposit of $110 has been paid?

• $1200

• $900

• $1100

• $1000