Consider the word grateful. if all of the letters are used, how many ways can the letters be arranged?

a. 36
b. 720
c. 5,040
d. 40,320

Correct option: d -> 40,320

Step-by-step explanation:

To find all the arrangements of letters in a word where all the letters are different, we just need to calculate the factorial of the number of letters.

The word "grateful" has 8 different letters, so the number of arrangements of letters is:

8! = 8*7*6*5*4*3*2 = 40,320 different arrangements

Correct option: d

13

step-by-step explanation:

distance formula is d=√(x2-x1)^2   +   (y2-y1)^2

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)