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What number multiplied by seven and then decreased by the same number equals 48?
To solve the equation where seven times a number minus the number equals 48, let’s break it down step-by-step. Let’s denote the unknown number as x. The equation we can set up from the problem is: 7x – x = 48 Now, we can simplify the left side of the equation: 6x = 48 Next, … Read more
How do you find an explicit solution for the initial value problem defined by the differential equation x² dy/dx = y + xy + 1 and the initial condition y(4) = ?
To solve the initial value problem given by the differential equation: x² dy/dx = y + xy + 1 we can start by rearranging and simplifying the terms in the equation. Step 1: Rearranging the Equation First, we rewrite the equation for clarity: dy/dx = (y + xy + 1)/x² This equation can be addressed … Read more
In a college with 300 students, where each student reads 5 newspapers and 60 students read every newspaper, how many newspapers are there in total?
To find the total number of newspapers in this college, let’s break down the information provided: There are 300 students in total. Each student reads 5 newspapers. 60 students read every single newspaper. Now, if 60 students read every newspaper, we can infer that these students form the core readership for the available newspapers. Since … Read more
How can I find the x-intercept and y-intercept of a line on a graph?
To determine the x-intercept and y-intercept of a line on a graph, you need to follow a few simple steps: Finding the X-Intercept The x-intercept is the point where the line crosses the x-axis. This occurs when the value of y is zero. Here’s how to find it: Identify the equation of the line if … Read more
How do you find the tangent if the cosine is one divided by four times the sine?
To find the tangent when given the relationship that cosine is one divided by four times the sine, we can start by defining the terms mathematically. We know that: tan(θ) = sin(θ) / cos(θ) According to the problem, we have: cos(θ) = (1/4) * sin(θ) We can rewrite this in terms of tangent: tan(θ) = … Read more
How can I find a polynomial function of degree 3 with real coefficients that has zeros at 3, 1, and 4, while ensuring that f(2) equals 24?
To find a polynomial function of degree 3 with real coefficients given the zeros at 3, 1, and 4, we can start by expressing the polynomial in its factored form: Let the polynomial be represented as: f(x) = a(x – 3)(x – 1)(x – 4) Here, a is a constant that we need to determine. … Read more
What is the probability of event A occurring given that event B has occurred, if A and B are independent events with P(A) = 0.05 and P(B) = 0.65?
To find P(A | B), the probability of event A occurring given that event B has occurred, we can use the property of independent events in probability. When two events A and B are independent, the occurrence of one does not affect the occurrence of the other. According to the definition of independent events: P(A … Read more
What are the dimensions and volume of a swimming pool that is 12 meters long, 6 meters wide, and 1 meter deep?
Dimensions of the Swimming Pool The swimming pool measures: Length: 12 meters Width: 6 meters Depth: 1 meter Calculating the Volume To find the volume of the swimming pool, we use the formula for the volume of a rectangular prism, which is: Volume = Length × Width × Depth Substituting in the values: Volume = … Read more
If I have the equation y = 7x^2 + 3, what will the value of y be when I input x = 4?
To find the output of the equation y = 7×2 + 3 when the input is x = 4, we will substitute the value of x into the equation and perform the necessary calculations. 1. Substitute x with 4: y = 7(4)2 + 3 2. Calculate (4)2: (4)(4) = 16 3. Now, replace (4)2 in … Read more