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2 years ago

Find the prime factorization of 108

Mathematics

1 answer:

Nimfa-mama [501]2 years ago

7 0

Answer:

2^2 * 3^3

Step-by-step explanation:

When breaking of 108 into factors, you first get 9 and 12. Then, the 9 gets split into a 3 and a 3. Meanwhile the 12 is split into a 3 and a 4. Finally the 4 is split into a 2 and a 2. So you end up with 2*2*3*3*3, which is the same as 2^2 * 3^3

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How do you write an equation in standard form given point (2,2) (0,-4)

notka56 [123]

The point-slope form:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (2, 2) and (0, -4). Substitute:

$m=\dfrac{-4-2}{0-2}=\dfrac{-6}{-2}=3\\\\y-2=3(x-2)$

The standard form:

$Ax+By=C$

$y-2=3(x-2)$ <em>use distributive property</em>

$y-2=3x-6$ <em>add 6 to both sides</em>

$y+4=3x$ <em>subtract y from both sides</em>

$4=3x-y$

<h3>Answer: 3x - y = 4</h3>

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2 years ago

Write the numbers three hundred and fifty-four thousand, two hundred and ten in figures (354,210).

GalinKa [24]

Answer:

Three hundred and fifty-four thousand, two hundred and ten =354210

Hundred thousand║Ten thousand║Thousand║Hundred║Tens║Ones

3 5 4 2 1 0

Step-by-step explanation:

6 0

1 year ago

A chemist examines 15 geological samples for potassium chloride concentration. The mean potassium chloride concentration for the

NikAS [45]

Answer:

$0.376-2.145\frac{0.0012}{\sqrt{15}}=0.375$

$0.376+2.145\frac{0.0012}{\sqrt{15}}=0.377$

And we are 95% confident that the true mean of chloride concentration is between 0.375 and 0.377 cc/ cubic meter

Step-by-step explanation:

Data provided

$\bar X=0.376$ represent the sample mean for the chloride concentration

$\mu$ population mean (variable of interest)

s=0.0012 represent the sample standard deviation

n=15 represent the sample size

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)

Since we need to find the critical value first we need to begin finding the degreed of freedom

$df=n-1=15-1=14$

The Confidence is 0.95 or 95%, the significance would be $\alpha=0.05$ and $\alpha/2 =0.025$ , and the critical value for this case with a t distribution with 14 degrees of freedom is $t_{\alpha/2}=2.145$