9 and 10
hope this helps!!!
Answer:
<h2>
k = 3</h2>
Step-by-step explanation:
The vertex is (d, e)
for quadratic function: f(x) = ax² + bx + c we have:
d = -b/a and d = (x₁ + x₂)/2
a = 1, b = k, x₁ = -4, x₂=-2
so:
d = -b/a = -k/1 = -k and d = (x₁ + x₂)/2 = (-4-2)/2 = -3
-k = -3
k = 3
The tree diagram is constructed and attached below in the image.
First we have to make a choice out of 3 subjects, so the probability of choosing art as the first subject is 1/3.
Once we have chosen art as the first subject, we have two choices. So the probability of choosing each option now is 1/2. Thus, the probability of choosing math, science is 1/2.
The probability of choosing the projects in order of art, math, science = 1/3 x 1/2 = 1/6
Therefore, the probability that the projects are in order of art, math, science is 1/6 (one over 6). So first option gives the correct answer.