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asambeis [7]
3 years ago
14

Solve 4^(x+2) = 12 for x using the change of base formula log base b of y equals log y over log b.

Mathematics
2 answers:
nalin [4]3 years ago
8 0

Answer:

x=ln(12)/ln(4)-2

Step-by-step explanation:

4^(x+2)=12

x+2=ln(12)/ln(4)

x=ln(12)/ln(4)-2

Lelu [443]3 years ago
7 0

Answer:

x \approx -0.208

Step-by-step explanation:

By applying logarithms to each side of the equation and some algebraic handling:

x+2 = \log_{4} 12

x + 2 = \frac{\log_{10} 12}{\log_{10} 4}

x = \frac{\log_{10}12}{\log_{10}4} - 2

x \approx -0.208

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Write an equation of the line that passes through the point (4, –5) with slope 2.
yan [13]
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A regression analysis between weight (y in pounds) and height (x in inches) resulted in the following least squares line: ŷ = 13
Lunna [17]

Answer:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

Step-by-step explanation:

We assume that they use least squares in order to create the regression equation

For this case we need to calculate the slope with the following formula:

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:

And the slope would be:

m=6

The means for x and y are given by:

\bar x= \frac{\sum x_i}{n}

\bar y= \frac{\sum y_i}{n}

And we can find the intercept using this:

b=\bar y -m \bar x

For this case we know that the line adjusted is:

y=6x +135

And for this case the interpretation for the slope would be that for every unit that the height in inches increase then the weight in pounds increase 6 units.

For the intercept of 135 represent the amount initial amount of weight for the scale.

3 0
3 years ago
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