# Various questions

Not exactly homework, but I still need help with them... I'm translating, so bare with me.

1
A biologist needs a mix of substances that consists of 23g of proteins, 6.2g of fat and 16g fluids. He has three substances of the following composition:

Code:
                  protein (%) fat (%) fluids (%)
substance 1      20           2         15
substance 2      10           6         10
substance 3      15           5         5
How much of substance 1 does the biologist have to use in a mix with the other 2 substances to obtain the mix asked for?

2
If $$x^4 + 4x^3 + 6px^2 + 4qx + r$$ can be divided by $$x^3 + 3x^2 + 9x + 3$$, then what is $$p (q+r)$$ ?

3
What value does x have in the equation $$2 cos^2 (3x + 30°) = 1$$ ?

I think it's 155, but I got that through hit and miss. Also, can't use my calculator.

4
In a study of ABO blood groups 6000 people have been tested. 1846 of them didn't have antigen A, nor antigen B. 2527 were positive for antigen A. 2234 were positive for antigen B. What percentage was found positive for both antigens?

5
What's the value of $$\int_{0}^{e-1} \frac{x-1}{x+1} dx$$ ?

Possible answers are e-5, e-3, e-1, 0.

6
True or false?
-The equation $$y^2 - 6y + 1 = 4x$$ is a parabole with maximum (-2,3)
-The equation $$y^2 + x^2 - 6y - 4x + 4 = 0$$ is a cirkel with radius 2.

7
At a certain production of CO2 in the human body, the arterial partial pressure of CO2 (pCO2) is in inverse relationship with alveolar ventilation. If the alveolar ventilation increases from 5 to 6.25 liters a minute, how much will pCO2 decrease (%) ?

Thanks a lot!

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