Answer:
41.67% probability that a student has a dog given that they have a cat
Step-by-step explanation:
We use the conditional probability formula to solve this question. It is

In which
P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: having a cat.
Event B: having a dog.
12 of 27 students have a cat:
This means that 
5 students who have a cat and a dog.
This means that 
What is the probability that a student has a dog given that they have a cat?

41.67% probability that a student has a dog given that they have a cat
From the statement given above, it can be deduced that the measure of the side of the figure is equal to 1 inch. Thus, the scale factor is 1:7. The ratio of their area should be 1:49. To get the area of the smallest figure, we simply divide the given area of the largest figure by 49, giving us the answer which is equal to 12 in².
Answer:
71.6056
Step-by-step explanation:
c² = a² + b² - 2abcosC°
29² = 30² + 15² - 2(30)(15)cosC°
841 = 900 + 225 - 900cosC°
-59 = 225 - 900cosC°
-284 = -900cosC°
71/225 = cosC°
cos⁻¹(71/225) = C°
C° = 71.6056