Answer:
A, B and D are true.
Step-by-step explanation:
g (x) = x² - 4x + 3
f (x) = x² - 4x
What this means is that;
g (x) = f (x) + 3
What this implies is that the graph of g (x) is equivalent to when we shift that of f function graph up by 3 units.
Since g (x) is essentially shifting of f (x) upwards by 3 units, it means the graphs will never intersect.
It also implies that the vertex of g (x) will be above that of f (x)
Also since it only moves up and not in any other direction, both functions will still have the same line of symmetry.
Thus, options A, B and D are correct
Quick answer Sin(570) = - 1/2
Comment
570 as an angle contains 1 complete revolution of the terminal arm. The terminal arm begins at the origin and the other (in this case swings around until it records 570° turning around the x axis in an anticlockwise direction.
Anticlockwise means going from 12 o'clock to 9 o'clock to 6 o'clock then 3 o'clock and back to 12 o'clock.
What is 570° (∅) degrees equivalent to?
We keep on subtracting 360 until we get a number between 0 and 360 inclusive.
Written this way 0 ≤∅≤360
570 - 360 = 210°
So we need to find the equivalent of 210°
Method
210° = 180° + 30°
This means that ∅ is 30° below the x axis in the 3rd quadrant.
Sin(30) = 1/2
In the third quadrant, the sine is minus. so
sin(210°) = - 1/2 <<<<<<< Answer
Answer:
a)
H - H - H
H - H - T
H - T - H
H - T - T
T - H - H
T - H - T
T - T - H
T - T - T
b)
0.125 = 12.5% probability that all three coins come up heads.
0.875 = 87.5% probability that there will be at least one tail.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Question a:
Considering H for heads, T for tails:
H - H - H
H - H - T
H - T - H
H - T - T
T - H - H
T - H - T
T - T - H
T - T - T
(b) What is the probability that all three coins come up heads?
One outcome(H - H - H) out of 8, so:
0.125 = 12.5% probability that all three coins come up heads.
Notice that the complement of the event "3 heads" is "at least one tail." Use this information to compute the probability that there will be at least one tail.
Sum of these probabilities is 100%, so:
1 - 0.125 = 0.875
0.875 = 87.5% probability that there will be at least one tail.