Answer:
35°
Step-by-step explanation:
From the sketch made, to obtain B we use the cosine angle formula :
We have 2 so des and an included angle
Cos B = (a² + c² - b²) / 2ac
First we obtain the side c
c² = a² + b² - 2ab CosC
c² = 11.2² + 6.7² - 2(11.7 * 6.7) * cos 72
c = 11.13
Using the value of c
Cos B = (a² + c² - b²) / 2ac
CosB = (11.2² + 11.13² - 6.7²) / (2*11.2*11.13)
Cos B = 204.4269 / 249.312
B = Cos^-1(204.4269 / 249.312)
B = 34.9°
Answer:
a) This is a permutation, there are 210 ways to do it
b) This is a permutation with 6 possibilities
c) This is a combination with a total of 1081575 possibilities
Step-by-step explanation:
a) Here the order does matter bacause it is not the same that they go to France in the weak trip than they go there for 2 days, as a result, this scenario is a permutation.
You need to pick 3 countries from a total of 7, but the order matters, so the total amount of ways to do this is
b) Here each permutation of 123 will give you a possible (and a different one from the others) lock-combination, so this is again a permutation.
The total amount of ways we have to do the selectio of the lock-combination is the total amount of permutations of a set of 3 elements, in other words, it is 3! = 6.
c) If you only cares about who advances to the finals, then the order doesnt matter here, you just want 8 people out of the 25 available. This is therefore a combination, and the total amount of possible cases are
.