A random variable $$X$$ has the probability distribution
| $$X=x$$ | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| $$P(X=x)$$ | 0.15 | 0.23 | 0.12 | 0.20 | 0.08 | 0.10 | 0.05 | 0.07 |
For the events $$E=\{X$$ is a prime number $$\}$$ and $$F=\{x<5\}, P(E U F)$$ is
The shaded area in the given figure is a solution set for some system of inequations. The maximum value of the function $$z=10 x+25 y$$ subject to the linear constraints given by the system is
The foot of the perpendicular from the point $$(1,2,3)$$ on the line $$\mathbf{r}=(6 \hat{\mathbf{i}}+7 \hat{\mathbf{j}}+7 \hat{\mathbf{k}})+\lambda(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$$ has the coordinates
Water is running in a hemispherical bowl of radius $$180 \mathrm{~cm}$$ at the rate of 108 cubic decimeters per minute. How fast the water level is rising when depth of the water level in the bowl is $$120 \mathrm{~cm}$$ ? (1 decimeter $$=10 \mathrm{~m}$$)