Answer:
The degrees of freedom associated with the critical value is 25.
Step-by-step explanation:
The number of values in the final calculation of a statistic that are free to vary is referred to as the degrees of freedom. That is, it is the number of independent ways by which a dynamic system can move, without disrupting any constraint imposed on it.
The degrees of freedom for the t-distribution is obtained by substituting the values of n1 and n2 in the degrees of freedom formula.
Degrees of freedom, df = n1+n2−2
= 15+12−2=27−2=25
Therefore, the degrees of freedom associated with the critical value is 25.
Answer:
182 seconds
Step-by-step explanation:
Given:
Time taken for first lap is 50 seconds and each subsequent lap takes 20% longer than previous
Solution:
Time taken for first lap = 50 sec
For second lap
Each subsequent lap takes 20% longer than previous
Previous lap time = 50 sec
second lap = 50 + 20% of 50
second lap 
second lap 
second lap 
For third lap
Each subsequent lap takes 20% longer than previous
Previous lap time = 60 sec
Third lap = 60 + 20% of 60




Time taken for 3 laps is equal to sum of all three laps time.


Therefore, it takes 182 seconds (3 min, 2 seconds) to run three laps
Imagine a right triangle where a and b are the legs and c is the hypothenuse.
Pitagora: a²+b²=c²
Divide by c
(a/c)²+(b/c)²=1
But a/c=sin(B) and b/c=cos(B)
Thus sin² + cos² = 1