1.### What is 15% of 200?

Answer:
30

Explanation:

To find 15% of 200, you multiply 200 by 0.15. The calculation 200 × 0.15 yields 30. This percentage calculation is a basic arithmetic operation where the percentage is converted into a decimal to facilitate multiplication. This method is universally applicable for finding percentages of any number, making it a fundamental concept in mathematics and everyday calculations.

2.### Solve for x: 2x + 6 = 16

Answer:
5

Explanation:

Solving the equation 2x + 6 = 16 involves isolating x. First, subtract 6 from both sides to get 2x = 10. Then, divide both sides by 2 to find x = 5. This basic algebraic technique of balancing equations is crucial for solving for unknown variables and is widely used in various mathematical and real-world applications.

3.### How many sides does a hexagon have?

Answer:
6

Explanation:

A hexagon is a six-sided polygon. This is a straightforward fact from geometry that categorizes shapes based on the number of sides they have. Knowing these characteristics is essential for understanding more complex geometric properties and relationships.

4.### What is the square root of 144?

Answer:
12

Explanation:

The square root of 144 is 12. This is determined because 12 multiplied by 12 equals 144. Square roots are fundamental in algebra and are used to solve equations involving squares, assess quadratic relationships, and have practical applications in real-life scenarios such as area calculations.

5.### If the area of a circle is 78.5, what is the radius? (Use π = 3.14)

Answer:
5

Explanation:

To find the radius when the area of a circle is given as 78.5 (and using π = 3.14), the formula for the area of a circle, A = πr², is used. Rearranging for r gives r = √(A/π) = √(78.5/3.14) ≈ 5. This computation involves algebraic manipulation and understanding of geometric formulas.

6.### What is the derivative of 3x^2?

Answer:
6x

Explanation:

The derivative of 3x^2 with respect to x is 6x. This result is obtained using basic rules of differentiation, which are foundational in calculus. Differentiation is used to find rates of change and slopes of curves, which are critical in fields such as physics, engineering, and economics.

7.### If 3x - 2y = 12 and x = 4, what is y?

Answer:
0

8.### What is the volume of a cube with edge length 3 cm?

Answer:
27

Explanation:

The volume of a cube with an edge length of 3 cm is calculated using the formula V = s³, where s is the length of a side. Substituting 3 for s gives V = 3³ = 27 cm³. This calculation is part of learning geometric properties and applying them to find dimensions of three-dimensional objects.

9.### How many outcomes are possible with 4 coin flips?

Answer:
16

Explanation:

For 4 coin flips, each flip has 2 possible outcomes (heads or tails). The number of possible outcomes for multiple events is found by raising the number of outcomes per event to the power of the number of events, thus 2^4 = 16. This concept is part of probability theory, which calculates the likelihood of different outcomes in scenarios.

10.### What is the median of the set {3, 7, 9, 12}?

Answer:
8

Explanation:

The median of the set {3, 7, 9, 12} is calculated by first arranging the numbers in ascending order (which they are), then finding the middle value(s). With four numbers, the median is the average of the two middle numbers, (7 + 9)/2 = 8. This statistic is used to find the central tendency of data, a fundamental concept in descriptive statistics.

×

Wait!

Here's an interesting quiz for you.