Consider all numbers consisting of four different digits all between 1 and 9 . How many of these are odd

1680

Step-by-step explanation:

Considering repeatition is not allowed.

We can  use permutation to reach to the required answer.

Consider four digits to be placed in four boxes. Now for the number to be odd, unit digit must be odd. Therefore, unit digit can only be filled by 1, 3, 5,7, or 9. That is 5 ways. Now, other three boxes can be filled with 8, 7 and 6 ways respectively.

Therefore, Total numbers = 5×8×7×6 = 1680

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

your answer is 228

step-by-step explanation:

add the top and bottom bases together, then divide them by 2, then multiply by the height.