Read the tree given below from left to right to answer the following questions. A tree diagram is shown. There are 3 branches extending from the root labeled "Score on part I" of the tree. The first branch from the root labeled "Score on part I" is labeled ">10" and goes to a vertex labeled "Score on part II". There are 2 branches extending from this vertex. The first branch from this vertex is labeled ">10" and goes to a vertex labeled "Math 120". The second branch from this vertex is labeled "10" and goes to a vertex labeled "Math 110". The second branch from the root labeled "Score on part I" is labeled "= 8, 9, 10" and goes to a vertex labeled "Score on part II". There are 2 branches extending from this vertex. The first branch from this vertex is labeled ">6" and goes to a vertex labeled "Math 110". The second branch from this vertex is labeled "6" and goes to a vertex labeled "Math 100". The third branch from the root labeled "Score on part I" is labeled "<8" and goes to a vertex labeled "Math 100". (a) A student scored 12 on part I and 7 on part II. What course should the student take? Math 100 Math 110 Math 120 (b) A student scored 9 on part I and 7 on part II. What course should the student take? Math 100 Math 110 Math 120 18. [-/5.55 Points] DETAILS MY NOTES ASK YOUR TEACHER question Prove the following statement by mathematical induction. For every integer n 0, 2n <(n + 2)!. Proof (by mathematical induction): Let P(n) be the inequality 2n < (n + 2)