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3 years ago

100 students are interviewed to see which of biology, chemistry or physics they prefer.

Mathematics

1 answer:

Anna11 [10]3 years ago

8 0

Answer: 41%

Step-by-step explanation:

15 girls prefer biology.

Find the boys who prefer biology;

There are 36 girls in total so;

= 100 - 36

= 64 boys interviewed

14 boys prefer Physics

= 64 - 14

= 50 boys prefer Biology and Chemistry

7 out of the 31 who prefer chemistry are girls so the boys who prefer chemistry are;

= 31 - 7

= 24 boys

Boys who prefer Biology;

= 50 - 24

= 26 boys

Total who prefer biology;

= 15 girls + 26 boys

= 41 students

Percentage = 41/100 = 41%

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What is the polynomial function of lowest degree with lead coefficient 1 and roots 1 and 1 + i? f(x) = x2 – 2x + 2 f(x) = x3 – x

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Answer:

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

Step-by-step explanation:

we know that

The <u><em>conjugate root theorem</em></u> states that if the complex number a + bi is a root of a polynomial P(x) in one variable with real coefficients, then the complex conjugate a - bi is also a root of that polynomial

In this problem we have that

The polynomial has roots 1 and (1+i)

by the conjugate root theorem

(1-i) is also a root of the polynomial

therefore

The lowest degree of the polynomial is 3

$f(x)=a(x-1)(x-(1+i))(x-(1-i))$

Remember that

The leading coefficient is 1

a=1

$f(x)=(x-1)(x-(1+i))(x-(1-i))\\\\f(x)=(x-1)[x^{2} -(1-i)x-(1+i)x+(1-i^2)]\\\\f(x)=(x-1)[x^{2} -x+xi-x-xi+2]\\\\f(x)=(x-1)[x^{2} -2x+2]\\\\f(x)=x^{3}-2x^{2} +2x-x^{2} +2x-2\\\\f(x)=x^{3}-3x^{2} +4x-2$