Consider the event "S" as "The three segments are the sides of a triangle." Remember that the probability of an event occurring is calculated according to:

$P(S)=\frac{Cases\ in\ favor\ of\ S}{Total\ cases}$

By dividing the stick into three segments, the possible cases that can be obtained writing each case in parenteses and the length of each piece as a number are:

(1, 1, 10), (1, 2, 9), (1, 3, 8), (1, 4, 7), (1, 5, 6), (2, 2, 8), (2 , 3, 7), (2, 4, 6), (2, 5, 5), (3, 3, 6), (3, 4, 5), (4, 4, 4).

which corresponds to a total of 12 total cases.

The necessary condition so that a triangle can be formed is that the sum of its two minor sides is greater than the greater side, therefore the favorable cases would be:

(2, 5, 5), (3, 4, 5), (4, 4, 4)

which corresponds to a total of 3 favorable cases. Using the probability formula we obtain:

$P(S)=\frac{Cases\ in\ favor\ of\ S}{Total\ cases}=\frac{3}{12}=0.25$

8 0

3 years ago

The variable z is inversely proportional to x. When x is 6, z has the value 0.5. What is the value of z when x= 14?

Lilit [14]

Z is inversely proportional to X is the same as
z is directly proportional to 1/X
which can be written like this:-
y=k/X
________
0.5=k/6
0.5*6=k/6*6
k=3 ;
________
z = 3/14
Z = 0.2

7 0

3 years ago