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adell [148]
3 years ago
9

If the discriminant of a quadratic equation is equal to -8, which statement describes the roots?

Mathematics
2 answers:
Dovator [93]3 years ago
5 0

Keywords

quadratic equation, discriminant, complex roots, real roots

we know that

The formula to calculate the <u>roots</u> of the <u>quadratic equation</u> of the form  ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}}{2a}

where

The <u>discriminant</u> of the <u>quadratic equation</u>  is equal to

b^{2}-4ac

if  (b^{2}-4ac)> 0 ----> the <u>quadratic equation</u> has two <u>real roots</u>

if  (b^{2}-4ac)=0 ----> the <u>quadratic equation</u> has one <u>real root</u>

if  (b^{2}-4ac)< 0 ----> the <u>quadratic equation</u> has two <u>complex roots</u>

in this problem we have that

the <u>discriminant</u> is equal to -8

so

the <u>quadratic equation</u> has two <u>complex roots</u>

therefore

the answer is the option A

There are two complex roots

SVETLANKA909090 [29]3 years ago
3 0
Hello there, the correct answer is:

A.
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Complete question:

The manager of a supermarket would like to determine the amount of time that customers wait in a check-out line. He randomly selects 45 customers and records the amount of time from the moment they stand in the back of a line until the moment the cashier scans their first item. He calculates the mean and standard deviation of this sample to be barx = 4.2 minutes and s = 2.0 minutes. If appropriate, find a 90% confidence interval for the true mean time (in minutes) that customers at this supermarket wait in a check-out line

Answer:

(3.699, 4.701)

Step-by-step explanation:

Given:

Sample size, n = 45

Sample mean, x' = 4.2

Standard deviation \sigma = 2.0

Required:

Find a 90% CI for true mean time

First find standard error using the formula:

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= \frac{2}{\sqrt{45}}

= \frac{2}{6.7082}

SE = 0.298

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Degrees of freedom, df = n - 1 = 45 - 1 = 44

To find t at 90% CI,df = 44:

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t_\alpha_/_2_, _d_f = t_0_._0_5_, _d_f_=_4_4 = 1.6802

Find margin of error using the formula:

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M.E = 0.298 * 1.6802

M.E = 0.500938 ≈ 0.5009

Margin of error = 0.5009

Thus, 90% CI = sample mean ± Margin of error

Lower limit = 4.2 - 0.5009 = 3.699

Upper limit = 4.2 + 0.5009 = 4.7009 ≈ 4.701

Confidence Interval = (3.699, 4.701)

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3 years ago
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Let B be the event that Andrea passes her test, and let A be the event 
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<span>So P(BlA) = P(A and B) / P(A) = (17/20) / (15/16) = (17/20)*(16/15) = 68/75.</span>
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