Given P(A) = 0.072, P(B) = 0.180, and P(C) = 0.027, and that events A, B, and C are mutually exclusive,then P(A or B or C) is 0.279
<u>Solution:
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Given that probability of event A is P(A) = 0.072
Probability of event B is P(B) = 0.180
Probability of event C is P(C) = 0.027
Also event A, B and C are mutually exclusive.
Need to determine P( A or B or C )
For mutually exclusive events
P( A or B or C ) = P(A) + P(B) + P(C)
= 0.072 + 0.180 + 0.027 = 0.279
Hence probability of occurrence of event A or event B or event C , where A , B and C are mutually exclusive events is 0.279.
Answer:
x=-6 y=7
Step-by-step explanation:
8x+5y=-13; x+y=1
Isolate x and substitute
(-13-5y)/8 +y=1
Isolate y
y=7
substitute y=7
(-13-5*7)/8=-6
Answer:
B. Square
Step-by-step explanation:
When in doubt, it can help to plot the points on a graph.
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By looking at the coordinate values, you see that the first two points have the same y-coordinate (0) and the other two points have the same y-coordinate (-4). These points are on horizontal lines that are 4 units apart.
Looking at the x-coordinates, you see that one pair of points has x-coordinates 4, and the other pair has x-coordinates 8. That is, these pairs of points are on vertical lines that are 4 units apart.
Vertical and horizontal lines are at right angles to each other. That means the figure must be a rectangle or square. The lengths of the sides are all 4 units, so the figure is a square.
Answer:
a = length of the base = 2.172 m
b = width of the base = 1.357 m
c = height = 4.072 m
Step-by-step explanation:
Suppose we want to build a rectangular storage container with open top whose volume is 12 cubic meters. Assume that the cost of materials for the base is 12 dollars per square meter, and the cost of materials for the sides is 8 dollars per square meter. The height of the box is three times the width of the base. What’s the least amount of money we can spend to build such a container?
lets call a = length of the base
b = width of the base
c = height
V = a.b.c = 12
Area without the top:
Area = ab + 2bc + 2ac
Cost = 12ab + 8.2bc + 8.2ac
Cost = 12ab + 16bc + 16ac
height = 3.width
c = 3b
Cost = 12ab + 16b.3b + 16a.3b = 12ab + 48b² + 48ab = 48b² + 60ab
abc = 12 → ab.3b = 12 → 3ab² = 12 → ab² = 4 → a = 4/b²
Cost = 48b² + 60ab = 48b² + 60b.4/b² = 48b² + 240/b
C(b) = 48b² + 240/b
C'(b) = 96b - 240/b²
Minimum cost: C'(b) = 0
96b - 240/b² = 0
(96b³ - 240)/b² = 0
96b³ - 240 = 0
96b³ = 240
b³ = 240/96
b³ = 2.5
b = 1.357m
c = 3b = 3*1.357 = 4.072m
a = 4/b² = 2.172m
Answer:
A. 2x+4y=20 B. x+6y=10 C. 3x+3y=13 D. 4x+2y=20
