Is the relation 1, 3, 4, 0, 3, 1, 0, 4, 2, 3 a function? Why or why not?
To determine whether the relation represented by the pairs (1, 3), (4, 0), (3, 1), (0, 4), (2, 3) is a function, we need to check if each input (the first element of each pair) is associated with exactly one output (the second element). In this case, let’s break down the pairs: (1, 3) (4, […]
Find the perimeter of the image below: 37 units, 38 units, 39 units, 40 units
To find the perimeter of a shape, we need to add up the lengths of all its sides. In this case, the information provided seems to suggest four sides with lengths of 37 units, 38 units, 39 units, and 40 units. Let’s calculate the perimeter: First side: 37 units Second side: 38 units Third side: […]
A store buys an item for dollar 50 and marks it up 100%. What is the price?
If a store buys an item for $50 and marks it up by 100%, the price can be calculated as follows: First, we determine the amount of the markup. A 100% markup on the cost means that the store will add an amount equal to the cost of the item to the original price. Since […]
For a Perfectly Symmetrical Distribution with μ = 30, What is the Mode?
In a perfectly symmetrical distribution, the mean, median, and mode are all equal. This characteristic features prominently in distributions such as the normal distribution. Given that the mean (μ) is 30 in this case, the mode of the distribution will also be 30. To elaborate, the mode of a distribution is the value that appears […]
How do you solve the equation 2x + 4x = 21?
To solve the equation 2x + 4x = 21, start by combining like terms on the left side. Here, you have 2x and 4x, which can be added together: 2x + 4x = 6x This simplifies our equation to: 6x = 21 Next, to isolate x, you need to divide both sides of the equation […]
Which of the following is not true about the median of a trapezoid?
The median of a trapezoid is often a topic of confusion, especially when it comes to understanding its properties. To clarify, let’s discuss the facts: The median of a trapezoid is the line segment that connects the midpoints of the two non-parallel sides. This segment is parallel to the bases and its length is equal […]
A sequence is defined by the recursive function f(n) = f(n-1) + f(n-2). If f(1) = 10, what is f(3)?
To solve for f(3) using the recursive function f(n) = f(n-1) + f(n-2), we first need to identify the values of f(2) and f(3). Given that f(1) = 10, we still need to find f(2). The recursive formula indicates that to find f(2), we need the values of f(1) and f(0). However, the problem does […]
What is the value of k when k = 28, k = 29, k = 31, k = 42?
The value of k, as provided in the question, takes on different values in each instance: 28, 29, 31, and 42. Each of these represents a specific case or scenario where k is defined. To clarify: When k = 28, the value of k is simply 28. When k = 29, the value of k […]
Draw a rough figure and label suitably in each of the following cases: a point P lies on line segment AB, XY and PQ intersect at M, line L contains E and F but not D, OP and OQ meet at O.
To illustrate the scenarios described, let’s draw rough figures for each case: Case A: Point P on Line Segment AB In this case, line segment AB is drawn as a straight line, and point P is marked along this segment. Ensure that P is positioned between points A and B. Case B: Intersections of XY […]
Evaluate the integral from 0 to 12 of cos(1x) dx
To evaluate the integral ∫₀¹² cos(1x) dx, we start by finding the antiderivative of cos(1x). Using the substitution technique, let u = 1x which implies du = dx. The integral now becomes: ∫ cos(u) du The antiderivative of cos(u) is sin(u) plus the constant of integration C. Thus, we have: sin(u) + C Substituting back […]