To determine the probability of drawing a red face card from a standard deck of 52 playing cards, you first need to know how many total face cards there are and how many of those are red. In a standard deck, there are three face cards in each suit: the King, Queen, and Jack. Since … Read more
To find the product of the two mixed numbers, 4 2/3 and 11 1/4, we first need to convert them into improper fractions. 1. Convert 4 2/3 to an improper fraction: 4 2/3 = (4 * 3 + 2) / 3 = (12 + 2) / 3 = 14/3 2. Convert 11 1/4 to an … Read more
To find an ordered pair that satisfies both inequalities y > 3x + 1 and y < x + 4, we need to analyze what these inequalities represent. 1. **Understanding the inequalities**: The first inequality, y > 3x + 1, represents all the points that lie above the line defined by the equation y = … Read more
To solve the equation x6 + 9×3 + 8 = 0, we can utilize a technique called u-substitution. The idea is to simplify the equation by substituting a new variable for the expression involved. Step 1: Make the substitutionLet’s set u = x3. This means that x6 = (x3)2 = u2. Rewriting the original equation … Read more
To determine the polar coordinates of the point (3, 3), we first need to convert these Cartesian coordinates to polar coordinates. In polar coordinates, a point is represented by the radius (r) and the angle (θ). 1. **Calculating the Radius (r)**: The radius can be calculated using the formula: r = √(x2 + y2) where … Read more
A regular 30-sided polygon, also known as a triacontagon, can be rotated around its center, and the degree of rotation refers to the angle at which the polygon can be rotated while still appearing unchanged. To find the degree of rotation for any regular polygon, you can use the formula: Degree of Rotation = 360° … Read more
To determine the total number of unique outfit combinations that Sam can create with his hats and scarves, we can use the basic principle of counting in combinatorics. This principle states that if you have m ways to do one thing and n ways to do another, then the total number of combinations of both … Read more
The prime factorization of a number is the process of breaking that number down into its prime number factors. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. To find the prime factorization of 30, we can start by dividing the number by the smallest prime number: Step … Read more
The number "seventeen thousand and seventeen" can be represented in figures as: 17,017 This number is made up of the following components: Seventeen thousand: This part is written as 17,000, where the digit 1 represents ten thousand, and the digit 7 represents seven thousand. Seventeen: The remaining part is written as 17. When combined, you … Read more
Trigonometric Values of 2π/3 Radians The angle 2π/3 radians is in the second quadrant of the unit circle. To find the sine, cosine, and tangent values of this angle, we can refer to the corresponding values from the reference angle. Reference Angle The reference angle for 2π/3 is given by: Reference angle = π – … Read more