Solution-
First 9 letters of alphabet are- A,B,C,D,E,F,G,H,I
Total number of ways of selection of 4 letters from 9 alphabets = 9C4
=9!÷((4!).(9-4)!) = 9!÷(4!×5!) = (9×8×7×6)÷(24) = 126
The number of ways of arranging these 4 numbers = 4! = 24
∴ Total number of possible permutations = 9C4×4! = 126×24 = 3024
∴ option number 2 is correct.
Answer:
A diagonal of this rectangle has length 10.
Step-by-step explanation:
The vertices (-4, 4) and (-4, -4) have the same x-coordinate (-4) and different y-coordinates (4 and -4). These two points are the endpoints of a vertical side of the rectangle which has length 4 - (-4) = 8.
Similarly, the vertices (2, -4) and (-4, -4) have the same y-coordinate (-4) but different x-coordinates (2 and -4). To find the horizontal dimension of the rectangle, we calculate 2 - (-4), which comes out to 6.
Thus, the width of the rectangle is 6 and the length is 8.
Using the Pythagorean Theorem, we find the length of a diagonal as follows:
d = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.
A diagonal of this rectangle has length 10.
Divide 49.2 by 6 to get 8.2, which is about 8
The kite forms a right angled triangle with hypotenuse of 50 ft. The height of the kite above the ground is the opposite of 60° angle.
Using the sine rule,
Sin 60 = Height of the kite above the ground/Hypotenuse
Therefore,
Height of the kite above the ground = Hypotenuse*Sin 60 = 50 *Sin 60 = 43.3 ft