Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the for
m d(x) times •Q(x)plus+R(x).
P(x=x^3 + 2x^2 - 11 x + 471
d(x)=x+9
P(x)=(x+9) (blank) + blank
P(x=x^3 + 2x^2 - 11 x + 471
d(x)=x+9
P(x)=(x+9) (blank) + blank
1 answer:
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Answer:
see explanation
Step-by-step explanation:
To find the y-intercept let x = 0, in the equation
6x - 3y = 15 → (1)
x = 0 : - 3y = 15 ⇒ y = - 5 ⇒ (0, - 5) ← y- intercept
x + 3y = - 8 → (2)
x = 0 : 3y = - 8 ⇒ y = - ⇒ (0, -
) ← y- intercept
Answer:
(a)
(b)
(c)
Step-by-step explanation:
Given
i.e. between 4 and 9
Solving (a): Probability that each of the 5 digit are different
Since there is no restriction;
The total possible selection is as follows:
(i.e. any of the 4 start digits)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
(i.e. any of the 10 digits 0 - 9)
So, the total is:
For selection that all digits are different, the selection is:
(i.e. any of the 4 start digits)
(i.e. any of the remaining 9)
(i.e. any of the remaining 8)
(i.e. any of the remaining 7)
(i.e. any of the remaining 6)
So:
So, the probability is:
Solving (b): At least 1 repeated digit
The probability calculated in (a) is the all digits are different i.e. P(None)
So, using laws of complement
We have:
So, we have:
Solving (c): An expression to model the probability.
<em>Using (a) as a point of reference, we have;</em>
Where
---- for selection of 5 i.e. n = 5
This can be rewritten as:
4 can be expressed as: 5 - 1
So, we have:
Substitute n for 5
This can be rewritten as:
So, the expression is:
<em>Where n represents the digit number</em>