Determine whether each statement is true or false. ff the statement is false, make the necessary change(s) to produce a true statement. In using the quadratic formula to solve the quadratic equation

$$5x^2 = 2x - 7,$$

we have a = 5, b = 2, and c = -7.

Think of a student behavior that exists at your school and that a teacher or the principal might want to change. Then devise a way to change that behavior by using behavior modification techniques. Write out your plan in a short paper.

Solve the equation.

$$6 ^ { x - 2 } = 36$$

Solve each equation. $\log _{4} x=\frac{3}{2}$

Each of exercises refers to the Euler phi function denoted

$$\phi$$

, which is defined as follows: For each integer

$$n \geq 1 , \phi ( n )$$

is the number of positive integers less than or equal to n that have no common factors with n except

$$\pm 1$$

. For example,

$$\phi ( 10 ) = 4$$

because there are four positive integers less than because there are four positive integers less than

$$\pm 1$$

; namely, 1, 3, 7, and 9. Prove that there are infinitely many integers n for which

$$\phi ( n )$$

is a perfect square.

Consider the two forces acting on the person who stands still-namely, the downward pull of gravity and the upward support of the floor. Are these forces equal and opposite? Do they form an action-reaction pair? Why or why not?

A spinner is divided into 12 congruent regions, colored red, blue, and green. Landing on red is twice as likely as landing on blue. Landing on blue and landing on green are equally likely. a. What is the probability of landing on green? Show your work or explain in words how you got your answer. b. How many regions of the spinner are colored green? Explain your reasoning.

One side of a regular pentagon measures 0.8 meter. What is the perimeter of the regular pentagon?

Solve each triangle using either the Law of Sines or the Law of Cosines. $a=4, c=5, B=55^{\circ}$

A store posted a sign to entice shoppers that read: "Our prices are rising slower than anyplace else in town." Restate the sign using calculus terminology.

Solve the following differential equations by using integrating factors. $x y^{\prime}=3 y+x^{2}$

Write expressions for K and $K_P$ for the following reactions.

$$\mathrm { CuO } ( s ) + \mathrm { H } _ { 2 } ( g ) \rightleftharpoons \mathrm { Cu } ( l ) + \mathrm { H } _ { 2 } \mathrm { O } ( g )$$

If the maximum intensity of radiation for a blackbody is found at 2.65

$$\mu \mathrm { m }$$

, what is the temperature of the blackbody?

Use your book or dictionary to define each term. Spontaneous generation _____.