To determine the probability of drawing a red face card from a standard deck of playing cards, we first need to understand the composition of the deck and what constitutes a red face card. A standard deck consists of 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades. Of these suits, … Read more
To factor the quadratic expression x² + 2x – 3, you’ll want to follow these steps: Identify the coefficients: In the expression x² + 2x – 3, the coefficients are as follows: A (the coefficient of x²) = 1 B (the coefficient of x) = 2 C (the constant term) = -3 Find two numbers … Read more
To convert the fraction 1/15 into a decimal, you’ll need to divide the numerator (1) by the denominator (15). Here’s how to do that: Perform the division: 1 ÷ 15. When you divide 1 by 15, you start by determining how many times 15 fits into 1. Since 15 is larger than 1, it fits … Read more
To integrate the function 1 + sin(x), we will proceed step by step. The integral we need to solve is: ∫ (1 + sin(x)) dx This integral can be split into two separate integrals: ∫ 1 dx + ∫ sin(x) dx Now, let’s solve each part: 1. Integrating 1: The integral of 1 with respect … Read more
To find the sum of the multiples of 4 from 16 to 100, we start by identifying the first and last multiples of 4 within that range. The first multiple of 4 in this range is 16, and the last multiple of 4 before reaching 100 is 100 itself, as 100 is also a multiple … Read more
Finding the Solution to 6x² = 60 To solve the equation 6x² = 60, we need to isolate the variable x. Here’s a step-by-step breakdown of the solution: Start with the equation: 6x² = 60 Divide both sides by 6: This will help to simplify the equation. x² = 10 Take the square root of … Read more
A day is typically understood to be 24 hours long. To find out what fraction of a day 4 hours represents, you can use a simple mathematical approach. First, express 4 hours as a fraction of 24 hours: Fraction = 4 hours / 24 hours Now, simplify this fraction: Fraction = 4/24 By dividing both … Read more
To find the first three common multiples of the given pairs of numbers, we start by determining the least common multiples (LCM) for each set. Finding Common Multiples of 6 and 8 1. **Identify the multiples:** Multiples of 6: 6, 12, 18, 24, 30, 36, 42, … Multiples of 8: 8, 16, 24, 32, 40, … Read more
To determine the missing number in the sequence 73, 17, 46, we need to identify a pattern or a rule that links these numbers. One approach to finding the missing number is to look for mathematical relationships. Here, we can search for any arithmetic operations that might tie these numbers together. If we observe the … Read more
To convert the fraction 7/12 into a decimal, you need to perform a division. The numerator of the fraction is 7 and the denominator is 12. This means you need to divide 7 by 12. You can do this calculation using a calculator or by hand. If you use a calculator, simply type in 7 … Read more