If you roll two fair six sided dice what is the probability that the sum is 4 or higher?
To determine the probability that the sum of two rolled dice is 4 or higher, we first need to know the total number of outcomes when rolling two six-sided dice. Since each die has 6 faces, the total number of outcomes is: 6 (for the first die) × 6 (for the second die) = 36 […]
How do you find the magnitude and direction of the vector difference a = 400i + 300j and b = 500i + 200j?
To find the vector difference of a and b, we will subtract vector b from vector a: a – b = (400i + 300j) – (500i + 200j) First, we can break this down into its components: i-components: 400 – 500 = -100 j-components: 300 – 200 = 100 So the resulting vector difference is: […]
Find the Exact Length of the Curve x^1 + 3y – y^3 = 1 and y = 9
To find the exact length of the curve given by the equation x^1 + 3y – y^3 = 1 and the line y = 9, we will first express the curve in terms of y and then calculate the length of the curve over the specified interval. 1. Start with the equation: x + 3y […]
The sum of 3 numbers in AP is 18. What is the product of the first and third number?
To find the product of the first and third numbers in an arithmetic progression (AP) where the sum of three numbers is 18, we start by letting the three numbers be: First number = a – d Second number = a Third number = a + d In an AP, the middle number is the […]
Consider the parametric equations below: x = t², y = t⁷. Sketch the curve by using the parametric equations to plot points.
To sketch the curve defined by the parametric equations x = t² and y = t⁷, we first need to calculate several points by substituting various values of t. Let’s choose values for t in a range to get a sense of how the curve behaves: For t = -2: x = (-2)² = 4 […]
Solve for x: 2x + 17 = 2x + 1 + 3 + 12
To solve the equation 2x + 17 = 2x + 1 + 3 + 12, we first simplify the right side. On the right side, we combine the constants: 1 + 3 + 12 = 16 Now the equation reads: 2x + 17 = 2x + 16 Next, we want to isolate the variable x. […]
What are the zeros of the polynomial function f(x) = x³ – 9x² – 20x?
To find the zeros of the polynomial function f(x) = x³ – 9x² – 20x, we first need to set the function equal to zero: f(x) = x³ – 9x² – 20x = 0 Next, we can factor the polynomial. First, we notice that each term includes an x, so we can factor x out: […]
Which is a zero of the quadratic function f(x) = 9x² + 54x + 19?
To find the zeros of the quadratic function, we need to solve the equation f(x) = 0. This involves using the quadratic formula: x = (-b ± √(b² – 4ac)) / 2a In this case, the coefficients are: a = 9 b = 54 c = 19 First, we compute the discriminant: b² – 4ac […]
The sum of two numbers is 24, one number is 2 times as large as the other. What are the numbers?
To find the two numbers, we can set up a simple equation. Let’s denote the smaller number as x. According to the problem, the larger number would then be 2x. The problem states that the sum of these two numbers is 24. Therefore, we can write the equation: x + 2x = 24 Simplifying this, […]
Find the least common multiple of the following polynomials 9x, 22x, and 3x^2
To find the least common multiple (LCM) of the polynomials 9x, 22x, and 3×2, we need to consider both the coefficients and the variables. First, let’s find the LCM of the coefficients: The coefficients are 9, 22, and 3. We can find the prime factorization of each number: 9 = 32, 22 = 2 * […]