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3 years ago

A number to the 12th power divided by the same number to the 9th power equals 125 what is the number

Mathematics

1 answer:

nadezda [96]3 years ago

7 0

If x to the 12th power is divided by x to the 9th power:

Since they share same bases, and are being divided, it would be the same as x^{12 - 9), or x^{3}

Now, simply find the cube root of 125, which is 5.

Therefore, the number (x) must be equal to 5.

Hope this helps! :)

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A hypothesis test is conducted at the .05 level of significance to test whether or not the population correlation is zero. If th

finlep [7]

Answer:

Th computed value of the test statistic is 3.597

Step-by-step explanation:

The null and the alternative hypothesis is as follows:

Null Hypothesis:

$\mathbf{H_o:}$ the population correlation coefficient is equal to zero

$\mathbf{H_a:}$ the population correlation coefficient is not equal to zero

The test statistics for Pearson correlation coefficient is thus computed as :

$t =\dfrac{r \sqrt{(n-2)}} { \sqrt{(1-(r)^2)} }$

where;

r = correlation coefficient = 0.60

n = sample size = 25

So;

$t =\dfrac{0.60 \sqrt{(25-2)}} { \sqrt{(1-(0.60)^2)} }$

$t =\dfrac{0.60 \sqrt{(23)}} { \sqrt{(1-0.36} }$

$t =\dfrac{0.60 *4.796} {0.8}$

t = 3.597

Comparing to a critical value of t (23 degrees of freedom two-tailed value) = 2.069

Decision Rule:

Since computed value of t is greater than the critical value of t; We reject the null hypothesis and accept the alternative hypothesis.

Conclusion:

We conclude that the population correlation coefficient significantly differs from 0 at 5% (0.05) level of significance.

6 0

3 years ago

3y-6=3x and y+2x=5 solve the system of linear equations by graphing PLEASE SHOW WORK

Dmitry_Shevchenko [17]

Answer:

(x, y) = (1, 3)

Step-by-step explanation:

The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.

___

If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.

3y -6 = 3x

To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.

3x -3y = -6

x/(-6/3) +y/(-6/-3) = 1

x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.

Plot the intercept points and draw a line through them.

y +2x = 5

The intercepts for this one are found by dividing by 5:

x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.

The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.

y = -2x + 5

The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).

Solution

When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.