What is the remainder when 2 x 3 x 4 x 2 x 32 x 18 x 3?
To find the remainder of the expression 2 x 3 x 4 x 2 x 32 x 18 x 3, we first need to calculate the product of these numbers. Let’s break it down step by step: 2 x 3 = 6 6 x 4 = 24 24 x 2 = 48 48 x 32 […]
If a car travels 340 miles on 20 gallons of gas, how far can it travel on 25 gallons of gas?
To determine how far the car can travel on 25 gallons of gas, we first need to find out how many miles the car can travel per gallon. We can do this by dividing the total miles traveled by the number of gallons used. Calculating miles per gallon (MPG): 340 miles ÷ 20 gallons = […]
The probability that an event happens is 0.42; what is the probability that the event won’t happen?
To find the probability that an event won’t happen, we can use a simple formula. The probability of an event not occurring is equal to 1 minus the probability of the event occurring. In this case, if the probability of the event happening is 0.42, then: P(Not Happening) = 1 – P(Happening) Substituting the value […]
How do you find f(x) over g(x) for the functions f(x) = 16x^5 – 48x^4 – 8x^3 and g(x) = 8x^2?
To find f(x) over g(x), we need to set up the fraction of the two functions: Given: f(x) = 16×5 – 48×4 – 8×3 g(x) = 8×2 We express this as: f(x) / g(x) = (16×5 – 48×4 – 8×3) / (8×2) Now, we can simplify the fraction: The first step is to divide each […]
How to Draw the Graph of the Equation x + 2y = 4?
To draw the graph of the equation x + 2y = 4, we need to rearrange the equation to express it in a more familiar form. Start by solving for y: 1. Rearrange the equation: 2y = 4 – x 2. Divide everything by 2: y = 2 – (1/2)x This equation is now in […]
How do you factor 32x³ + 4?
To factor the expression 32x³ + 4, we start by looking for common factors in both terms. Noticing that both terms share a factor of 4, we can factor that out: 32x³ + 4 = 4(8x³ + 1) Next, we recognize that 8x³ + 1 can be expressed as a sum of cubes, since 8x³ […]
How to Find the Area of a Trapezoid with Bases of 8cm and 16cm and a Height of 10cm?
To find the area of a trapezoid, you can use the formula: Area = 0.5 × (Base1 + Base2) × Height In this case, the bases are 8cm and 16cm, and the height is 10cm. Let’s plug these values into the formula: Area = 0.5 × (8cm + 16cm) × 10cm This simplifies to: Area […]
Determine Whether the Geometric Series is Convergent or Divergent: 10, 8, 64, 512
To determine if the given geometric series is convergent or divergent, we first need to identify the common ratio and the nature of the series. A geometric series can be expressed in the form: a + a * r + a * r^2 + … where a is the first term and r is the […]
Find the Exact Length of the Curve y = 1 + 2x^3, 0 ≤ x ≤ 1
To find the exact length of the curve defined by the function y = 1 + 2x^3 between x = 0 and x = 1, we need to use the formula for the arc length of a curve given by the formula: L = \int_{a}^{b} \sqrt{1 + \left(\frac{dy}{dx}\right)^2} \, dx First, let’s calculate the derivative […]
If the HCF of 85 and 153 is expressible in the form of 85m + 153, then find the value of m?
To find the value of m such that the highest common factor (HCF) of 85 and 153 can be expressed in the form of 85m + 153, we first need to calculate the HCF of 85 and 153. We can use the prime factorization method to do this: 85 can be factored into 5 and […]