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4 years ago

The function g(x) = 8(4x) is reflected across the x-axis to create f(x).

Mathematics

2 answers:

Andre45 [30]4 years ago

6 0

Answer:

$f(x) = -8(4)^x$

Step-by-step explanation:

We have been given the equation of g(x) is $g(x)=8(4)^x$

When we reflect a function f(x) about the x-axis then the equation of function becomes -f(x).

Now, f(x) is created by reflecting across the function g(x) about x axis. Hence, we have

f(x) = -g(x)

$f(x) = -8(4)^x$

Thus, we can fill -8 in the blank provided.

Andrej [43]4 years ago

4 0

to reflect across the x axis , we multiply the function by negative

So the function reflected across the x axis should be

$f(x) = -8 (4)^x$

f(x) = ____-8_____ (4)^x

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Step-by-step explanation:

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2 years ago

A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained p

Studentka2010 [4]

Using the z-distribution, it is found that the needed sample sizes are:

a) 242

b) 1842

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

99% confidence level, hence $\alpha = 0.99$ , z is the value of Z that has a p-value of $\frac{1+0.99}{2} = 0.995$ , so $z = 2.575$ .

Item a:

The estimate is:

$\pi = 0.223 - 0.189 = 0.034$

The sample size is <u>n for which M = 0.03</u>, then:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 2.575\sqrt{\frac{0.034(0.966)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.034(0.966)}$

$\sqrt{n} = \frac{2.575\sqrt{0.034(0.966)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.034(0.966)}}{0.03}\right)^2$

$n = 241.97$

Rounding up, a sample of 242 is needed.

Item b:

No prior estimates, hence $\pi = 0.5$ is used.

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.03 = 2.575\sqrt{\frac{0.5(0.5)}{n}}$

$0.03\sqrt{n} = 2.575\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{2.575\sqrt{0.5(0.5)}}{0.03}$

$(\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.5(0.5)}}{0.03}\right)^2$

$n = 1841.8$

Rounding up, a sample of 1842 is needed.

For more on the z-distribution, you can check brainly.com/question/25404151

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3 years ago

Read 2 more answers

Find dy/dx for y=log (tan2x)

nekit [7.7K]

Answer:

$\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

Step-by-step explanation:

y = log (tan 2x)

Applying chain rule:

$\frac{dy}{dx} = \frac{d}{dx} (1st function) . \frac{d}{dx} (2nd function). \frac{d}{dx}(3rd function)$

$\frac{dy}{dx} = \frac{d}{dx} log(tan 2x) . \frac{d}{dx} tan2x. \frac{d}{dx} 2x$

$\frac{dy}{dx} = \frac{1}{tan2x} \times sec^{2}2x \times 2$

$\frac{dy}{dx} = \frac{2sec^{2}2x }{tan2x}$

Now since $sec^{2}x = \frac{1}{cos^{2}x } \ and\ tanx = \frac{sinx}{cosx}$

∴ $\frac{dy}{dx} = \frac{2cos2x }{sin2x cos^22x}$

∴ $\frac{dy}{dx} = \frac{2}{sin2x cos2x}$

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