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3 years ago

Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below:

1 answer:

5 0

X = -4
As g(x) is replaced by g(-4)
plug in -4 for x inside the equation.
g(-4) = (-4) - 1g(-4) = -5
Plug in -4 for x in f(x)f(-4) = 4(-4) - 4f(-4) = -16 - 4f(-4) = -20
Now solve for f(x) over g(x)
remember, f(x) = -20, and g(x) = -5
-20/-5 = 4
4 should be your answer
hope this helpsClick to let others know, how helpful is it

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A researcher wishes to be 95% confident that her estimate of the true proportion of individuals who travel overseas is within 3%

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Answer: a) 683 b) 1067

Step-by-step explanation:

The confidence interval for population proportion is given by :-

$p\pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}$

a) Given : Significance level : $\alpha=1-0.95=0.05$

Critical value : $z_{\alpha/2}}=\pm1.96$

Margin of error : $E=0.03$

Formula to calculate the sample size needed for interval estimate of population proportion :-

$n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.2(0.8)(\dfrac{1.96}{0.03})^2=682.951111111\approx683$

Hence, the required sample size would be 683 .

b) If no estimate of the sample proportion is available then the formula to calculate sample size will be :-

$n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\=0.25(\dfrac{1.96}{0.03})^2=1067.11111111\approx1067$

Hence, the required sample size would be 1067 .

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3 years ago

Elliot uses 3/8 pound of clay to make a charm for a necklace. how much clay does he use to make 4 charms?

Lapatulllka [165]

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3 years ago

Read 2 more answers

What is the inverse of this function

just olya [345]

G(x) = (25 - x)/5     First lets call g(x) by its other name - y

y = (25 - x)/5         Now switch the x and y

x = (25 - y)/5        Solve for y which is now the inverse - call this $g^{-1}(x)$

5x = 25 - y
y = 25 - 5x      this is the inverse so $g^{-1}(x)$ = 25 - 5x

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3 years ago

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mr_godi [17]

The image of the right rectangular prism is missing, so i have attached it.

Answer:

volume of the right rectangular prism = 625 in³

Step-by-step explanation:

The rectangular prism is made of equal-sized cubes. Thus, let's first find the volume of 1 cube.

Formula for volume of one cube is;

V = a³

where

a is the length of one side of the cube

We are told that this length is 2½ inches

Thus;

a = 2½ = 5/2 inches

>> V = (5/2)³

>> V = 125/8 in³

Now, in the rectangular prism attached, if we count the number of cubes we have, it is equal to 40 cubes

Therefore, the volume of the prism is;

Volume of one cube × 40

>> volume of the prism = (125/8) × 40

volume of the prism = 625 in³

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