Advanced Math MCQ Quiz - Objective Question with Answer for Advanced Math - Download Free PDF

Given:

Initial population (P₀) = 50

Growth rate (r) = 0.1 per hour

Time (t) = 10 hours

Formula used:

P(t) = P₀ × e^rt

Where e ≈ 2.718, r = Growth rate, t = time.

Calculations:

∴ The approximate population after 10 hours is 136 cells

Given: The sum of a number and twice its square is 105.

Let the number be denoted as x.

Concept Used:

The problem involves solving a quadratic equation using trial and error or logical substitution.

The equation can be represented as: x + 2x² = 105

Calculation: Start solving the equation step by step:   x + 2x² = 105

⇒ Substitute x = 7: 7 + 2 × 7² = 105

This satisfies the equation.

Final Answer:

∴ The correct number is x = 7.

The function provides the profit years after the product launch. implies that after 7 years, the profit is approximately dollars.

Option 1 is correct, as it directly reflects the profit at . 

Substitute into . Compute . , so . Then, . . Therefore, . The correct answer is 132.5.

Let be the width of the rectangle. The length is . The area is given by . This simplifies to . Dividing by , we have . Taking the square root of both sides gives or . Since width cannot be negative, .

Choice C is correct. The first expression (1.5x - 2.4)² can be rewritten as (1.5x - 2.4)(1.5x - 2.4). Applying the distributive property to this product yields (2.25x² - 3.6x - 3.6x + 5.76)-(5.2x² - 6.4). This difference can be rewritten as (2.25x² - 3.6x - 3.6x + 5.76) + (-1)(5.2x² - 6.4). Distributing the factor of -1 through the second expression yields 2.25x² - 3.6x - 3.6x + 5.76 - 5.2x² + 6.4. Regrouping like terms, the expression becomes (2.25x² - 5.2x²) + (-3.6x - 3.6x) + (5.76 + 6.4). Combining like terms yields -2.95x² - 7.2x + 12.16.

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

Given: The sum of a number and twice its square is 105.

Let the number be denoted as x.

Concept Used:

The problem involves solving a quadratic equation using trial and error or logical substitution.

The equation can be represented as: x + 2x² = 105

Calculation: Start solving the equation step by step:   x + 2x² = 105

⇒ Substitute x = 7: 7 + 2 × 7² = 105

This satisfies the equation.

Final Answer:

∴ The correct number is x = 7.

The correct answer is . It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 14 teaspoons is equivalent to teaspoons. Note that 14/3, 4.666, and 4.667 are examples of ways to enter a correct answer.

The correct answer is 73,920. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 112 furlongs is equivalent to , or 73,920 feet.

The correct answer is 40,260. It's given that 1 furlong = 220 yards and 1 yard = 3 feet. It follows that a distance of 61 furlongs is equivalent to . or 40,260 feet.

Choice A is correct. Since 1 kilometer is equal to 1,000 meters, it follows that 90 kilometers is equal to 90(1,000)=90,000  meters. Since 1 hour is equal to 60 minutes and 1 minute is equal to 60 seconds, it follows that 1 hour is equal to 60(60) = 3,600 seconds. Now is equal to , which reduces to  or 25 meters per second. 
Choices B, C, and D are incorrect and may result from conceptual or calculation errors. 

Choice C is correct. It's given that 3 teaspoons is equivalent to 1 tablespoon. Therefore, 44 tablespoons is equivalent to , or 132 teaspoons.
Choice A is incorrect. This is equivalent to approximately 15.66 tablespoons, not 44 tablespoons.
Choice B is incorrect. This is equivalent to approximately 29.33 tablespoons, not 44 tablespoons.
Choice D is incorrect. This is equivalent to approximately 58.66 tablespoons, not 44 tablespoons.

Choice A is correct. It's given that t = 4u. Multiplying both sides of this equation by 2 yields 2t = 2(4u), or 2t = 8u.
Choice B is incorrect and may result from dividing, instead of multiplying, the right-hand side of the equation by 2. Choices C and D are incorrect and may result from calculation errors.

The correct answer is 102. It's given that 1 yard is equivalent to 3 feet. Therefore, 34 yards is equivalent to . or 102 feet.

Choice B is correct. It's given that 1 yard = 36 inches. Therefore, 612 inches is equivalent to  which can be rewritten as or 17 yards. 36
Choice A is incorrect. This is the number of yards that are equivalent to 2.124 inches.
Choice C is incorrect. This is the number of yards that are equivalent to 20,736 inches.
Choice D is incorrect. This is the number of yards that are equivalent to 793,152 inches.