For the answer to the question above the probability of exactly x successes is
P(X=x)=b(x;n,p) = (nCx)(p^x)((1-p)^(n-x))
where nCx is number of combinations of n things taken x at a time, and "^" means exponentiation.
n = 10
p = 0.2
P(X=7) = 10C7*(0.2^7)*(0.8^3) = 0.00079
P(X=8) = 10C8*(0.2^8)*(0.8^2) = 0.00007
P(X=9) = 10C9*(0.2^9)*(0.8^1) = 0.00000
P(X=10) = 10C10*(0.2^10)*(0.8^0) = 0.00000
.00079 + .00007 + 0 + 0 = .00086 = .0009 rounded
Answer: The correct option is,
C. x + 12 ≤ 2(x − 3)
Step-by-step explanation:
Given inequalities,
x + 12 ≤ 5 − y and 5 − y ≤ 2(x − 3)
Let a = x + 12, b = 5 - y and c = 2(x-3)
Here, a ≤ b and b ≤ c
Since, by using the transitive property of inequality,
⇒ a ≤ c
⇒ x + 12 ≤ 2(x − 3)
Therefore, OPTION C is correct.
<u>Answer-</u>
<em>End behavior for increasing x represents that </em><em>the height of each bounce will approach 0.</em>
<u>Solution-</u>
From the graph the exponential equation is,

From the properties of negative exponential function properties, as x increases, the value of y decreases.
So, in this case, as x or number of bounce increases, y or the height of bounce decreases. And eventually the value becomes zero.
Therefore, end behavior for increasing x represents that the height of each bounce will approach 0.