A3x3x4 cuboid is painted blue and cut into 1x1 cubes. what is the expected value for the painted sides of a randomly selected cube?

A 3 x 3 x 4 cuboid can be cut into 3(3) (4) = 36 pieces of 1 x 1 cubes.

Out of the 36 pieces of 1 x 1 cubes, there are no 1 x 1 cube with the four sides painted, there are eight 1 x 1 cubes with simply 3 sides painted, there are twenty 1 x 1 cubes with only 2 sides tinted, there are 6 cubes with only 1 side painted and there are 2 cubes with no side painted.

The chance that the four sides of a randomly selected cube is painted is 0.

The likelihood that only 3 sides of a randomly selected cube is painted is 8 / 36 = 2 / 9.

The chance that only 2 sides of a randomly selected cube is painted is 20 / 36 = 5 / 9.

The likelihood that only 1 side of a randomly selected cube is painted is 6 / 36 = 1 / 6.

The probability that no side of a randomly selected cube is painted is 2 / 36 = 1 / 18.

Thus, the expected value for the painted sides of a randomly selected cube is given by 4(0) + 3(2 / 9) + 2(5 / 9) + 1(1 / 6) + 0( 1 / 18) = 2 / 3 + 10 / 9 + 1 / 6 = 35 / 18 = 1.94

900 degrees

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it