Alan

Use the calculator on the home page here. Press 2nd, followed by atan (atan is the same as tan^-1)

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First find the mean, E(x), and standard deviation, SD(x), of x.

Then to get the mean of 2x + 5:  E(2x+5) = 2*E(x) +5

and the standard deviation of 2x + 5:  SD(2x+5) = 2*SD(x)     (Note: you don't add on the 5 for the SD)

E(x) = 0*0.2 + 1*0.3 + 2*0.4 + 3*0.1

You can crunch the numbers.

56(v - 8) = 24(v + 8)

56v - 56*8 = 24v + 24*8

56v - 24v = 24*8 + 56*8

(56 - 24)v = (24 + 56)*8

32v = 80*8

...

Don't know why some of the above numbers are blue!  A weird feature of doing this on a tablet instead of a PC I guess!

There was 20% left, so: 125*20/100 = 25 g

The LCM of 6 and 8 is 24, so express both fractions in terms of 24ths:

2/6 = 8/24

3/8 = 9/ 24

So:  8/24 + 9/24 = 17/24

I assume you are talking about a 30-60-90 degree right angled triangle.  There are an infinite number of possible side lengths!  However they will all be in the ratios 1:2:sqrt(3). (where the 2 represents the hypotenuse).

The energy required to stretch the spring away from equilibrium by distance x is given by (1/2)kx^2, so, in this case:

(1/2)k(1.25^2 - 0.75^2) = 100

k(25/16 - 9/16) = 200

k = 200 N/m.     (Since 25/16 - 9/16 = 1)

(Note that the energy is the integral of force with respect to distance here, as it becomes increasingly difficult to stretch the spring the further it is away from equilibrium).

You have to construct a best-fit straight line to the data first. Have a look at https://www.youtube.com › watch for example.