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3 years ago

What is 5√28 + √63 in simplest radical form? PLEASE HELP ME!

1 answer:

8 0

$\bf 5\sqrt{28}+\sqrt{63}~~ \begin{cases} 28=2\cdot 2\cdot 7\\ \qquad 2^2\cdot 7\\ 63=3\cdot 3\cdot 7\\ \qquad 3^2\cdot 7 \end{cases}\implies 5\sqrt{2^2\cdot 7}+\sqrt{3^2\cdot 7} \\\\\\ 10\sqrt{7}+3\sqrt{7}\implies \stackrel{\textit{adding like-terms}}{13\sqrt{7}}$

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Solve for x: 3/2+1/2x=2x

kotykmax [81]

Answer:

x=1

Step-by-step explanation:

3/2+1/2x=2x

Multiply each side by 2 to get rid of the fractions

2(3/2+1/2x)=2x*2

3+x = 4x

Subtract x from each side

3+x-x = 4x-x

3 = 3x

Divide each side by 3

3/3 = 3x/3

1 =x

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3 years ago

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2 years ago

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Use the addition expression 64+(-15)+(-5) to find how much memory is left on his phone.

Lyrx [107]

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3 years ago

Consider the following random sample from a normal population: 14, 10, 13, 16, 12, 18, 15, and 11. What is the 95% confidence in

seraphim [82]

Answer:

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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".

Data: 14, 10, 13, 16, 12, 18, 15, 11

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

$\bar X=13.625$ represent the sample mean

$\mu$ population mean (variable of interest)

s=2.669 represent the sample standard deviation

n=8 represent the sample size

Calculate the confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

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

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,7)".And we see that $t_{\alpha/2}=2.365$

Now we have everything in order to replace into formula (1):

$13.625-2.365\frac{2.669}{\sqrt{8}}=11.393$

$13.625+2.365\frac{2.669}{\sqrt{8}}=15.857$

So on this case the 95% confidence interval would be given by (11.393;15.857)

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3 years ago