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3 years ago

Enter the correct answer in the box. Factor the expression x^2+ 4x - 12

Mathematics

1 answer:

kakasveta [241]3 years ago

7 0

Answer:

The answer to your question is: ( x + 6 ) ( x - 2 )

Step-by-step explanation:

Factor x² + 4x - 12 = 0

Find two numbers that added gives +4 and if we multiply them get -12

We can find these numbers by decomposing -12 in its prime factors

12 2

6 2 12 = 2 x 2 x 3

3 3 now combine the numbers to get -12 and + 4

1 2 and 2 x 3 = 6

and 2 x 6 = 12

Then

( x + 6 ) ( x - 2 )

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Step-by-step explanation:

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A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selec

VMariaS [17]

Answer:

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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".

$\bar X=19.1$ represent the sample mean

$\mu$ population mean (variable of interest)

s=1.5 represent the sample standard deviation

n=9 represent the sample size

Solution to the problem

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:

$df=n-1=9-1=8$

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,8)".And we see that $t_{\alpha/2}=$

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

$19.1-3.355\frac{1.5}{\sqrt{9}}=17.42$

$19.1+3.355\frac{1.5}{\sqrt{9}}=20.78$

And the best option would be:

C. [17.42,20.78]

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3 years ago

Find the equation of a line that is parallel to y = 2x + 3 and passes through (-1, -1).

drek231 [11]

Answer:

y = 2x +1

Step-by-step explanation:

The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:

y = 2x + b

-1 = 2(-1) +b . . . substitute for x and y

2 -1 = b . . . . . . add 2

1 = b

So the equation for the parallel line is ...

y = 2x + 1