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2 years ago

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F(x)=3x 2 +24x+48f, left parenthesis, x, right parenthesis, equals, 3, x, squared, plus, 24, x, plus, 48 What is the value of th

e discriminant of fff? How many distinct real number zeros does fff have?

1 answer:

neonofarm [45]2 years ago

3 0

Answer:

The discriminant of function is 0. There one distinct real number zero of $f(x)$ (repeated roots).

Step-by-step explanation:

We are given the following function in the question:

$f(x)=3x^2 +24x+48$

We have to calculate the discriminant of the function.

Comparing to

$f(x) = ax^2+bx+c$

We get,

$a = 3\\b=24\\c = 48$

Discriminant is given by:

$D = b^2-4ac$

Putting values, we get,

$D = (24)^2-4(3)(48) = 0$

Thus, the discriminant of function is 0.

Since, the discriminant is zero, the function have repeated real roots. Thus, one distinct real number zero of $f(x)$ .

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At the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

Step-by-step explanation:

We are given that the mean gross annual incomes of certified welders are normally distributed with the mean of $20,000 and a standard deviation of $2,000.

The ship building association wishes to find out whether their welders earn more or less than $20,000 annually.

<u><em>Let </em></u> $\mu$ <u><em> = mean gross annual incomes of certified welders</em></u>

So, Null Hypothesis, $H_0$ : $\mu$ = $20,000

Alternate hypothesis, $H_A$ : $\mu \neq$ $20,000

Here, null hypothesis states that the mean income of welders is equal to $20,000.

On the other hand, alternate hypothesis states that the mean income of welders is not $20,000.

Also, the test statistics that would be used here is <u>One-sample z test</u> <u>statistics</u> as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

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Now, at the 0.10 level of significance the z table gives critical values of -1.645 and 1.645 for two-tailed test.

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Answer:

95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

Step-by-step explanation:

We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).

In the first stages of a clinical trial, it was successful for 7 out of the 14 women.

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<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

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P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%

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P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

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<u />

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= [0.238 , 0.762]

Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].

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