1.Find the number of pairwise comparisons that would take place in an election with 13 candidates
Answer :78
2.If there are 171 total pairwise comparisons in a different election, how many candidates are running?how would i find the answer for question 2 i need help pls!!!
19
78 is correct for the first one
2nd:
n(n-1)/2 = 171
n^2 - n - 342
(n - 19)(n + 18) = 0
n = 19 or n = -18, but n > 0
n=19, there were 19 running
To find the number of candidates running in an election based on the total pairwise comparisons, you can use the following formula:
Number of comparisons = n(n-1)/2,
where n represents the number of candidates.
Let's substitute the given values into the formula and solve for n:
171 = n(n-1)/2.
To simplify the equation, multiply both sides by 2:
342 = n(n-1).
Rewrite the equation in standard quadratic form:
n^2 - n - 342 = 0.
Now, we need to factorize the quadratic equation or use the quadratic formula to solve for n. The factors of -342 that add up to -1 are -19 and 18.
Therefore, the equation can be factored as:
(n - 19)(n + 18) = 0.
Setting each factor equal to zero, we get:
n - 19 = 0 or n + 18 = 0.
Solving for n:
n = 19 or n = -18.
Since the number of candidates cannot be negative in this context, we discard n = -18.
Therefore, the number of candidates running in the election with 171 pairwise comparisons is 19.
To find the number of candidates in an election given the total number of pairwise comparisons, you can use the formula:
n(n - 1) / 2 = total comparisons
Where n represents the number of candidates.
Let's apply this formula to the second question:
171 = n(n - 1) / 2
To solve this equation, we can multiply both sides by 2:
342 = n(n - 1)
Rearranging the equation:
n^2 - n - 342 = 0
Now we have a quadratic equation. We can solve it by factoring or using the quadratic formula.
Factoring the equation:
(n - 19)(n + 18) = 0
From this equation, we find two possible solutions: n = 19 or n = -18. Since the number of candidates cannot be negative, we choose n = 19.
Therefore, in the second election, there are 19 candidates running.