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4 years ago

Factor completely 2x2 + 28x + 96.

Mathematics

2 answers:

Evgesh-ka [11]4 years ago

4 0

Hi Kiara

2x²+28x+96

First thing you need to find the common factor

So the common factor is 2

2(x+6)(x+8)

I hope that's help:0

Why 2 is the common factor ?

Because we were looking for a number that can divide all of them at the same time without decimal, so that's why :)

Stels [109]4 years ago

4 0

Factor completely
2x^2 + 28x + 96
= 2(x^2 + 14x + 48)
= 2(x + a)(x + b)

find a,b that a+b=14, ab=48
let's try
a, b ... a+b
2,14 ... 18
4,12 ... 16
6,8 ... 14 *** found

2x^2 + 28x + 96 = 2(x + 6)(x + 8)

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Answer:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

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If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

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In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=0.475$

The sample deviation calculated $s=0.183$

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 0.5$

Alternative hypothesis: $\mu \neq 0.5$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

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We can replace in formula (1) the info given like this:

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P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=8-1=7$

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