Name the line and plane shown in the diagram

Data:

15 16 14 15 19 17

n=6 points

sum is 96

mean is 96/6 = 16

Now we look at the absolute deviations, each of which is the absolute value of a score minus the mean, basically the distance of the score to the mean .

Scores 15 16 14 15 19 17

AbsDev 1 0 2 1 3 1

The sum of the absolute deviations is 8 and there are six of them so the

Mean Absolute Deviation = 8/6 = 4/3

Answer: 2. 8/6

7 0

3 years ago

Evaluate square root of 16 minus x end root when x = 8.

My name is Ann [436]

$\sqrt{16-x}$
x=8
16-8=8
$\sqrt{8}$

Use a calculator to find the square root of 8.

7 0

3 years ago

The solution to this system of equations lies between the x-values -2 and -1.5. At which x-value are the two equations approxima

drek231 [11]

Hello,
$\left \{ {{y= \dfrac{1}{x+2} } \atop {y=x^2+2}} \right. \\\\

 \left \{ {{y= \dfrac{1}{x+2} } \atop {\dfrac{1}{x+2}=x^2+2}} \right. \\\\

 \left \{ {{y= \dfrac{1}{x+2} } \atop {x+2= \dfrac{1}{x^2+2} }} \right. \\\\

 \left \{ {{y= \dfrac{1}{x+2} } \atop {x= \dfrac{1}{x^2+2} -2}} \right. \\\\


$
x=-1.81053571 and y= 5,27803957

Download xls

3 0

3 years ago

Read 2 more answers

A dartboard has a circumference of 78.5 in.What is the diameter?

satela [25.4K]

$2 \pi r = circumference$
so,
$\frac{circumference}{2 \pi } = radius$

it equals 12.49 or 12.5 depending on rounding

I hope this helps!

4 0

4 years ago

Read 2 more answers

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

3 years ago