Answer:
They are not independent
Step-by-step explanation:
Given
E = Occurrence of 1 on first die
F = Sum of the uppermost occurrence in both die is 5
Required
Are E and F independent
First, we need to list the sample space of a roll of a die
Next, we list out the sample space of F
In (1): the sample space of E is:
So:
In (2): the sample space of F is:
So:
For E and F to be independent:
Substitute values for P(E) and P(F)
This gives:
However, the actual value of P(E and F) is 0.
This is so because and have 0 common elements:
So:
Compare and .
These values are not equal.
Hence: the two events are not independent
Answer:
A) y = (x + 3)² + 4
B) y = (x - 3)² + 2
C) y = (x - 1)² - 5
Step-by-step explanation:
2 units UP means that the vertex will be shifted from (-3 , 2) to (-3, (2 + 2) or (-3, 4)
As the y = (x + 3)² will still be zero at x = -3, we just need to change the "+ 2" to
"+ 4" to shift the curve upward by 2
y = (x + 3)² + 4
When we want to shift the curve to the right, we want the vertex to move from (-3, 2) to (3, 2)
This means that the term in parenthesis must be zero with our desired x value
(3 + C)² = 0
3 + C = 0
C = -3
y = (x - 3)² + 2
4 units right and 7 units down mean that the vertex is desired at (1, -5)
(1 + C)² = 0
C = -1
y = (x - 1)² - 5
Answer:
Theoretical probability is what that you expect to happen to you while experimental is what actually happen when you try it out.
Answer:
⅓x + y = 5⅓
or
⅓x + y = 5.3333333
or
⅓x + y = 16/3
Step-by-step explanation:
Solve for slope using rise/run
Y2 - Y1 / X2 - X1
(6) - (5) / (-2) - (1)
1 / -3
Slope: -⅓
y = -⅓x + b
solve for b using one of the points
I'll be using (1,5)
Substitute the point into the equation
5 = -⅓(1) + b
5 = -⅓ + b (add ⅓ to both sides)
+⅓ +⅓
5⅓ = b
5⅓ can also be written as 16/3 or 5.333333
The equation is now:
y = -⅓x + 5⅓
Convert to standard form by adding ⅓x to both sides
y = -⅓x + 5⅓
+⅓x +⅓x
Solution: ⅓x + y = 5⅓
