$$\begin{array} { c } { \text { Find a Hamiltonian circuit in } } \\ { \quad \operatorname { Cay } \left( \{ ( a , 0 ) , ( b , 0 ) , ( e , 1 ) \} : Q _ { 4 } \oplus Z _ { 3 } \right) } \end{array}$$

Show that a

$$3 \times 7$$

matrix A with nullity(A) = 4 must have

$$\text { colspace} ( A ) = \mathbb { R } ^ { 3 } .$$

Is

$$\text { rowspace} ( A ) = \mathbb { R } ^ { 3 } ?$$

What is the solution of the inequality

$$- 3 x + 2 \leq 14 ?$$

$$F.x \leq - 4\quad G. x \geq - 4\quad H. x \leq 4\quad I. x \geq 4$$

Name the integer that matches each letter on the number line: Q

If the parentheses are removed from

$$\left( 3 m ^ { 2 } - 5 m \right) + \left( 12 m ^ { 2 } + 7 m - 10 \right)$$

, is the new expression equivalent to the original? If the parentheses are removed from

$$\left( 3 m ^ { 2 } - 5 m \right) - \left( 12 m ^ { 2 } + 7 m - 10 \right)$$

, is the new expression equivalent to the original? Explain.

Here are coordinates for elght points in the coordinate plane (q > p > 0). A(0,0), B(p, 0), C(q, 0), D(p + q, 0), E(0, q), F(p, q), G(q, q), H(p + q, q). Which four points, if any, are the vertices for each type of figure? parallelogram

Solve the equation using the quadratic formula. If the equation has no real solution, so state. x²-6x-16=0

Identify the percent of change as an increase or a decrease. Then find the percent of change. Original : 40; New: 42

Of 26 employees at Wegmans supermarket, 15 work as cashiers and 11 stock shelves. If 3 of the 26 employees are selected at random to work over time, determine the probability that all 3 are cashiers.

The first term of an arithmetic sequence is 10, and the tenth term is 2. (a) Find the common difference and the 100th term of the sequence. (b) Find the partial sum of the first ten terms.

Describe the sample space S of the experiment and list the elements of the given event. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) A letter is chosen at random from those in the word Mozart; the letter is neither a nor m.

Light travels at a speed of approximately 186,000 miles per second. Scientists use a unit of measurement known as a light-year for expressing distances from Earth to stars and other objects far away. A light-year is the distance light can travel in one year. Determine the number of seconds in one year (365 days). Express this result in scientific notation.

Why is sound louder when a vibrating source is held to a sounding board?

Are all the significant figures reported for a measured value accurately known? Explain.