Answer: 1) 
2) 55 points
Step-by-step explanation:
1) A= 8w + 18, w=1.25
A = 8(1.25) + 18
A = 10 + 18
A = 28ft^2
2) 25 points to start with, additional 5 points per magazine they sell, m = number of magazines they sell
total points = 25 + 5m
How many if they sell 6?
total = 25 + 5(6)
= 25 + 30
total = 55
Divide
8/1 / 2/3
Keep change flip
8/1 x 3/2
Simplify
4/1 x 3/1
12/1
He can make 12 2/3 ounce peanuts with 8 ounces of peanuts.
Answer:
P(A)=0.55
P(A and B)=P(A∩B)=0.1265
P(A or B)=P(A∪B)=0.7635
P(A|B)=0.3721
Step-by-step explanation:
P(A')=0.45
P(A)=1-0.45=0.55
P(B∩A)=?
P(B|A)=0.23
P(B|A)=(P(A∩B))/P(A)
0.23=(P(A∩B))/0.55
P(A∩B)=0.23×0.55=0.1265
P(A∪B)=P(A)+P(B)-P(A∩B)
=0.55+0.34-0.1265
=0.7635
P(A|B)=[P(A∩B)]/P(B)=0.1265/0.34 ≈0.3721
Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.
Step-by-step explanation:
The equation of a circle in the center-radius form is:
(1)
Where
are the coordinates of the center and
is the radius.
Now, we are given the equation of this circle as follows:
(2)
And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:
(3)
Rearranging the equation:
(4)
(5)
Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of
:
<u>For the first parenthesis:</u>

We can rewrite this as:

Hence in this case
and
:

<u>For the second parenthesis:</u>

We can rewrite this as:

Hence in this case
and
:

Then, equation (5) is rewritten as follows:
(6)
<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>
Rearranging:
(7)
At this point we have the circle equation in the center radius form 
Hence:



<span>Answer:
The cylinder has equation y^2 + z^2 = 1 (with x in [0, 2]).
So, we can write the volume â«â«â« 1 dV as
â«(x = 0 to 2) â«(z = -1 to 1) â«(y = -âš(1 - z^2) to âš(1 - z^2)) 1 dy dz dx.</span>