How many halves are in the following<br> 12, 10, 13, 15,8 and 5

charle [14.2K]

Answer:

A'(4, -4)
B'(0, -3)
C'(2, -1)
D'(3, -2)

Step-by-step explanation:

The coordinate transformation for a 270° clockwise rotation is the same as for a 90° counterclockwise rotation:

(x, y) ⇒ (-y, x)

The rotated points are ...

A(-4, -4) ⇒ A'(4, -4)

B(-3, 0) ⇒ B'(0, -3)

C(-1, -2) ⇒ C'(2, -1)

D(-2, -3) ⇒ D'(3, -2)

_____

<em>Additional comment</em>

To derive and/or remember these transformations, it might be useful to consider where a point came from when it ends up on the x- or y-axis.

A point must have come from the -y axis if rotating it 270° CW makes it end up on the +x-axis. A point must have come from the x-axis if rotating it 270° makes it end up on the +y axis. That is why we write ...

(x, y) ⇒ (-y, x) . . . . . . the new x came from -y; the new y came from x

4 0

2 years ago

The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of

Karo-lina-s [1.5K]

Answer:

a) $P(\bar X$

b) $P(98$

c) $P(\bar X$

d) $P(93$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(99.9,30)$

Where $\mu=99.9$ and $\sigma=30$

We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:

$\bar X \sim N(\mu =99.9 , \frac{\sigma}{\sqrt{n}}= \frac{30}{\sqrt{38}}=4.87)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X$

$=P(Z$

Part b

For this case we want this probability:

$P(98$

$=P(\frac{98-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-0.39$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.39$

Part c

If we apply this formula to our probability we got this:

$P(\bar X$

Part d

For this case we want this probability:

$P(93$

$=P(\frac{93-99.9}{\frac{30}{\sqrt{38}}}$

And we can find this probability on this way:

$P(-1.42$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-1.42$

3 0

3 years ago

Pls help me what is the equation for this graph pls get it right :)

rewona [7]

Answer: Y= 1/8x -2

Step-by-step explanation:

Y = mx+ b

Slope = y2-y1/x2-x1 = -1+2 / 8-0 = 1/8

Initial Y-Value = -2

5 0

2 years ago

Read 2 more answers

In every bar graph , line graph , or scatter plot , the vertical axis should include the following

alexgriva [62]

It should include zero

8 0

3 years ago

Segment PH is graphed on the coordinate grid where P is (-31,8) and H is (29,-10). Point E is the midpoint of segment PH. If poi

maks197457 [2]

Answer:

The coordinates of point A are (-11 , 2)

Step-by-step explanation:

- The coordinates of point P are (-31 , 8)

- The coordinates of point H are (29 , -10)

- Point E is the mid-point of segment PH

- The coordinates of the the mid-point are:

→ $x=\frac{x_{1}+x_{2}}{2}$ and $y=\frac{y_{1}+y_{2}}{2}$

∵ E is the mid-point of segment PH

∴ The x-coordinate of point E is $x=\frac{-31+29}{2}=-1$

∴ The x-coordinate of point E is -1

∴ The y-coordinate of point E is $y=\frac{8+-10}{2}=-1$

∴ The y-coordinate of point E is -1

∴ The coordinates of point E are (-1 , -1)

- Point A is graphed $\frac{2}{3}$ of the way along the segment from P to E

- That mean the distances from points P to A is 2 parts and from P to E

is 3 parts, then the distance from A to E is "3 - 2" = 1 part

- So point A divides the line segment PE at ratio 2 : 1 from P

- The coordinates of the division point are:

→ $x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and $y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

∵ Point A divides PE at ratio 2 : 1

∵ The coordinates of point P are (-31 , 8)

∵ The coordinates of point E are (-1 , -1)

∴ The x-coordinate of point A is $x=\frac{(-31)(1)+(-1)(2)}{2+1}= -11$

∴ The x-coordinate of point A is -11

∴ The y-coordinate of point A is $x=\frac{(8)(1)+(-1)(2)}{2+1}=2$

∴ The y-coordinate of point A is 2

∴ The coordinates of point A are (-11 , 2)

* The coordinates of point A are (-11 , 2)

3 0

2 years ago

How many halves are in the following 12, 10, 13, 15,8 and 5