If A and B are Independent Events with P(A) = 0.5 and P(B) = 0.5, What is P(A | B)?
To find P(A | B), we first need to understand the concept of independent events. When two events A and B are independent, the occurrence of one does not affect the occurrence of the other. This leads us to a critical formula: P(A | B) = P(A) This means that the probability of A occurring […]
Find f(g(f(g(fg)) and fg and their domains if f(x) = 4x and g(x) = x^2 + 3x
To find f(g(f(g(fg)))) and fg, we first need to clearly define our functions: f(x) = 4x g(x) = x² + 3x Let’s start with fg: fg means f(g(x)). We first calculate g(x): g(x) = x² + 3x Now plug g(x) into f(x): f(g(x)) = f(x² + 3x) = 4(x² + 3x) = 4x² + 12x […]
How to Find the Length of a Diagonal of a Rectangle
To find the length of a diagonal of a rectangle, you can use the Pythagorean theorem. The diagonal forms a right triangle with the length and width of the rectangle. If you denote the length of the rectangle as a and the width as b, the formula for the diagonal d is: d = √(a² […]
A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the center of the circle.
To find the distance of the chord from the center of the circle, we can use the relationship between the radius, the distance from the center to the chord, and half the length of the chord. First, let’s denote: Radius of the circle (r) = 10 cm Length of the chord (L) = 16 cm […]
If a process requires the reduction from 40 at rate of 5, calculate temperature after 10 hours.
To calculate the temperature after 10 hours, we first need to understand the reduction process. The starting temperature is 40, and it reduces at a rate of 5 units per hour. After 10 hours, the total reduction in temperature would be: Reduction rate: 5 units/hour Time: 10 hours Total reduction = 5 units/hour * 10 […]
What are all the roots of the function f(x) = x^3 – 9x^2 + 26x – 24, given that one root is x = 2? Use the Remainder Theorem.
To find all the roots of the polynomial function f(x) = x^3 – 9x^2 + 26x – 24, given that one root is x = 2, we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial f(x) is divided by (x – r), the remainder of that division is f(r). When […]
How Many Degrees is 1 Radian?
1 radian is approximately equal to 57.2958 degrees. To understand this better, let’s look at how the conversion between radians and degrees works. Radians and degrees are both units used to measure angles. The full circle is 360 degrees, which is equivalent to 2π radians. To convert from radians to degrees, you can use the […]
How to Find the Vertical and Horizontal Asymptotes of a Rational Function
To find the vertical and horizontal asymptotes of a rational function, you should follow these steps: Finding Vertical Asymptotes Vertical asymptotes occur where the function approaches infinity, typically where the denominator is equal to zero (and the numerator is not zero at those points). To find these points: Identify the denominator of the rational function. […]
What are all the roots of the function given that one factor is x²?
To find the roots of the function represented by the polynomial f(x) = 4x³ + 4x² + 16x + 16, we can factor out the known factor, which is x². Using polynomial long division or synthetic division, we divide f(x) by x²: 4x + 16 ________________ x² | 4x³ + 4x² + 16x + 16 […]
How to Write an Equation for the Translation of y = 6x with Asymptotes at x = 4 and y = 5?
To find the equation that describes the translation of the function y = 6x while incorporating the asymptotes x = 4 and y = 5, we will begin by understanding what these asymptotes represent. The line x = 4 indicates a vertical asymptote, which means that our function will approach this vertical line but never […]