Answer:
Step-by-step explanation:
If you plot the directrix and the focus, you can see that the focus is to the left of the directrix. Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific. The formula for the parabola that opens to the left is
We will solve this for x at the end. The negative is out front because it opens to the left. If it opened to the right, it would be positive.
The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus. Since the vertex is directly between both the directrix and the focus, each distance is the same. P = 1. Filling in what we have now:
which simplifies to
Now we will solve it for x.
and
so
Answer:
3.4
Step-by-step explanation:
divide it all into a calculator
Answer:
Option C and Option D have exactly one solution.
Step-by-step explanation:
The equation will have exactly one solution when it completely solves and we get value of x.
Checking all choices
(Choice A)
-19x + 18 = -19x + 18
-19x+19x=18-18
0=0
(infinite solutions)
(Choice B)
-19x -18 = -19x + 18
-19x+19x=18+18
0≠36
(no solution)
(Choice C)
19x + 18 = -19x + 18
19x+19x=18-18
38x=0
x=0
(One solution)
(Choice D)
19x - 18 = -19x + 18
19x+19x=18+18
38x=36
x=36/38
x=18/19
(One solution)
So, Option C and Option D have exactly one solution.
We need to correctly choose exactly 4 out of the 6 drawn numbers.
Apply hypergeometric distribution:
a=number of correctly chosen numbers = 4
A=number of correct (drawn) numbers = 6
b=number of incorrectly chosen numbers = 2
B=number of undrawn numbers = 44-6 = 38
Then by the hypergeometric distribution
P(a,b,A,B)
=C(A,a)C(B,b)/C(A+B,a+b) [C(n,r)=combination of r objects taken out of n]
=C(6,4)C(38,2)/C(44,6)
=15*703/7059052
= 10545/7059052
= 0.001494 (to the nearest millionth)
Answer: probability of winning third prize is 10545/7059052=0.001494
