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AveGali [126]
3 years ago
13

Find the coordinates of the midpoint of the segment whose endpoints are H(5, 13) and K(7, 5). (12, 18) (9, 7) (2, 8) (6, 9)

Mathematics
1 answer:
____ [38]3 years ago
4 0

Answer: D. (6, 9)

<u>Step-by-step explanation:</u>

Midpoint is the "average" of the x's and y's:

Given: (5, 13) and (7, 5)

Midpoint: (\dfrac{5+7}{2},\dfrac{13+5}{2})

             = (\dfrac{12}{2},\dfrac{18}{2})

              = (6, 9)

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Mr. Acosta, a sociologist, is doing a study to see if there is a relationship between the age of a young adult (18 to 35 years o
Alik [6]

Answer:

There is a relationship between the age of a young adult and the type of movie preferred.

Step-by-step explanation:

In this case we need to test whether there is a significance relationship between the age of a young adult and the type of movie preferred.

The hypothesis can be defined as:

<em>H₀</em>: Age of a young adult and movie preference are independent.

<em>Hₐ</em>: Age of a young adult and movie preference are not independent.

The test statistic is given as follows:

\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}

Consider the table below.

The formula to compute the expected frequencies is:

E_{i}=\frac{\text{Row Total}\times \text{Column Total}}{\text{Total}}

The Chi-square test statistic value is:

\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}=2.6013

The significance level of the test is, <em>α</em> = 0.05.

The degrees of freedom of the test is,

df = (r - 1)(c - 1)

   = (3 - 1)(3 - 1)

   = 2 × 2

   = 4

Compute the <em>p</em>-value as follows:

<em>p</em>-value = 0.6266

*Use a Chi square table.

As the <em>p-</em>value is more than the significance level the null hypothesis was failed to be rejected.

Thus, concluding that there is a relationship between the age of a young adult (18 to 35 years old) and the type of movie preferred.

5 0
3 years ago
On a coordinate plane, a line goes through (negative 12, negative 2) and (0, negative 4). A point is at (0, 6).
mariarad [96]

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line ⇒ 1st

Step-by-step explanation:

Parallel lines have:

  • Same slopes
  • Different y-intercepts

The formula of the slope of a line which passes through points (x_{1},y_{1}) and (x_{1},y_{1}) is m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

∵ The given line passes through points (-12 , -2) and (0 , -4)

∴ x_{1} = -12 , x_{2} = 0

∴ y_{1} = -2 , y_{2} = -4

- Use the formula of the slope above to find the slope of the given line

∵ m=\frac{-4-(-2)}{0-(-12)}=\frac{-4+2}{12}=\frac{-2}{12}=\frac{-1}{6}

∴ The slope of the given line is \frac{-1}{6}

∵ The two lines are parallel

∴ Their slopes are equal

∴ The slope of the parallel line = \frac{-1}{6}

∵ The parallel line passes through point (0 , 6)

- The form of the linear equation is y = mx + b, where m is the slope

  and b is the y-intercept (y when x = 0)

∵ m = \frac{-1}{6} and b = 6

∴ The equation of the parallel line is y = \frac{-1}{6} x + 6

Let us check which point is on the line by substitute the x in the equation by the x-coordinate of each point to find y, if y is equal the y-coordinate of the point, then the point is on the line

Point (-12 , 8)

∵ x = -12 and y = 8

∵ y = \frac{-1}{6} (-12) + 6

∴ y = 2 + 6 = 8

- The value of y is equal the y-coordinate of the point

∴ Point (-12 , 8) is on the line

Point (-12 , 8) is on the line that passes through (0, 6) and is parallel to the given line

Learn more:

You can learn more about the equations of parallel lines in brainly.com/question/9527422

#LearnwithBrainly

4 0
3 years ago
Read 2 more answers
Maria is making a scale drawing of her basement, which is 12 yards long. if she let's 1/2 inch represent 1 yard how many inches
andrezito [222]

Answer:

the correct answer would be 6 inches.

Step-by-step explanation:

12*.5=6


7 0
3 years ago
Find the six trig function values of the angle 240*Show all work, do not use calculator
-BARSIC- [3]

Solution:

Given:

240^0

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

sin240^0=sin(180+60)

Using the trigonometric identity;

sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny

Hence,

\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

cos240^0=cos(180+60)

Using the trigonometric identity;

cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny

Hence,

\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\  \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\  \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

tan240^0=tan(180+60)

Using the trigonometric identity;

tan(180+x)=tan\text{ }x

Hence,

\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\  \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}

To get cosec 240 degrees:

\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\  \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}

To get sec 240 degrees:

\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\  \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\  \\ Thus, \\ sec240^0=-2 \end{gathered}

To get cot 240 degrees:

\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\  \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\  \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\  \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}

5 0
1 year ago
HELP ME NOW ASAP PLEASE
sergejj [24]

Answer:

D. There are points on the graph with the same x-coordinate but different y-coordinate.

Step-by-step explanation:

A relation is a function if and only if each element of the range, corresponding with y-axis, is associated with only one element of the domain, corresponding with x-axis. In this case, the graphed relation is not a function, since for all element of the domain, except 0, are related to two distinct elements of the range.

Hence, correct answer is D.

6 0
3 years ago
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