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3 years ago

If f(x)=x+7 and g(x)=1/x-13 what is the domain of (f times g)(x)

1 answer:

7 0

$(f\cdot g)(x)=f(x)\cdot g(x)\\\\\text{We have}\ f(x)=x+7\ \text{and}\ g(x)=\dfrac{1}{x-13}.\\\\\text{Substitute}\\\\(f\cdot g)(x)=(x+7)\cdot\dfrac{1}{x-13}=\dfrac{x+7}{x-13}\\\\\text{The domain:}\\\\x-13\neq0\qquad\text{add 13 to both sides}\\\\x\neq13\\\\Answer:\ \boxed{x\in\mathbb{R}-\{13\}}\to\boxed{\text{All real numbers except 13}}$

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In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that th

deff fn [24]

Answer:

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the average room price is significantly different from $108.50

Step-by-step explanation:

From the question we are told that

The sample size is n = 64

The average price is $\= x = \$ 112$

The population standard deviation is $\sigma = \$ 16$

The level of significance is $\alpha = 0.05$

The population mean is $\mu = \$ 108.5$

The null hypothesis is $H_o : \mu = 108.50$

The alternative hypothesis is $H_a : \mu \ne 108.50$

Generally the test statistics is mathematically represented as

$z = \frac{\= x - \mu }{ \frac{ \sigma}{\sqrt{n} } }$

=> $z = \frac{112 - 108.50 }{ \frac{ 16}{\sqrt{64} } }$

=> $z = 1.75$

From the z table the area under the normal curve to the left corresponding to 1.75 is

$P( Z > 1.75) = 0.040059$

Generally p-value is mathematically represented as

$p-value = 2 * P( Z > 1.75)$

=> $p-value = 2 * 0.040059$

=> $p-value = 0.08012$

From the values obtained we see that $p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is

There is no sufficient evidence to show that the average room price is significantly different from $108.50

3 0

3 years ago

4294 divided by 68

Nataly_w [17]

Answer:

1. 63.1. 2.22.5 3. 74.3 4. 56.1

8 0

3 years ago

How to estimate 96 Times 34 what is the answer

Marrrta [24]

When it says to estimate, I always think of doing it by hand to show work. So set it up like this:

x 34

So follow it out multiplying across 4*6 and 4*9 carrying over as needed to get it to look like this:

x 34

384

Do the same for the 3 to get this:

x 34

384

2880

Add 384+2880=3264

Your final answer is 3,264

6 0

3 years ago

This question is realy hard so helpp

LUCKY_DIMON [66]

Answer:

Algebrically the result can be written as -

$9 {x}^{2} + 24x + 16$

Step-by-step explanation:

Let the number be 'x'.

When multiplied by 3 , algebrically it is written as "3x".
When 4 is added to 3x , algebrically it is written as "3x + 4".
When (3x + 4) is squared completely , algebrically it is written as - ${(3x + 4)}^{2} = 9 {x}^{2} + 24x + 16$

8 0

3 years ago

What is the area of the figure below?

stepan [7]

The answer is,
= 22.5 × 2
= 90 in. squared

6 0

3 years ago

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