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zhannawk [14.2K]

2 years ago

10

If g(x) = 8x^6 and f(x) = log4 (2x) then f(g(x)) = ?

1 answer:

Lena [83]2 years ago

8 0

$\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\begin{cases} g(x)=8x^6\\\\ f(x)=\log_4(2x) \end{cases}\qquad \qquad \begin{array}{llll} f(~~g(x)~~)=\log_4[~2g(x)~] \\\\\\ f(~~g(x)~~)=\log_4[~2(8x^6)~] \end{array} \\\\\\ f(~~g(x)~~)=\log_4(16x^6)\implies f(~~g(x)~~)=\log_4(4^2x^6) \\\\\\ f(~~g(x)~~)=\log_4(4^2)~~ + ~~\log_4(x^6)\implies \boxed{f(~~g(x)~~)=2~~ + ~~6\log_4(x)}$

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drug sniffing dogs must be 95% accurate in their responses because their handlers don't want them to miss durgs and also don't w

GenaCL600 [577]

Answer:

95% Confidence interval: (0.8449,0.9951)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 50

Number of times the dog is right, x = 46

$\hat{p} = \dfrac{x}{n} = \dfrac{46}{50} = 0.92$

95% Confidence interval:

$\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting the values, we get:

$0.92 \pm 1.96(\sqrt{\dfrac{0.92(1-0.92)}{50}})\\\\ = 0.92\pm 0.0751\\\\=(0.8449,0.9951)$

(0.8449,0.9951) is the required 95% confidence interval for the proportion of times the dog will be correct.

7 0

2 years ago

use the poisson distribution to find the indicated probability. if the random variable x has a poisson distribution with mean of

Hitman42 [59]

$P(X=2)=\frac{e^{-6} 6^{2}}{2}=0.045$

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3 years ago

Which of the following is true for f(x) = -2 sin(x) - 3?

Naddik [55]

Answer:

Step-by-step explanation:

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2 years ago

What is the product of 8/6 and 5/10 in simplest radical form?

Gre4nikov [31]

The answer is 8/3 but if your simplifying then the answer is 2 2/3 and if you want it in decimal form then the answer is 2.6 :)

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2 years ago

WILL GIVE BRAINLIEST What is the perimeter of the track, in meters? Use π = 3.14 and round to the nearest hundredth of a meter.

Ivenika [448]

Answer:

Perimeter = 317 m

Step-by-step explanation:

Given track is a composite figure having two semicircles and one rectangle.

Perimeter of the given track = Circumference of two semicircles + 2(length of the rectangle)

Circumference of one semicircle = πr [where 'r' = radius of the semicircle]

= 25π

= 25 × 3.14

= 78.5 m

Length of the rectangle = 80 m

Perimeter of the track = 2(78.5) + 2(80)

= 157 + 160

= 317 m

Therefore, perimeter of the track = 317 m

7 0

3 years ago