tone arm with 10gr mass with 15 gram weight cartridge?

what is important = Resonance frequency within 7-12Hz, mostly it would do the trick. (The RF has to fall down into a precise interval of frequencies: some say between 8 -12 Hz, but reasonably it would be better between 9 -11 Hz).

And yes the general rule is:

a moderately high or a very high compliance cartridge to a low mass arm (up to 10gr).

a moderate to low compliance one to a moderate mass tonearm (11 -20gr).

(Screws are always added to the arm mass - something between 0,5-1gr).

A cartridge having 5-10cu is considered a very low compliance cartridge, a range between 10-20cu is medium compliance, and values above 30 suggest a very high compliance.

and what about the cartridge weight to match the arm mass?

Make sure though that counterweight is ok to balance the arm.

but how do i convert cu to the values that manufactures give?
and what is the effect of the cart weight?

μm/mN=...X10-6cm/dyn=cu

effective mass of tonearm, cartridge mass and cartridge compliance, should produce the desired resonance frequency.

and at the end of the day if sound quality is good (most important) then you forgett all the formulas.

If you are using a Japanese cartridge you will have to double the value from 100hz to 10 hz!

For example: Say we have an arm of with a published Effective mass of 12 grams and a Japanese cartridge weight of 10 grams, with a compliance of 5cu/dyne/100 Hz. Effective Mass of the arm is another topic in its own right and often not published by the arm manufacturer or not published accurately. But for our example we are using a trusted arm manufacturer with good engineering design. We want to know the RF of the tonearm/cartridge combo. The first thing we have to do is to transform the compliance from 100 Hz to 10 Hz by doubling the value of 5, which will become 10. Next we will add up the different masses: 10 g (stylus) + 12 g (arm) +1 g (screws) + other things (like finger lift, in this case let us say they are zero) = total 23 g. Then we multiply 10 x 23 = 230 The square root of 230 is around 15.17. Finally: 159 ÷ 15.17 = 10.48 Hz, a value that places itself in the desired interval of 8 -12 Hz. Another quick way to check compatibility is to plot the predicted resonance using the graph below. Add the weight of cartridge and screws to the Effective Mass of the Arm (manufacturer should publish this). Look across to the Dynamic Compliance (manufacturer should publish this) and hopefully it falls somewhere in the 8-12hz zone.

Here is a calculation chart!

http://www.mh-audio.nl/Calculators/RF.html