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Dmitry_Shevchenko [17]
3 years ago
6

A polynomial has x-intercepts of 3, 0, and –1, and passes through the point (1, –8). Which of the following functions could repr

esent this graph? 1. x3 – 2x2 – 3x 2. x2 – 2x – 3 3. 2x2 – 4x – 6 4. 2x3 – 4x2 – 6x
Mathematics
1 answer:
Brilliant_brown [7]3 years ago
3 0

Answer:

option 4

Step-by-step explanation:

Given the x- intercepts say x = a, x = b, x - c then the corresponding factors are

(x - a), (x - b), (x - c) and the polynomial is the product of the factors

Here the x- intercepts are x = 3, x = 0, x = - 1, thus the factors are

(x - 3), (x - 0), (x - (- 1) , that is

(x - 3), x and (x + 1) , then

y = ax(x - 3)(x + 1) ← where a is a multiplier

To find a substitute (1, - 8) into the equation

- 8 = a(1 - 3)(1 + 1) = - 4a ( divide both sides by - 4 )

a = 2, thus

y = 2x(x - 3)(x + 1) ← expand factors using FOIL

   = 2x(x² - 2x - 3) ← distribute by 2x

    = 2x³ - 4x² - 6x

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Use long multiplication to evaluate.

225000000


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Step-by-step explanation:

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It is known that 25% of inhabitants of a community favour a political party A.
Keith_Richards [23]

Answer:

i) P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669

ii) P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317

P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211

P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669

And replacing we got:

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iii) P(X

Step-by-step explanation:

Let X the random variable of interest "number of inhabitants of a community favour a political party', on this case we now that:

X \sim Binom(n=20, p=0.25)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part i

We want this probability:

P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669

Part ii

We want this probability:

P(X\geq 3)

And we can use the complement rule and we have:

P(X\geq 3) = 1-P(X

And if we find the individual probabilites we got:

P(X=0)=(20C0)(0.25)^0 (1-0.25)^{20-0}=0.00317

P(X=1)=(20C1)(0.25)^1 (1-0.25)^{20-1}=0.0211

P(X=2)=(20C2)(0.25)^2 (1-0.25)^{20-2}=0.0669

And replacing we got:

P(X \geq 3) = 1- [0.00317+0.0211+0.0669]= 0.90883

Part iii

We want this probability:

P(X

And replacing we got:

P(X

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Answer:

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Step-by-step explanation:

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