Answer:
The answer to the question is;
The probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls is 
.
Step-by-step explanation:
The probability of success = 1/2 =
probability of failure = 1/2
Since we have 4 success we then have 9 failures and the given probability can be solved as ₁₃C₄ × 1/2ⁿ×1/2¹³⁻ⁿ
Therefore we have
₁₃C₄ × 1/2⁴×1/2⁹ = 715/8192
That is the probability that there are exactly 4 successes or exactly 4 failures in the 13 rolls = 715/8192.
Answer:
P(x) = x^4 -16x^3 +76x^2 -72x -100
Step-by-step explanation:
The two roots 1-√3 and 1+√3 give rise to the quadratic factor ...
... (x -(1-√3))(x -(1+√3)) = (x-1)^2 -(√3)^2 = x^2 -2x -2
The complex root 7-i has a conjugate that is also a root. These two roots give rise to the quadratic factor ...
... (x -(7 -i))(x -(7 +i)) = (x-7)^2 -(i)^2 = x^2 -14x +50
The product of these two quadratic factors is ...
... P(x) = (x^2 -2x -2)(x^2 -14x +50) = x^4 +x^3(-14 -2) +x^2(50 +28 -2) +x(-100+28) -100
... P(x) = x^4 -16x^3 +76x^2 -72x -100
Answer:
The roots of the equation are x = 
and x = 
and there are no real roots of the equation given above
Step-by-step explanation:
To solve:
5x² − 3x + 17 = 9
or
⇒ 5x² − 3x + 17 - 9 = 0
or
⇒ 5x² − 3x + 8 = 0
Now,
the roots of the equation in the form ax² + bx + c = 0 is given as:
x = 
in the above given equation
a = 5
b = -3
c = 8
therefore,
x = 
or
x = 
or
x = 
and x = 
or
x = and x =
here i = √(-1)
Hence,
The roots of the equation are x = and x =
and there are no real roots of the equation given above
Answer:
$244.25
Step-by-step explanation:
First, the question is asking what the change in her savings account balance is each month. So, you know that you are looking for the amount that is lost each month. When it says that at the end of the year, she has payed $2,931 , what is implied is that she has spent that much over 12 months. So all that is needed to do is divide her balance change over the year by 12 to find the monthly balance change.
