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Scorpion4ik [409]

3 years ago

9

Nielsen ratings are based on televisions in 50005000 households. Nielsen estimates that 12 comma 00012,000 people live in these

households. Suppose Nielsen reports that American Idol had 6565% of the TV audience. Interpret this result with a 95% confidence interval, based on a sample size of 12 comma 00012,000 people.

1 answer:

avanturin [10]3 years ago

6 0

Answer:

We are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%

Step-by-step explanation:

-From the given information, $\hat p=0.65$ .

-We calculate the confidence interval using this value at 95% confidence level:

$CI=\hat p\pm z \sqrt{\frac{\hat p(1-\hat p)}{n}}\\\\\\=0.65\pm 1.96\times \sqrt{\frac{0.65\times 0.35}{12000}}\\\\\\=0.65\pm 0.0085\\\\\\=[0.6415,0.6585]$

So, the 95% confidence interval is (0.6515,0.6585).

Hence, we are 95% confident that the true proportion of TV audience is between 65.15% and 65.85%.

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sesenic [268]

Hello! :)

$\large\boxed{\frac{-e^{\frac{3}{x}} (3 + 2x )}{x^{4}}}$

Find the derivative using the quotient rule:

$\frac{f(x)}{g(x)} = \frac{g(x) * f'(x) - f(x) * g'(x)}{(g(x))^{2}}$

In this instance:

$f(x) = e^{\frac{3}{x} }\\\\g(x) = x^{2}$

Use the following properties to find the derivative of f(x) and g(x):

$e^{u} = u' * e^{u}\\\\x^{n} = nx^{n-1}$

Use the quotient rule:

$\frac{x^{2} * (e^{\frac{3}{x}} * (-3x^{-2})) - e^{\frac{3}{x}} * 2x }{(x^{2} )^{2}}$

Simplify the numerator:

$\frac{(e^{\frac{3}{x}} * (-3)) - e^{\frac{3}{x}} * 2x }{(x^{2} )^{2}}$

Factor out $e^{\frac{3}{x}}$

$\frac{e^{\frac{3}{x}} (-3 - 2x )}{x^{4}}$

Factor out -1 from the numerator:

$\frac{-e^{\frac{3}{x}} (3 + 2x )}{x^{4}}$

And we're done! Thanks for posting the question to my 1000th answer!

7 0

3 years ago

Read 2 more answers

Evaluate the discriminant of -3x2+5-4=0

krok68 [10]

Answer:

-23

Step-by-step explanation:

A quadratic equation is given to us and we are interested in finding the discriminant of the quadratic equation . As we know that ,

If the quadratic equation is in Standard form ,

$\sf\longrightarrow ax^2+bx + c = 0$

The discriminant is ,

$\sf\longrightarrow D = b^2-4ac$

The given quadratic equation is ,

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On comparing it with the Standard form , we have ,

a = (-3)
b = 5
c = (-4)

So that ,

$\sf\longrightarrow D = (5)^2 - 4(-3)(-4)\\$

$\sf\longrightarrow D = 25 - 48\\$

$\sf\longrightarrow \bf D = -23$

Also note that if D < 0 , then the roots are complex conjugates .

<h3>Hence the discriminant is (-23).</h3>

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<em>I hope this helps you</em>

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2 years ago

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scoray [572]

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3 years ago

The difference of two numbers is 19. The larger number is three more than twice the smaller. Find the numbers.

iren [92.7K]

Let x=the larger number
y=the smaller number
If the difference of two numbers is 19,then
$x - y = 19$
If the larger number is 3 more than twice the smaller,
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subsituting
$x = 2y + 3 \: to \: x - y = 19$
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