A random experiment consists of tossing a fair coin five times and recording the number of tails. What is the sample space?
1 answer:
You might be interested in
Answer:
x = 2
Step-by-step explanation:
The relevant rule of logarithms is ...
log(a/b) = log(a) -log(b)
This lets us combine the logs on the left to get ...
log((6 +7x)/(3x -2)) = log(5)
Taking anti-logs gives ...
(6 +7x)/(3x -2) = 5
6 +7x = 5(3x -2) . . . . . multiply by (3x -2)
7x +6 = 15x -10 . . . . . eliminate parentheses
8x = 16 . . . . . . . . . . . add 10-7x to both sides
x = 2 . . . . . . . . . . . . . divide by 8
The solution is x = 2.
_____
The graph shows the left side of the equation is equal to the right side for x=2.
The coefficient of y is 8, which is 4p, so p=2. That is the distance the directrix is below the vertex. The directrix is below the vertex because the parabola opens upward.
The vertex can be found by completing the square.
x^2 +16x +64 = 8y -16 +64
(1/8)(x +8)^2 -6 = y +6
The vertex is (-8, -6), so the directrix is ...
y = -8
The vertex can be found by completing the square.
x^2 +16x +64 = 8y -16 +64
(1/8)(x +8)^2 -6 = y +6
The vertex is (-8, -6), so the directrix is ...
y = -8