A continuous-time Markov chain with state space S nonzero transition rates q(1, 2) = g(2, 3) = q(3, 1) = q(4, 1) = 1 and q(1,4) = q(3, 2) = q(3, 4) = g(4, 3) = 2. (a) Provide (i) the transition rate graph, (ii) the holding time parameters, (iii) the generator matrix, and (iv) the transition matrix for the embedded Markov chain. (b) How long on average will the Markov chain stay in each state before moving to the next state? (c) If the chain is at state 3 and moves next to state 4, how long on average will it stay in state 3 in this case?

Find the volume V of the described solid S
A cap of a sphere with radius r and height h.
V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?
a. $f(x)=3$
b. $g(x)=5-2x$
c. ${\displaystyle h\left(x\right)=\frac{2}{x}+3}$
d. $t(x)=5(x-2)$

Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a
A)Rhombus;
B)Parallelogram;
C)Kite;
D)none of these

What is the order of the numbers from least to greatest.
${\displaystyle A=1.5\times {10}^3}$,
${\displaystyle B=1.4\times {10}^{-1}}$,
${\displaystyle C=2\times {10}^3}$,
${\displaystyle D=1.4\times {10}^{-2}}$

Write the numerical value of ${\displaystyle 1.75\times {10}^{-3}}$

Solve for y. 2y - 3 = 9
A)5;
B)4;
C)6;
D)3

How to graph ${\displaystyle y=\frac{1}{2}x-1}$?

How to graph ${\displaystyle y=2x+1}$ using a table?

simplify ${\displaystyle \sqrt{257}}$

How to find the vertex of the parabola by completing the square ${\displaystyle x^2-6x+8=y}$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.