Part 1: The general form for this matches y^2 = -4cx, which implies that this opens to the left. (Imagine assigning any value of y, whether positive or negative, which would result in a positive left-hand value. Then to match this sign, the value of x must be negative so that the right-hand side becomes positive as well.)
Part 2: The distance from the vertex to the directrix is given by c. This equation has its vertex at the origin (0, 0). If it opens to the left, the directrix is a vertical line to the right of the origin. This equation is y^2 = -4(1/2)x, so c = 1/2, and the directrix has the equation x = 1/2.
Part 3: The focus is inside the parabola, but it is the same distance from the vertex as the directrix. This distance is 1/2 units, and it will be to the left of the vertex. So the focus is at (-1/2, 0).
Answer:
<u>65 </u>cups of hot chocolate.
Step-by-step explanation:
55.25/0.85 = 65
Answer:

Step-by-step explanation:

Probability of drawing a heart from one deck:

Therefore, probability of drawing a heart from each of 3 decks:

Answer:
m = 
Step-by-step explanation:
Given
y = mx + b ( subtract b from both sides )
y - b = mx ( divide both sides by x )
= m
Answer:
0.8340
Step-by-step explanation:
The aim of this question is to find the probability that the student makes it to the second class prior to when the lecture commences.
Provided that A, B, and C are independent of each other from the full complete question.
Then; we want P(A + C < B)
So A
N (2, 1.5)
B
N (10, 1)
C
N (6, 1)
P(A + C - B < 0)
Since they are normally distributed( i.e. A + C - B)
Then;
E(A + C -B) = E(A) + E(C) - (B)
E(A + C -B) = 2 - 10 + 6
E(A + C -B) = -2
Var(A+C -B) = Var(A) + Var (B) + Var (C)
Var(A + C -B) = (1.5)² + (1)² + (1)²
Var(A + C -B) = 4.25
The standard deviation = 
The standard deviation = 2.06155


