If you roll two fair six sided dice what is the probability that both dice show an odd number?
To determine the probability that both dice show an odd number, we first need to identify the odd numbers on a six-sided die. The odd numbers are 1, 3, and 5. This means there are a total of 3 odd numbers out of 6 possible outcomes for each die. Now, the probability of rolling an […]
What is the simplified expression for 4 power 4 multiplied by 4 power 3 over 4 power 5?
To simplify the expression 44 × 43 ÷ 45, we can use the properties of exponents. The property states that when multiplying two powers with the same base, we add the exponents. Therefore, we can first simplify the numerator: 44 × 43 = 44 + 3 = 47 Now we have: 47 ÷ 45 Next, […]
Find the slope and y-intercept of the line ax + by = 0
To find the slope and y-intercept of the line defined by the equation ax + by = 0, we need to rearrange this equation into the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. Let’s rearrange the equation: Start with the original equation: ax […]
How to Determine if a Graph is Symmetric with Respect to the Origin
To determine if a graph is symmetric with respect to the origin, you need to check if it satisfies the following condition: for every point (x, y) on the graph, the point (-x, -y) must also be on the graph. This means that if you were to rotate the graph 180 degrees around the origin, […]
Find the value of the expression 2x³ + 3y² + 17 when x = 3 and y = 4
To find the value of the expression 2x³ + 3y² + 17 when x = 3 and y = 4, we first need to substitute the values of x and y into the expression. Starting with the expression: 2x³ + 3y² + 17 Substituting x = 3 and y = 4: 2(3)³ + 3(4)² + […]
What is a Three Dimensional Shape?
A three dimensional shape, often referred to as a 3D shape, is an object that has three dimensions: length, width, and height. Unlike two dimensional shapes, which only have length and width, a three dimensional shape occupies space and can be measured in all three directions. Common examples of three dimensional shapes include cubes, spheres, […]
How to Solve the Inequality 2x < 1 x 2?
To solve the inequality 2x < 1 * 2, we first simplify the right side of the inequality. 1. Calculate the right side: 1 * 2 = 2. 2. Now, the inequality looks like this: 2x < 2. 3. Next, we need to isolate x. To do so, we can divide both sides of the […]
A histogram is not appropriate for displaying which of the following types of information?
A histogram is not suitable for displaying categorical data. Histograms are designed to show the distribution of continuous numerical data by representing the frequency of data points within specific ranges (bins). For instance, if you have a dataset that includes categories like ‘red’, ‘blue’, and ‘green’, using a histogram would not be appropriate. Instead, a […]
How do you solve x² + 12x + 6 = 0 using the completing the square method?
To solve the equation x² + 12x + 6 = 0 using the completing the square method, follow these steps: Move the constant to the other side: Start by isolating the constant term on one side of the equation. We rewrite the equation as: x² + 12x = -6 Complete the square: To complete the […]
How to Find the Original Price of a Discounted Item
To find the original price of a discounted item, you can use a simple formula. First, you need to know the discount percentage and the final price after the discount has been applied. The formula is: Original Price = Final Price / (1 – Discount Percentage). For example, if an item is on sale for […]