What is 4 percent as a fraction?
To convert 4 percent into a fraction, we start by understanding what percent means. The term ‘percent’ means ‘per hundred,’ so 4 percent can be written as: 4 percent = 4/100 Next, we can simplify this fraction. Both the numerator (4) and the denominator (100) can be divided by their greatest common divisor, which is […]
What is the length of one side of a rhombus if diagonals ef and fh are 16 and 12, respectively?
To find the length of one side of the rhombus, we can use the properties of a rhombus and the Pythagorean theorem. In a rhombus, the diagonals bisect each other at right angles. Given the lengths of the diagonals ef = 16 and fh = 12, we first find their half-lengths. The half-lengths of the […]
How to Draw a Box and Whisker Plot for Given Data?
To draw a box and whisker plot for the data set 21, 29, 25, 20, 36, 28, 32, 35, 28, 30, 29, 25, 21, 35, 26, 35, 20, 19, we first need to follow several steps: Order the Data: Arrange the numbers in ascending order: 19, 20, 20, 21, 21, 25, 25, 26, 28, 28, […]
Find an equation in standard form for the hyperbola with vertices at (0, 4) and foci at (0, 5)
To find the equation of the hyperbola, we start by identifying the key components from the information given. The vertices of the hyperbola are at points (0, 4) and since they are vertically aligned, we can determine their coordinates as: Vertex 1: (0, 4) Vertex 2: (0, -4) The distance between the center of the […]
What is the remainder when you divide 4x³ + 5x² + 3x + 1 by x²?
To find the remainder when dividing a polynomial by another polynomial, we can apply polynomial long division or use the Remainder Theorem. In this case, we want to divide the polynomial 4x³ + 5x² + 3x + 1 by x². When dividing by x², the remainder will be a polynomial of degree less than 2. […]
Simplify the following expression: 2x + 4y + 3x^2 + 7y + 16x
To simplify the expression 2x + 4y + 3x^2 + 7y + 16x, we will first combine like terms. 1. Identify the like terms: The terms with ‘x’: 2x and 16x The terms with ‘y’: 4y and 7y The term with ‘x^2’: 3x^2 2. Combine the ‘x’ terms: 2x + 16x = 18x 3. Combine […]
How to Write a Repeating Decimal as a Fraction
Converting a repeating decimal to a fraction can initially seem challenging, but it’s a straightforward process. Here’s how to do it step by step. Let’s take a repeating decimal as an example: 0.6666…, where the 6 repeats indefinitely. Step 1: Assign the repeating decimal a variable. Let’s say: x = 0.6666… Step 2: Multiply by […]
The equation of a line is x + 5y = 12, what is the y-intercept of the line?
To find the y-intercept of the line given by the equation x + 5y = 12, we first need to express the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. We can start by isolating y. First, we can rearrange the […]
What is the solution of log2x 3125 3?
To solve the equation log2(x) = 3125/3, we first need to understand the meaning of the logarithm. The equation states that the base 2 logarithm of x is equal to 3125/3. This can be rewritten in exponential form. The definition of logarithm tells us that if logb(a) = c, then bc = a. In our […]
A spinner is numbered from 1 through 10; what is the probability of obtaining a number less than 2?
To find the probability of obtaining a number less than 2 when spinning a spinner numbered from 1 to 10, we first need to identify the possible outcomes. The spinner has 10 numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. When we consider numbers less than 2, the only number that […]