Mathematics Questions

Short Answer To calculate the median of a data set, first organize the values in ascending order. Then, identify the middle positions (12th and 13th) and average them; in this case, both are 17, resulting in a median of 17. Step 1: Organize the Data Set Begin by listing all the values in your data […]

Short Answer The process of transformation involves moving points in geometry and includes rotation, reflection, dilation, and translation. Rotation specifically preserves the shape and size of a figure, such as a trapezoid, while changing its orientation, illustrating the fundamental properties of geometric transformations. Step 1: Understanding Transformation Transformation is the process of moving a point

Short Answer Convenience sampling involves selecting readily accessible participants, potentially leading to bias, while voluntary sampling relies on individuals’ self-selection based on interest, resulting in a more engaged but possibly unrepresentative group. The key differences include accessibility for convenience sampling versus personal interest for voluntary sampling, as well as how participants are selected and the

Short Answer The reflection of triangle XYZ across line MN maintains symmetric properties, ensuring that all corresponding angles and distances, such as angle X’Z’Y’ being equal to 90¬¨‚àû, are preserved. Additionally, line segments like BZ’ and BZ remain equal due to the symmetry of the reflection. Step 1: Understand the Reflection Concept In this scenario,

Short Answer The answer explains a piecewise function defined as f(x) = 3 for x < 1 and f(x) = x for x ‚a• 1. The graph features a constant line at y = 3 for x < 1 and transitions to a linear function beginning at (1, 1) for x ‚a• 1, with appropriate

Short Answer The function has a positive leading coefficient and an odd degree, resulting in negative values as x approaches negative infinity. It crosses the x-axis at roots -6 and -2, becoming positive after -6 and returning to negative after -2, while touching the x-axis at root 0 without crossing it, remaining negative until it

Short Answer The steps to analyze angles in quadrilateral ABCD inscribed in a circle begin by understanding the relationship between arcs and angles, applying the Inscribed Angle Theorem to derive angle measures. Finally, it’s demonstrated that angles A and C, along with angles B and D, are supplementary, confirming the relationships in the quadrilateral. Step

Short Answer The analysis of parallelogram ABCD reveals that its diagonals bisect each other, leading to the conclusion that triangles ABC and BCD are isosceles with equal sides. Thus, all adjacent sides are equal, confirming that ABCD is a rhombus. Step 1: Understand the Parallelogram Properties Begin by recognizing the characteristics of the parallelogram ABCD

Short Answer To find the radius of a circle with an area less than 1 dm¬≤, we use the area formula A = œAr¬≤ and set up the inequality œAr¬≤ < 1. By rearranging, we find r¬≤ < 1/œA, leading to a maximum radius of approximately 0.5642 dm, which rounds to less than 0.56 dm.

Short Answer Mutually exclusive events cannot occur simultaneously, meaning if one event happens, the other cannot. To determine if two events A and B are mutually exclusive, check if the probability P(A AND B) is zero; if not, they can occur together, confirming they are not mutually exclusive. Step 1: Understand Mutually Exclusive Events Mutually