Answer:
The last graph
Step-by-step explanation:
We transform functions in the following ways:
- multiplying the function by a number to stretch or shrink it
- multiplying by a negative to flip the orientation of the function
- adding/subtracting a value to the input x to shift it horizontally
- adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.
Looking at the equation we can see 
- Vertically shrunk by 0.5
- Negative leading coefficient to flip the graph's orientation
- Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
- Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)
The last graph has vertex (-3,-2) and satisfies the the equation.
Answer:
Both of them can be simplified.
Recall that 4 = 2^2.
2^7 / 4^2 = 2^7 / (2^2)^2 = 2^7 / 2^4 = 2^(7-4) = 2^3 = 8
Similarly, 2^7 / 2^4 = 2^(7-4) = 2^3 = 8
The answers to both exercises are 8.
Answer:
yes
Step-by-step explanation:
Let’s say, hypothetically speaking, you chose the second marble without replacing the first marble so, events are hypothetically dependent. Events are dependent if the occurrence of one hypothetical event hypothetically does affect the likelihood that the other events occur. The probably of two or more dependent events A and B is the probability of A times the probability of B after A hypothetically occurs
P(A and B) = P(A) x P(B after A)
Choose the first marble
The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.
P(red)=1/4
Choose the second marble
Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.
P(green) = 1/3
The probability of choosing red and then, hypothetically, green is:
P(red and green) = P(red) x P(green)
=1/4 x 1/3
= 1/12
P(red and green) is hypothetically equal to 1/12 on a hypothetical account.
Final hypothetical answer: 1/12
