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3 years ago

If 8^y = 16^y+2, what is the value of y? A) -8 B) -4 C) -2 D) -1

Mathematics

1 answer:

Sonbull [250]3 years ago

5 0

For this case we have the following expression:

$8 ^ y = 16^{ y + 2}$

We know that:

$8 = 2 * 2 * 2 = 2 ^ 3\\16 = 2 * 2 * 2 * 2 = 2 ^ 4$

Rewriting the expression we have:

$2^{ 3(y)} = 2^ {4 (y + 2)}\\2^{3y} = 2^{4y + 8}$

For equality to be met we have to:

$3y = 4y + 8\\3y-4y = 8\\-y = 8\\y = -8$

ANswer:

The value of the variable "y" is -8.

Option A

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Answer:

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Step-by-step explanation:

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3 years ago

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gtnhenbr [62]

Answer:

a) $r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

b) $m=\frac{64.5}{2000}=0.03225$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

Step-by-step explanation:

Part a

The correlation coeffcient is given by this formula:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$

For our case we have this:

n=4 $\sum x = 200, \sum y = 5.37, \sum xy = 333, \sum x^2 =12000, \sum y^2 =9.3501$

$r=\frac{4(333)-(200)(5.37)}{\sqrt{[4(12000) -(200)^2][4(9.3501) -(5.37)^2]}}=0.9857$

The correlation coefficient for this case is very near to 1 so then we can ensure that we have linear correlation between the two variables

Part b

$m=\frac{S_{xy}}{S_{xx}}$

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=12000-\frac{200^2}{4}=2000$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=333-\frac{200*5.37}{4}=64.5$

And the slope would be:

$m=\frac{64.5}{2000}=0.03225$

Now we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{200}{4}=50$

$\bar y= \frac{\sum y_i}{n}=\frac{5.37}{4}=1.3425$

And we can find the intercept using this:

$b=\bar y -m \bar x=1.3425-(0.03225*50)=-0.27$

So the line would be given by:

$y=0.3225 x -0.27$

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3 years ago

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Ilia_Sergeevich [38]

Answer:

Step-by-step explanation:

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Read 2 more answers

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When you're given diameter or "d" which represents the is equal to the radius times 2. So, for example, number 8 the diameter is 26 so, the radius is 13. Use the formula for area just like in number 7 to find the area of this circle.

Make sure you pay attention to what information youre given (whether its "d", Diameter, "r" or radius. Use those two lists of steps for solving numbers 7 through 12.

For numbers 13-15: use the number (22/7) instead of 3.14 or the pi button on your calculator and do the same steps!!!!!

Let me know if you still need help after this:) happy math solving!

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