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2 years ago

What does the r value (correlation coefficient) represent

Mathematics

1 answer:

Ganezh [65]2 years ago

7 0

Answer:

That is the relationship of data, If it is close to 1 they are closely related if its closer to 0 there is almost no relationship, If it is negative, there is a downward slope if it is itll have an upward slope

Step-by-step explanation:

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Write in expanded form <br> 1) 531.029

Paraphin [41]

Answer:

expanded for everything

Step-by-step explanation:

Expanded Form of 531.029:

531.029 = (5 * 102) + (3 * 101) + (1 * 100) + (2 * 1/102) + (9 * 1/103)

531.029 = (5 * 100) + (3 * 10) + (1 * 1) + (2 * 1/100) + (9 * 1/1,000)

531.029 = 500 + 30 + 1 + 2/100 + 9/1,000

531.029 = 500 + 30 + 1 + 0.02 + 0.009

4 0

2 years ago

Solve for x. 2/x+2 + 1/5 = 6/x+5

olganol [36]

Answer:

Exact Form:

x=−107

Decimal Form:

x=−1.428571

Mixed Number Form:

x=−137

Step-by-step explanation:

5 0

2 years ago

How do I find the integral<br> ∫10(x−1)(x2+9)dxint10/((x-1)(x^2+9))dx ?

defon

$\int\frac{10}{(x-1)(x^2+9)}\ dx=(*)\\\\\frac{10}{(x-1)(x^2+9)}=\frac{A}{x-1}+\frac{Bx+C}{x^2+9}=\frac{A(x^2+9)+(Bx+C)(x-1)}{(x-1)(x^2+9)}\\\\=\frac{Ax^2+9A+Bx^2-Bx+Cx-C}{(x-1)(x^2+9)}=\frac{(A+B)x^2+(-B+C)x+(9A-C)}{(x-1)(x^2+9)}\\\Updownarrow\\10=(A+B)x^2+(-B+C)x+(9A-C)\\\Updownarrow\\A+B=0\ and\ -B+C=0\ and\ 9A-C=10\\A=-B\ and\ C=B\to9(-B)-B=10\to-10B=10\to B=-1\\A=-(-1)=1\ and\ C=-1$

$(*)=\int\left(\frac{1}{x-1}+\frac{-x-1}{x^2+9}\right)\ dx=\int\left(\frac{1}{x-1}-\frac{x+1}{x^2+9}\right)\ dx\\\\=\int\frac{1}{x-1}\ dx-\int\frac{x+1}{x^2+9}\ dx=\int\frac{1}{x-1}-\int\frac{x}{x^2+9}\ dx-\int\frac{1}{x^2+9}\ dx=(**)\\\\\#1\ \int\frac{1}{x-1}\ dx\Rightarrow\left|\begin{array}{ccc}x-1=t\\dx=dt\end{array}\right|\Rightarrow\int\frac{1}{t}\ dt=lnt+C_1=ln(x-1)+C_1$

$\#2\ \int\frac{x}{x^2+9}\ dx\Rightarrow \left|\begin{array}{ccc}x^2+9=u\\2x\ dx=du\\x\ dx=\frac{1}{2}\ du\end{array}\right|\Rightarrow\int\left(\frac{1}{2}\cdot\frac{1}{u}\right)\ du=\frac{1}{2}\int\frac{1}{u}\ du\\\\\\=\frac{1}{2}ln(u)+C_2=\frac{1}{2}ln(x^2+9)+C_2$

$\#3\ \int\frac{1}{x^2+9}\ dx=\int\frac{1}{x^2+3^2}\ dx=\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3\\\\therefore:\\\\\#1;\ \#2;\ \#3\Rightarrow(**)=ln(x-1)+C_1-\frac{1}{2}ln(x^2+9)+C_2-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C_3$

$\boxed{=ln(x-1)-\frac{1}{2}ln(x^2+9)-\frac{1}{3}tan^{-1}\left(\frac{x}{3}\right)+C}$

4 0

3 years ago

Simplify 27 to the negative 2 thirds power. 9 1 over 9 negative 1 over 9 −9

zimovet [89]

Answer:

The answer is 1/9 ⇒ the second answer

Step-by-step explanation:

* In the exponential functions we have some rules

(1) b^(-m) = 1/(b^m) (for all nonzero real numbers b)

- If we have negative power we reciprocal the base

to get positive power

(2) (b^m)^n = b^(mn)

- If we have power over power we multiply them

* In our problem: $(27)^{-\frac{2}{3}}$

- At first change 27 to b^n

∵ 27 = 3 × 3 × 3 = 3³

∴ $27^{-\frac{2}{3}}=(3^{3})^{-\frac{2}{3}}$

* Lets use rule (2)

∴ $27^{-\frac{2}{3}}=3^{-2}$ ⇒ 3 × -2/3 = -2

* Use rule (1)

∴ $3^{-2}=\frac{1}{3^{2}}=\frac{1}{9}$ ⇒ reciprocal the fraction to change the sig of the power

* The answer is 1/9

6 0

2 years ago

Find two positive numbers satisfying the given requirements. the product is 242 and the sum is a minimum. (smaller value) (large

Pepsi [2]

The two positive numbers satisfying the given requirements are 15.56 and 15.56

For given question,

Let x and y be two positive numbers satisfying the given requirements.

⇒ xy = 242 .............(1)

The sum of given two positive numbers is a minimum.

Let the sum of given two positive numbers is S.

⇒ x + y = S ............(2)

From equation(1),

⇒ y = 242/x

Substitute above value of y in equation (2),

⇒ x + y = S

⇒ S = x + (242 / x)

Now, for above equation we find the derivative of x with respect to x.

⇒ 0 = 1 - $\frac{242}{x^{2} }$

⇒ 242/x² = 1

⇒ x² = 242

⇒ x = ±15.56

Since the numbers are positive, x = 15.56

For x = 15.56

⇒ y = 15.56

Therefore, the two positive numbers satisfying the given requirements are 15.56 and 15.56

Learn more about the equation here:

brainly.com/question/649785

#SPJ4

8 0

1 year ago