Prove χ(G)χ(G)>=n for chromatic number of graph and its complement Let us denote by χ(G) the chromatic number, which is the smallest number of colours needed to colour the graph G with n vertices. Let G be the complement of G. Show that (a) χ(G)+χ(G)<=n+1 (b) χ(G)χ(G)>=n I was able to prove (a) using induction. Any hints on proving (b)?

What is the range of the function ${\displaystyle y=x^2}$?

The domain and range of $y=\sin <!--\; \; -->x$ is
A)$R,[0,\mathrm{\infty <!--\; \infty \; -->}]$
B)$R,[-<!--\; -\; -->1,1]$
C)$R,[-<!--\; -\; -->\mathrm{\infty <!--\; \infty \; -->},\mathrm{\infty <!--\; \infty \; -->}]$
D)$R,[1,\mathrm{\infty <!--\; \infty \; -->}]$

Mean of the squares of the deviations from mean is called the:
Variance
Standard deviation
Quartile deviation
Mode

How to evaluate P(10,2)?

What is the effect of wind speed on evaporation?

What is the range of a linear function?

Find the range of ${\displaystyle \frac{x^2}{1-x^2}}$

State the main limitations of statistics.

What is the range of the function y = x?

Tell whether the statement is true or false : A data always has a mode.

In most cases,_____variables are not considered to be equal unless they are exactly the same.

A local newspaper in a large city wants to assess support for the construction of a highway bypass around the central business district to reduce downtown traffic. They survey a random sample of 1152 residents and find that 543 of them support the bypass. Construct and interpret a 95% confidence interval to estimate the proportion of residents who support construction of the bypass.

$3+3x3-3+3=?$What is the right answer and how?

Define lateral displacement.