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3 years ago

What is the answer to this?

Mathematics

1 answer:

konstantin123 [22]3 years ago

3 0

Answer:

$\huge\boxed{-6}$

Step-by-step explanation:

Since we know the values of a, b, and c, we can substitute them into our expression and get the value.

$-2b + | -3c + a |\\\\-2(6) + |-3(-3) + -3 |$

A negative multiplied by a negative gets us a positive.

$-2(6) + |9 + -3 |$

Adding a negative is the same as subtracting a positive.

$-2(6) + |9 -3 |\\-2(6) + 6$

$-2 \cdot 6 = -12\\\\-12+6\\\\-6$

Hope this helped!

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Therefore, the sampling distribution of $\bar{x}$ is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

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Step-by-step explanation:

Let X be the number of hours a legal professional works on a typical workday. Imagine that X is normally distributed with a known standard deviation of 12.6.

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A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

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$n = 250$

The sample mean is

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Since the sample size is quite large then according to the central limit theorem, the sample mean is approximately normally distributed.

The population mean would be the same as the sample mean that is

$\mu = \bar{x} = 9 \: hours$

The sample standard deviation would be

$s = {\frac{\sigma}{\sqrt{n} }$

Where is the population standard deviation and n is the sample size.

$s = {\frac{12.6}{\sqrt{250} }$

$s = 0.7969 \: hours$

Therefore, the sampling distribution of $\bar{x}$ is normal with a mean equal to 9 hours and a standard deviation of 0.7969 hours.

The population mean confidence interval is given by

$\text {confidence interval} = \mu \pm MoE\\\\$

Where the margin of error is given by

$$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\$

Where n is the sampling size, s is the sample standard deviation and is the t-score corresponding to a 95% confidence level.

The t-score corresponding to a 95% confidence level is

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025

Degree of freedom = n - 1 = 250 - 1 = 249

From the t-table at α = 0.025 and DoF = 249

t-score = 1.9695

$MoE = t_{\alpha/2}(\frac{\sigma}{\sqrt{n} } ) \\\\MoE = 1.9695\cdot \frac{12.6}{\sqrt{250} } \\\\MoE = 1.9695\cdot 0.7969\\\\MoE = 1.569\\\\$

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The 95% interval estimate of the population mean $\mu$ is

LCL = 7.431 hours to UCL = 10.569 hours

8 0

3 years ago

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lesantik [10]

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3 years ago

I’ll give you 20 points if you help me

Nat2105 [25]

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Step-by-step explanation:

Put the argument value into the function and simplify the result.

f(g(x)) = f(x -3) = 2(x- 3) +1 = 2x -6 +1

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3 years ago