The distance between the two points P (15,x)and Q(x,-5)is 20.
1 answer:
Answer:
x = - 5, x = 15
Step-by-step explanation:
Assuming you require to find the values of x
Calculate the distance PQ using the distance formula and equate to 20
d =
with (x₁, y₁ ) = P (15, x ) and (x₂, y₂ ) = Q (x, - 5 )
PQ = = 20 ( square both sides )
(- 5 - x)² + (x - 15)² = 20² ← expand factors on left side using FOIL
25 + 10x + x² + x² - 30x + 225 = 400
2x² - 20x + 250 = 400 ( subtract 400 from both sides )
2x² - 20x - 150 = 0 ( divide through by 2 )
x² - 10x - 75 = 0
consider the factors of the constant term (- 75) which sum to give the coefficient of the x- term (- 10)
the factors are - 15 and + 5 , since
- 15 × 5 = - 75 and - 15 + 5 = - 10 , then
(x - 15)(x + 5) = 0
equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 15 = 0 ⇒ x = 15
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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