An experimenter is randomly sampling 3 objects in order from among 48 objects. what is the total number of samples in the sample space? 17296 14190 311328 103776 85140

103776

Step-by-step explanation:

The size of the sample space is calculated using permutation. Permutation will be used because in question it is mentioned that sampling objects are sampled in order from 48 objects. The order is discussed so, the permutation is used.

nPr=n!/(n-r)!=48P3=48!/(48-3)!=48!/45!=103776

Hence the total number of objects in sample space are 103776.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

x/3-10=8

x/3=18

x=48