A rectangle has a perimeter of 28 units, an area of 48 square units, and sides that are either horizontal or vertical. If one ve
rtex is the point (−5, −7) and the origin is in the interior of the rectangle, find the vertex of the rectangle that is opposite (−5, −7).
1 answer:
Answer:
Opposite coordinate of (−5, −7) = (1,1)
Step-by-step explanation:
Let the sides of rectangle be a and b
Perimeter = 2 ( a+b ) = 28
a + b = 14
Area = ab = 48
The sides with sum 14 and product 48 is 8 and 6.
a = 8 and b = 6
Since origin is inside the circle, the side with 8 unit is parallel to y axis and side with 6 unit is parallel to x axis
Opposite coordinate of (−5, −7) = (−5+6, −7+8) =(1,1)
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Answer:
The expected value of the safe bet equal $0
Step-by-step explanation:
If
is a finite numeric sample space and
for k=1, 2,..., n
is its probability distribution, then the expected value of the distribution is defined as
What is the expected value of the safe bet?
In the safe bet we have only two possible outcomes: head or tail. Woodrow wins $100 with head and “wins” $-100 with tail So the sample space of incomes in one bet is
S = {100,-100}
Since the coin is supposed to be fair,
P(X=100)=0.5
P(X=-100)=0.5
and the expected value is
E(X) = 100*0.5 - 100*0.5 = 0