Two Angles Are Complementary: One Contains 30 More Than the Other. Find Both Angles.
Let’s denote the smaller angle as x. Since the other angle contains 30 degrees more, we can represent it as x + 30. According to the definition of complementary angles, the sum of the two angles is 90 degrees. This gives us the equation: x + (x + 30) = 90 Simplifying this equation: Combine […]
If a rectangular office space is 72 feet wide and has a 410 foot perimeter, what is its area?
To find the area of the rectangular office space, we first need to determine its length. We know the width and the perimeter. The formula for the perimeter (P) of a rectangle is: P = 2 * (Length + Width) Given that the perimeter is 410 feet and the width is 72 feet, we can […]
How many feet of yarn can you buy for $52 if Ben’s General Store sells it for $4 a foot?
To find out how many feet of yarn you can buy for $52 at Ben’s General Store, you need to divide the total amount of money you have by the price per foot of yarn. In this case, the price per foot is $4. Here’s the calculation: Total money available: $52 Price per foot of […]
What is the 15th term of the sequence 20, 16, 12?
To find the 15th term of the sequence 20, 16, 12, we first need to identify the pattern in the sequence. Observing the numbers, we see that each term decreases by 4: 20 – 4 = 16 16 – 4 = 12 From this, we can ascertain that the sequence is an arithmetic series where […]
What is the area of a rhombus?
The area of a rhombus can be calculated using the formula: Area = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals of the rhombus. A rhombus is a type of polygon that is a quadrilateral (four sides) with all sides having equal length. The diagonals of a rhombus […]
What is the equation of a circle with a center at (1, 4) and a point on the circle at (4, 8)?
To find the equation of a circle, we can use the standard form of a circle’s equation, which is given by: (x – h)² + (y – k)² = r² In this equation, (h, k) is the center of the circle and r is the radius. In our case, the center is given as (1, […]
How do you find the standard deviation of a probability distribution?
Finding the standard deviation of a probability distribution involves a few essential steps, and it’s important to understand both discrete and continuous distributions as they use slightly different formulas. For a discrete probability distribution, you can find the standard deviation using the following steps: Calculate the mean (μ), which is the expected value of the […]
What is the average arithmetic mean of all the multiples of ten from 10 to 190 inclusive?
To find the average arithmetic mean of all the multiples of ten from 10 to 190, first, we need to identify the multiples of ten within this range: 10, 20, 30, …, 190. These numbers form an arithmetic series where: The first term (a) is 10. The last term (l) is 190. The common difference […]
Which of the following is the solution to the differential equation dy/dx = ey * x with initial condition y(0) = ln(4)?
To solve the differential equation dy/dx = ey * x with the initial condition y(0) = ln(4), we can use separation of variables. We start by rearranging the equation: dy/ey = x dx Next, we integrate both sides. The left side can be integrated using the substitution u = ey, leading to: -e-y = (1/2)x2 […]
What is the amplitude, period, and midline of f(x) = 4 cos(2x) + 3?
To analyze the function f(x) = 4 cos(2x) + 3, we can identify its amplitude, period, and midline based on its form. Amplitude The amplitude of a cosine function is the coefficient in front of the cosine term. In this case, the coefficient is 4. This means the amplitude is 4. Amplitude represents the maximum […]