Answer:
The median. 80 because the mean is 80.454545
Step-by-step explanation:
The triangle Sum Theorem says that the sum of all the angles in a triangle has to equal 180 degrees. Since all three sides (and, consequently, angles) in an equilateral triangle are the same, you can divide 180 by 3 to find the measure of any angle of an equilateral triangle (60 degrees).
6 1/3 = 6 2/6 = 5 8/6
The bottom one is confusing, sorry.
Given:
x = 2 3 4 5 6
y = 20 ; 45 ; 80; 125;180
The constant variation for the quadratic variation is 5.
y = 5x²
y = 5(2²) = 5(4) = 20
y = 5(3²) = 5(9) = 45
y = 5(4²) = 5(16) = 80
y = 5(5²) = 5(25) = 125
y = 5(6²) = 5(36) = 180
Answer:
a) 1/2
b) 1/n
c) 1/4
Step-by-step explanation:
a) For each permutation, either 1 precedes 2 or 2 precedes 1. For each permutation in which 1 precedes 2, we can swap 1 and 2 to obtain a permutation in which 2 preceds 1. Thus, half of the total permutations will involve in 1 preceding 2, hence, the probability for a permutation having 1 before 2 is 1/2.
c) If 2 is at the start of the permutation, then it is impossible for 1 to be before 2. If that is not the case, then 1 has a probability of 1/n-1 to be exactly in the position before 2. We can divide in 2 cases using the theorem of total probability,
P( 1 immediately preceds 2) = P (1 immediately precedes 2 | 2 is at position 1) * P(2 is at position 1) + P(1 immediately precedes 2 | 2 is not at position 1) * P(2 is not at position 1) = 0 * 1/n + (1/n-1)*(n-1/n) = 1/n.
d) We can divide the total of permutations in 4 different groups with equal cardinality:
- Those in which n precedes 1 and n-1 precedes 2
- those in which n precedes 1 and 2 precedes n-1
- those in which 1 precedes n and n-1 precedes 2
- those in which 1 precedes n and 2 precedes n-1
All this groups have equal cardinality because we can obtain any element from one group from another by making a permutations between 1 and n and/or 2 and n-1.
This means that the total amount of favourable cases (elements of the first group) are a quarter of the total, hence, the probability of the event is 1/4.
