<span>Answer:
The two events are independent. In the given scenario, P(M and N) =0.25
Explanation:
1) Independent events are those that do not affect each other. In this case the number that you roll does not change the flip of the coin. So, whatever number you get with the die, the probabilities of landing tail or head when tossing the coin are the same.
2) The probability of the two simultaneous events: getting an odd number and landing a tail, since they are independent, is equal to the product of the two independent events:
P(M and N) = P(M) x P (N) (only because they are independent)
3) The probability of getting and odd number is 0.5 (half of the numbers are odd and half are even => probability = 1/2)
4) The probability of the coin lands tail is 0.5 (1/2).
5) Then the joint probability is 0.5 x 0.5 = 0.25</span>
The translation is
... (x, y) ⇒ (x -3, y +6) . . . . . 3 units left, 6 units up
Then
... A(-1, 2) ⇒ A'(-1-3, 2+6) = A'(-4, 8)
... B(1, 5) ⇒ B'(1 -3, 5 +6) = B'(-2, 11)
Answer:
So x=4 and y=-5 would work.
Step-by-step explanation:
When you multiply complex conjugates, you get a real result.
Example:

I replace
with -1 since
.
is a real number (there is no imaginary part, no i).
So what is the conjugate of 4+5i?
4-5i
So x=4 and y=-5 would work.
A multiple of the complex conjugate would work as well.




This is still a real number; there is no imaginary part,no i.
Answer:
32 nd term
Step-by-step explanation:
The formula for the sequence is
n² + 1 ( that is 1 added to each square number )
Equate to 1025 and solve for n
n² + 1 = 1025 ( subtract 1 from each side )
n² = 1024 ( take the square root of both sides )
n =
= 32