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Ratling [72]
3 years ago
15

Write a polynomial function $f$ of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.

Write the function in standard form -5,-1,2
Mathematics
1 answer:
olganol [36]3 years ago
4 0

Answer:

f(x) = x^{3} + 4x^{2} -7x^{} -10^{}

Step-by-step explanation:

The zeros of the polynomial function are given us as -5,-1,2

If the zeros of a polynomial function are α,β,ω, the polynomial function can be obtained using the expression below:

f(x) = (x - α)(x - β)(x - ω)

where α = -5, β = -1, and ω = 2

f(x)=(x-(-5) )(x -(-1))(x - 2) = (x+5)(x+1)(x-2)\\\\f(x)=(x+5)(x^{2} -2x + x -2) = (x+5)(x^{2}  -x-2)\\\\f(x)=x(x^{2}  -x-2)+5(x^{2}  -x-2)\\\\f(x)= x^{3} - x^{2} -2x + 5x^{2} - 5x - 10\\\\f(x)= x^{3} + 4x^{2} -7x - 10

<em>NB: To arrive at the answer, expand the brackets and after expansion, collect like terms to obtain the final answer</em>

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2 years ago
A sample of 500 people are asked,"If you could have a new vehicle, would you want asport utility vehicle or a car?" The result o
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The complete table would be the follwing:

A.

To get this probability, we take the total number people who pefer an SUV, and divide it by the total number of people in the sample

P(S)=\frac{210}{500}

B.

To get this probability, we take the total number of females, and divide it by the total number of people in the sample

P(F)=\frac{315}{500}

C.

To get this probability, we take the total number of females who pefer a car, and divide it by the total number of people in the sample

P(F\cap C)=\frac{263}{500}

D.

\begin{gathered} P(F\cup S)=P(F)+P(S)-P(F\cap S) \\ \rightarrow P(F\cup S)=\frac{315}{500}+\frac{210}{500}-\frac{52}{500} \\  \\ \Rightarrow P(F\cup S)=\frac{473}{500} \end{gathered}

E.

\begin{gathered} P(S|M)=\frac{P(S\cap M)}{P(S)} \\  \\ \rightarrow P(S|M)=\frac{\frac{158}{500}}{\frac{210}{500}} \\  \\ \Rightarrow P(S|M)=\frac{158}{210} \end{gathered}

F.

\begin{gathered} P(M|S)=\frac{P(M\cap S)}{P(S)} \\  \\ \rightarrow P(M|S)=\frac{\frac{158}{500}}{\frac{185}{500}} \\  \\ \Rightarrow P(M|S)=\frac{158}{185} \end{gathered}

In the final question we're being asked for:

P((M\cap S)\cap(M\cap C))

This is:

P(M\cap S)\cdot P(M\cap C)\frac{158}{500}\cdot\frac{27}{500}=0.017

Therefore, this probability is 0.017

8 0
10 months ago
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