Answer:
D is the answer
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The plus 7 at the end will shift the graph 7 units up. Replace y with f(x).
Then we have g(x) = f(x) + 7. Adding 7 to y = f(x) will increase the y value by 7.
Solution :
We have to prove that
(De-Morgan's law)
Let
then
and 
and so
and
.
Thus,
and so 
Hence,
.........(1)
Now we will show that 
Let
⇒
Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.
and 
Therefore,
and we have
.............(2)
From (1) and (2),
Hence proved.
Answer:
The dimensions of the bar are width = 4.68099 feet and length = 10.06198 feet
Step-by-step explanation:
A chocolate bar has a rectangular shape, therefore it's area is given by the following formula:
area = width*length
In this case the length is 0.7 feet longer than twice the width, therefore:
length = 2*width + 0.7
Applying the second equation on the first one and using the data from the question we have:
47.1 = width*(2*width + 0.7)
47.1 = 2*width² + 0.7*width
2*width² + 0.7*width = 47.1
width² + 0.35*width = 23.55
width = 
width = 4.68099 or width = -5.03099
Since the width can't be negative, it can only be 4.68099 feet.
length = 2*4.68099 + 0.7 = 10.06198 feet.
Let red marbles = X.
The probability is 1 out of 5, written as 1/5
1/5 in terms of red marbles is equal to the number of red marbles divided by 5x, where 5x is the total number of marbles.
1/5 = x/5x
Now you have 5x total marbles, x red and 4x blue.
Add 5 more red and the new probability is:
(x+5)/(5x+5) = 1/3
Simplify:
3x+15 = 5x+5
Now solve for x:
Subtract 3x from both sides:
15 = 2x +5
Subtract 5 from each side:
2x = 10
Divide both sides by 2:
x = 10/2
X = 5
There were originally 5 red marbles.