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Otrada [13]
2 years ago
6

the sum of three consecutive even integers is 6 subtracted from 4 times the middle number. Find the 3 numbers

Mathematics
1 answer:
anygoal [31]2 years ago
8 0

Answer:

The three consecutive even integers are 4,6,8

Step-by-step explanation:

Let the three consecutive even integers be  2x, 2x+2, 2x + 4

Middle number = 2x +2

2x + 2x+2 + 2x + 4 = 4* (2x+2) - 6

6x + 6 = 4*2x + 4*2 - 6

6x + 6 = 8x + 8 -6

6x + 6 = 8x + 2

6x - 8x = 2 -6

-2x = -4

x = -4/-2

x = 2

The three consecutive even integers are  

2x = 2*2 = 4

2x+2 = 2*2 +2 =4 + 2 = 6

2x + 4 = 2*2+4 = 4+4 = 8

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When consumers apply for credit, their credit is rated using FICO (Fair, Isaac, and Company) scores. Credit ratings are given be
Flura [38]

Answer:

a) The 99% confidence interval would be given by (589.588;731.038)

b) If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.  

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".

The data is:

661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706

Part a

Compute the sample mean and sample standard deviation.  

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}  

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

=AVERAGE(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)

On this case the average is \bar X= 660.313

=STDEV.S(661, 595, 548, 730, 791, 678, 672, 491 ,492, 583, 762 ,624 ,769, 729, 734, 706)

The sample standard deviation obtained was s=95.898

Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =16<30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. The degrees of freedom are given by:

df=n-1=16-1=15

We can find the critical values in excel using the following formulas:

"=T.INV(0.005,15)" for t_{\alpha/2}=-2.95

"=T.INV(1-0.005,15)" for t_{1-\alpha/2}=2.95

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}  

And if we find the limits we got:

660.313- 2.95\frac{95.898}{\sqrt{16}}=589.588  

[tex]660.313+ 2.95\frac{95.898}{\sqrt{16}}=731.038/tex]  

So the 99% confidence interval would be given by (589.588;731.038)

Part b

If we see the confidence interval the 620 is included on the interval we don't have enough evidence to reject the rating is 620. But since we need a score that at least 620 and our lower limit is 589.588 we cant conclude that all the clients would have a score that at least of 620.  

4 0
2 years ago
A submarine was located 200 feet below sea level. If it ascends 55 feet and then drops 87 feet, then which integer represents th
kirill [66]

Answer:

-232

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
3x - 6 + 4 = -20
V125BC [204]

Answer:

I'm not sure what all that extra stuff is supposed to mean, but the answer to the top question is: x = -6

Step-by-step explanation:

3 0
3 years ago
Where dose this number go on the number line?
dusya [7]
It would go after four as it equates to about 4.2
6 0
2 years ago
Read 2 more answers
A line’s equation is given in point-slope form:<br> y−6=(−23)(x+6)<br> This line’s slope is?
Nikolay [14]

The slope of the line is -23

<h3>How to determine the slope of the line?</h3>

The line’s equation is given in point-slope form:

y − 6 = (−23)(x + 6)

The line’s equation in point-slope is represented as:

y − y1 = m(x - x1)

Where

m represents the slope

By comparing y − y1 = m(x - x1) and y − 6 = (−23)(x + 6), we have

m = -23

Hence. the slope of the line is -23

Read more about slope at:

brainly.com/question/3493733

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6 0
1 year ago
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