Answer:
Step-by-step explanation:
From the given information:
a.
Compute 
:
b.
Compute P(A ∩ B)
P(A ∩ B) = P(A) +P(B) - P(A∪B)
P(A ∩ B) = 0.32 + 0.46 - 0.57
P(A ∩ B) = 0.21
Thus, since P(A ∩ B) ≠ 0, we can say that they are not mutually exclusive.
c.
P(A ∩ C) = P(A) +P(C) - P(A∪C)
P(A ∩ C) = 0.32 + 0.23 -0.55
P(A ∩ C) = 0
Thus, since P(A ∩ C) = 0, we can say that they are both mutually exclusive.
d. To determine P[(A ∪ B ∪ C)′]
i.e. none of the events occurring
Then :
P(B ∩ C) = 0.46 +0.23 -0.49
P(B ∩ C) = 0.20
Therefore:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B ) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
P(A ∪ B ∪ C) = 0.32 + 0.46 + 0.23 - 0.21 - 0 - 0.20 + 0
P(A ∪ B ∪ C) = 0.60
Exactly right down to the last step, but some errors in combining terms.
(6m^5 + 3 – m^3 – 4m) – (–m^5 + 2m^3 – 4m + 6)
= (6m^5 + 3 – m^3 – 4m) + (m^5 – 2m^3 + 4m – 6)
= 6m^5 + 3 + (–m^3) + (–4m) + m^5 + (–2m^3) + 4m + (–6)
= [6m^5 + m^5] + [3 + (–6)] + [(–m^3) + (–2m^3)] + [(–4m) + 4m]
= (6+1)m^5 +(-1-2)m^3 +(-4+4)m +(3-6)
= 7m^5 – 3m^3 – 3
Answer: 343 in³
Explanation: In this problem, we're asked to find the volume of a cube.
It's important to understand that a cube is a type of rectangular prism and the formula for the volume of a rectangular prism is shown below.
<em>Volume = length × width × height</em>
In a cube however, the length, width, and height are all the same. So we can use the formula side × side × side instead.
So the formula for the volume of a cube is side × side × side or s³.
So to find the volume of the given cube, since each side has a length of 7 inches, we can plug this information into the formula to get (7 in.)³ or (7 in.)(7 in.)(7 in).
7 x 7 is 49 and 49 x 7 is 343.
So we have 343 in³.
So the volume of the given cube is 343 in³.
C; a percent is out of 100. All you have to do is change the denominator into 100. Since 5x20=100, you have to multiply 3/5 top and bottom by 20. Your product should be 60.
Answer:
Perpendicular.
Step-by-step explanation:
For parallel lines slopes are equal.
The slope of y = x + 3 is 1 and the slope of y = -x - 5 is -1 so they are not parallel.
For perpendicular lines m1*m2 = -1 (where m1 and m2 are the slopes).
So these 2 lines are perpendicular.
