32. A data set is normally distributed

Rationalize the numerator. <img src="https://tex.z-dn.net/?f=%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7B144x%20%7D%20%7D%7B%20%5Csq

Simora [160]

rationalizing the numerator, or namely, "getting rid of that pesky radical at the top".

we simply multiply top and bottom by a value that will take out the radicand in the numerator.

$\bf \cfrac{\sqrt[3]{144x}}{\sqrt[3]{y}}~~
\begin{cases}
144=2\cdot 2\cdot 2\cdot 2\cdot 3\cdot 3\\
\qquad 2^3\cdot 18
\end{cases}\implies \cfrac{\sqrt[3]{2^3\cdot 18x}}{\sqrt[3]{y}}\implies \cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}
\\\\\\
\cfrac{2\sqrt[3]{ 18x}}{\sqrt[3]{y}}\cdot \cfrac{\sqrt[3]{(18x)^2}}{\sqrt[3]{(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)(18x)^2}}{\sqrt[3]{(y)(18x)^2}}\implies \cfrac{2\sqrt[3]{(18x)^3}}{\sqrt[3]{18^2x^2y}}$

$\bf \cfrac{2(18x)}{\sqrt[3]{324x^2y}}~~
\begin{cases}
324=2\cdot 2\cdot 3\cdot 3\cdot 3\cdot 3\\
\qquad 12\cdot 3^3
\end{cases}\implies \cfrac{36x}{\sqrt[3]{12\cdot 3^3x^2y}}
\\\\\\
\cfrac{36x}{3\sqrt[3]{12x^2y}}\implies \cfrac{12x}{\sqrt[3]{12x^2y}}$

3 0

2 years ago

Read 2 more answers

8×6+(12-4)÷2 Options: 58, 52, 56, or 28

Virty [35]

Answer: 52

Step-by-step explanation:

8x6+(12-4)÷2

Parenthesis' first

8x6+8÷2

multiplication next

48+8÷2

Division next

48+4

52

6 0

2 years ago

How to represent 57.036 using fractions

egoroff_w [7]

$57.\underbrace{036}_{3}=\dfrac{57036}{1\underbrace{000}_{3}}=\dfrac{57036:4}{1000:4}=\dfrac{14259}{250}$

6 0

2 years ago

Determine the quadrant when the terminal side of the angle lies according to the following conditions: cos (t) < 0, csc (t) &

Bess [88]

Answer:

The angle is in the second quadrant.

Step-by-step explanation:

The cosecant of an angle is the same as the reciprocal of the sine of that angle. In other words, as long as $\sin (t) \ne 0$ ,

$\displaystyle \csc t = \frac{1}{\sin t}$ .

Therefore, $\csc(t) > 0$ is equivalent to $\sin (t) > 0$ .

Consider a unit circle centered at the origin. If the terminal side of angle $t$ intersects the unit circle at point $(x,\, y)$ , then

$\cos (t) = x$ , and
$\sin(t) = y$ .

For angle $t$ ,

$x = \cos(t) < 0$ , meaning that the intersection is to the left of the $y$ -axis.
$y = \sin(t) > 0$ , meaning that the intersection is above the $x$ -axis.

In other words, this intersection is above and to the left of the origin. That corresponds to second quadrant of the cartesian plane.

6 0

2 years ago

In the xy -coordinate plane, the coordinates of point s are (-2,-6), and coordinates of point T are (18,9). Point Q lies on line

ira [324]

Answer:

(6,0)

Step-by-step explanation:

The coordinates of the points dividing the line segment in ratio m:n can be calculated as:

$(\frac{mx_{2}+nx_{1}}{m+n} ,\frac{my_{2}+ny_{1}}{m+n} )$

Here x1, y1 are the coordinates of first point S (-2, -6) and x2, y2 are the coordinates of second point T(18, 9).

In this case m will be 2 and n will be 3 as the ratio is 2:3

Using all these values we can find the coordinates of point Q

$( \frac{2(18)+3(-2)}{2+3},\frac{2(9)+3(-6)}{2+3} )\\\\ = (\frac{30}{5} ,\frac{0}{5} )\\\\ =(6,0)$

Thus, the coordinates of point Q which divides the line segment ST in ratio of 2:3 are (6,0)

5 0

2 years ago