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lapo4ka [179]
3 years ago
10

Consider the following quadratic equations.

Mathematics
1 answer:
vesna_86 [32]3 years ago
5 0

1. x² + 3x + 3 = 0     (not factorable so need to use quadratic formula)

x = \frac{-3+/-\sqrt{3^{2}-4(1)(3)}} {2(1)}

x = \frac{-3+/-\sqrt{9-12}} {2}

x = \frac{-3+/-\sqrt{-3}} {2}

x = \frac{-3+/-i\sqrt{3}} {2}

x + \frac{3+i\sqrt{3}} {2} = 0  and   x + \frac{3-i\sqrt{3}} {2} = 0

There are 2 COMPLEX ROOTS

2. x² - 2x - 3 = 0

                 ∧

                1 -3 = -2 (this equals "b" so it is factorable)

  (x - 3)(x + 1) = 0

   x - 3 = 0        x + 1 = 0

      x = 3              x = -1

There are 2 REAL ROOTS

3. x² - 6x + 9 = 0

                   ∧

                 -3 -3 = -6 (this equals "b" so it is factorable)

 (x - 3)² = 0

    x = 3, x = 3

There is 1 REAL DOUBLE ROOT

4. -x² + 3 = 0    

            3 = x²

    +/- √3 = x

There are 2 IRRATIONAL ROOTS

******************************************************************************

The quadratic expression −x²+3 has only one real factor, (x−3). FALSE

The solutions to x²−2x−3=0 are x=1 or x=−3   FALSE

The quadratic expression x²+3x+3 has two complex factors, (x + \frac{3+i\sqrt{3}}{2})(x + \frac{3-i\sqrt{3}} {2})  TRUE

The solutions to −x²+3=0 are x=3 or x=−3. FALSE

The quadratic expression x²−6x+9 has two complex factors, (x+3) and (x−3). FALSE

The solutions to x²+3x+3=0 are x = \frac{-3+i\sqrt{3}} {2} or x = \frac{-3-i\sqrt{3}} {2}  TRUE

The solution to x²−6x+9=0 is x=3 TRUE

The quadratic expression x²−2x−3 has two real factors, (x−3) and (x+1). TRUE

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0% probability that at least 1,500 will agree to respond

Step-by-step explanation:

I am going to use the binomial approximation to the normal to solve this question.

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Can be approximated to a normal distribution, using the expected value and the standard deviation.

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The standard deviation of the binomial distribution is:

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Normal probability distribution

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In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 15000, p = 0.09

So

\mu = E(X) = np = 15000*0.09 = 1350

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{15000*0.09*0.91} = 35.05

What is the probability that at least 1,500 will agree to respond

This is 1 subtracted by the pvalue of Z when X = 1500-1 = 1499. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{1499 - 1350}{35.05}

Z = 4.25

Z = 4.25 has a pvalue of 1.

1 - 1 = 0

0% probability that at least 1,500 will agree to respond

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4 years ago
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