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Okay thanks

A loose definition of a normal distribution is when the data follows a bell curve.

The number of minutes to complete a maraton and the pareticipants age varies from person to person and could plausibly follow a bell curve.

However, the number of miles in a marathon is a fixed value, and is not normally distributed.

What is making your life meaningless???

I think it is the first one because it is closest to the pionts

I do not have all of the graphing utilities.....   Plot all of the  x,y points on the coordinat plane ....then plot each of the equations on the same plane to see which one most closely matches the plotted points.    G'luck!  Show us what you find.....

1.5 plus or minus  -0.5   =     1.5  + (-0.5) = 1      OR    1.5 - (-0.5) = 1.5 + .5 = 2        1 or 2

If the distance to the x axis is 6, then y = 6  or  -6

so the point becomes   x , 6     or   x , -6

It is 5 units to 8,3   (this rules out  y = -6) so we are working with  x,6

distance formula:

5= sqrt[ ( x-8)^2 + (6-3)^2 ]

5 = sqrt [(x-8)^2 +9 ]                        square both sides

25 = (x-8)^2 + 9

16 = (x-8)^2            which shows that   x-8 = 4 or -4     so x = 12 or 4   

Question states x<8   so that rules out x= 12    and we are left with  x = 4 

So the point becomes  x = 4 y = 6          (4,6 )

Distance formula from the origin (0,0)  =    d = sqrt [ (4-0)^2 +(6-0)^2] =  sqrt (52)       so   n = 52

There are a lot more than that, I have a hint that says it involves square roots but that's honestly all I know, I might just give up if nobody here understands it either lol (Thanks for trying though :3)

x = k y^2     and y = kz^3     where k = some constant

   we can combine the constants and sub z^3 in for y

x = k (z^3)^2 = k z^6        now sub in x = -16   and z = 2

-16 = k (2)^6

k = -1/4 

so the equation becomes   x = -1/4 z^6      NOW, sub in z = 1/2

                                           x = -1/4 (1/2)^6 = - 1/256

5 parts + 3 parts + 7 parts = 15 parts

caleb has 4 more parts than brianna and those 4 parts = 9.60

Set up a ratio

9.60/4parts = x/15 parts

15 (9.60/4) = x = total =   L  36.00 total

42 -100 = NEGATIVE 58

Why did you post this same question 6 times?

You are right!  But I'll leave it to someone else to include that!

Better method Alan, but you've still missed the 2 at the front of z.

Here's a simpler way!

.

As follows:

(Can't help feeling there's probably a simpler way!)

\(\text{You start with a configuration of 3 charges separated by a distance }s\\ \text{By symmetry each pair of charges generates the same energy and thus }\\ \text{each configuration generates }\dfrac{15}{3} = 5J\\ \text{Now we move the charge to the midpoint between two other charges}\\ \text{Our new configuration is one pair separated by distance }s\\ \text{and 2 other pairs separated by distance }\dfrac s 2\)

\(\text{The pair separated by }s \text{ generates }5J \text{ as before}\\ \text{The energy stored is inversely proportional to the distance between them}\\ \text{so halving the distance doubles the energy}\\ \text{thus we have two pairs that generate }2 \cdot 5J = 10J \text{ each}\\ \text{Totaling these up we have } E = (5+10+10) = 25J\)

Thank you. This is helpful.

Do you intend a finite width setup as pictured?

In this case the pegs at either end only deflect back towards the center.

I get 6

The period is pi

The frequency =  1 / period  =   1 / pi

g(x)=3x+5, and then f(3x+5)=1/(3x+7). h(1/(3x+7)=1/(3x+7)

Since we have the point (0, -1)   this is the y intercept ....so  c = -1

And we have this system of equations

a(-1)^2 + b(-1) - 1  =  -5

a(2)^2 + b(2) - 1 = 1

Simplifying these, we have

a - b = - 4         (1)

4a + 2b = 2   ⇒  2a + b  = 1       (2)

Add (1) and (2)   and we have that

3a = -3

a = - 1

So  a - b = -4       

-1 - b = - 4

b = 3

So.....the equation of the parabola is

y = -x^2 + 3x - 1

Here's the graph : https://www.desmos.com/calculator/pgv8twlmd1

Remember that    1 / e   =  e^(-1)

So.....

ln (1 / e)   =   ln e^(-1)    

And by  a log property.....   ln a^b   =  b * ln a

So

ln e^(-1)  =   -1 * ln  e

But ln e   =  1   .....so

(-1) * (1)  =   -1