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3 years ago

Solve the exponential equation:

Mathematics

1 answer:

seraphim [82]3 years ago

6 0

Step-by-step explanation:

2⁵ˣ = 8ˣ⁺²

2⁵ˣ = (2³)ˣ⁺²

2⁵ˣ = 2³ˣ⁺⁶

5x = 3x + 6

2x = 6

x = 3

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What is the equation of the best-fitting regression line? Find this in two ways. First, using the regression analysis part of th

Lemur [1.5K]

Step-by-step explanation:

Regression analysis is used to infer about the relationship between two or more variables.

The line of best fit is a straight line representing the regression equation on a scatter plot. The may pass through either some point or all points or none of the points.

Method 1:

Using regression analysis the line of best fit is: $y=\alpha +\beta x+e$

Here α = intercept, β = slope and e = error.

The formula to compute the intercept is:

$\alpha =\bar y-\beta \bar x$

Here $\bar y$ and $\bar x$ are mean of the y and x values respectively.

$\bar y=\frac{\sum y_{i}}{n} \\\bar x=\frac{\sum x_{i}}{n}$

The formula to compute the slope is:

$\beta =\frac{\sum (x-\bar x)(y - \bar y)}{\sum (x=\bar x)^{2}}$

And the formula to compute the error is:

$e=y-\alpha -\beta x$

Method 2:

The regression line can be determined using the descriptive statistics mean, standard deviation and correlation.

The equation of the line of best fit is:

$(y-\bar y)=r\frac{\sigma_{x}}{\sigma_{y}} (x-\bar x)$

Here r = correlation coefficient = $r=\frac{Cov (x,y)}{\sqrt{\sigma^{2}_{x}\sigma^{2}_{y}} }$

$\sigma_{x}$ and $\sigma_{y}$ are standard deviation of x and y respectively.

$\sigma_{x}=\frac{1}{n}\sum (x-\bar x)^{2} \\\sigma_{y}=\frac{1}{n}\sum (y-\bar y)^{2}$

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3 years ago

What is the slope of this line?

nataly862011 [7]

Answer: $-\frac{8}{5}$

Remember: RISE/RUN (y/x). Lines that are increasing have a positive slope, and lines that are decreasing have a negative slope.

You can find the slope in two ways:

1. Useful if the line is graphed: count the units between 2 points on the line.

Let's use the points (-1, 4) and (4, -4).

(-1, 4) is 8 units higher than (4, -4) and 5 units to the left of (4, -4).

Because the line is decreasing, the slope is negative.

Therefore, the slope is $-\frac{8}{5}$ .

2. Useful if the line is not graphed: find the difference between the y-coordinate values divided by the difference of the x-coordinate values.

Let's use the points (-1, 4) and (4, -4).
$\frac{-4 - 4}{4 - (-1)} = \frac{-8}{5}$

Therefore, the slope is $-\frac{8}{5}$ .

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3 years ago

Read 2 more answers

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Harman [31]

Answer:

Step-by-step explanation:

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2 years ago

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Probability theory predicts that there is 77.6% chance of a particular soccer player making 2 penalty shots in a row. If the soc

Sav [38]

P(at least 1 missed shot) = 100 - 77.6 = 22.4%

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2 years ago

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Given the function f(x) = 2x+4 and the domain: {-1,0,1},determine the range

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Answer:

f(x) = 2x + 4 domains {-1, 0, 1}

range {2, 4, 6}

(please mark brain if this helps and is correct)

Step-by-step explanation:

to solve f(x) to find the range you would want to input all the domain numbers in the equation f(x) to get the range of all the numbers you need

step 1: take the first domain number and input it into your equation where x is

ex: 2x + 4 [2(-1) + 4] = -2 + 4 = 2

step 2: add the second domain number and input it into your equation where x is

ex: 2x + 4 [2(0) + 4] = 0 + 4 = 4

step 3: add the last domain number and input it into your equation where x is

ex: 2x + 4 [2(1) + 4] = 2 + 4 = 6

Now we have determined what the range is

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2 years ago