The area of a circle can be calculated using the formula: A = πr² where A is the area, π (pi) is a constant approximately equal to 3.14, and r is the radius of the circle. To find the area, we first need to determine the radius. The radius is half of the diameter. Given … Read more
The number 16 can be represented using exponents by identifying it as a power of another number. In this case, 16 is a power of 2. This means that 16 can be written as: 16 = 24 This tells us that 2 is multiplied by itself 4 times: 2 × 2 × 2 × 2 … Read more
To translate the function f(x) = 15x upwards by 4 units, you need to adjust the function’s output value. For any function f(x), translating it up by k units involves adding k to the function. In this case, k is 4. So, the translated function can be obtained by adding 4 to the original function’s … Read more
The probability of obtaining three heads in a row when tossing a fair coin can be calculated using the basic principles of probability. When you toss a coin, there are two possible outcomes: heads (H) or tails (T). Therefore, for each toss of the coin, the probability of getting heads is: P(H) = 1/2 Since … Read more
To find what three-fourths of sixteen is, you can use a simple mathematical operation involving fractions. Here’s how to do it step by step: Understand the fraction: Three-fourths can be represented as the fraction 3/4. Multiply: To find three-fourths of a number, you multiply that number (in this case, 16) by the fraction 3/4. So … Read more
10 to the first power, denoted as 101, is quite simple to understand. When you raise a number to the power of 1, the result is always the number itself. This principle applies across all real numbers. Therefore, when you calculate 101, you are literally saying, “What is 10 multiplied by itself one time?” The … Read more
To convert the fraction 3/12 into a decimal, you need to perform the division of the numerator (the top number) by the denominator (the bottom number). Here’s a step-by-step breakdown: Identify the numerator and denominator: In this case, 3 is the numerator and 12 is the denominator. Perform the division: Divide 3 by 12. This … Read more
Calculating the Area of a Regular Hexagon To find the area of a regular hexagon, we can use the formula: A = rac{3 ext{√3}}{2} imes r^2 Where A is the area and r is the radius of the circumscribed circle (which is also the distance from the center to a vertex). In this case, the … Read more
The length of the diagonal of a right rectangular prism can be calculated using the 3-dimensional version of the Pythagorean theorem. A right rectangular prism has three dimensions: length (l), width (w), and height (h). The diagonal (d) of the prism connects opposite corners and can be found using the following formula: d = √(l² … Read more
To calculate the value of 5 to the power of 9, you would multiply 5 by itself a total of 9 times. This expression can be written mathematically as: 5^9 = 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 If we break it down step by … Read more