The faces of a cubical die are each labeled with a different prime number, and each of the six smallest prime numbers (2, 3, 5, 7, 11, 13) is on exactly one face of the die. The die will be rolled twice. What is the probability that the product of the two numbers rolled will be even? Express your answer as a common fraction
Naming clockwise, regular pentagon COUNT has vertices C, O, U, N, T, respectively. Point X is right in the center of this pentagon so that line segments from X to each vertex create congruent triangles. If point C is rotated 144° counterclockwise about the point X, what original vertex is the image of point C?
The preimage of square ABCD has its center at (8, −8) and has an area of 4 square units. The top side of the square is horizontal. The square is then dilated with the dilation center at (0, 0) and a scale factor of 2. What are the coordinates of the vertex of the image of square ABCD that is farthest from the origin?
A set of data includes all of the positive odd integers less than 100, the positive, two-digit multiples of 10, and the numbers 4, 16 and 64. All included integers appear exactly once in the data. What is the positive difference between the median and the mean of the set of data? Express your answer as a decimal to the nearest thousandth.
The formula for the volume of a sphere is V = (4/3)πr\(^3\) , where r is the radius of the sphere. Alex places a particular sphere into a cubic box with sides of 10 meters. If the sphere is tangent to each of the box’s faces, what is the volume of the sphere? Express your answer as a decimal to the nearest tenth.