Classify each real number as either rational or irrational.

$$1 . \overline { 23 }$$

Explain how you solve each problem. Show all your work. Mr. Shaw paid $38.86 for 11.5 gallons of gasoline. How much did he pay per gallon?

Evaluate the expression without using a calculator.

$$64 ^ { 1 / 5 }$$

Determine whether each statement is always, sometimes, or never true. Explain your reasoning. If the product of two fractions is negative, then their quotient is positive.

Determine whether the statements that follow are true or false, and justify your answer: If $A^2 = I_2$, then matrix $A$ must be either $I_2$ or $-I_2$.

solve the system by the method of elimination. {3x + 4y = -26 , 7x - 5y = 11

Simplify the expression.

$$\frac{x + 4}{x^2 + 12x + 32}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. First factoring out the greatest common factor makes it easier for me to determine how to factor the remaining factor, assuming that it is not prime.

$$\langle 1,2,0 \rangle \times \langle 3,0,4 \rangle$$

=___

In exercising, a weight lifter loses 0.150 kg of water through evaporation, the heat required to evaporate the water coming from the weight lifter's body. The work done in lifting weights is $1.40 \times 10 ^ { 5 } \mathrm { J }$

Assuming that the latent heat of vaporization of perspiration is $2.42 \times 10 ^ { 6 } \mathrm { J } / \mathrm { kg }$ find the change in the internal energy of the weight lifter.

State the amplitude, period, vertical shift, and equation of the midline for each function. Then graph the function.

$$y = \frac { 1 } { 3 } \sin \theta + 7$$

Choose the letter of the correct term or concept below to complete the sentence. a. validity b. reliability c. norms d. intelligence e. triarchic theory f. emotional intelligence g. heritability h. cultural bias i. objective j. projective. The ability of a test to yield the same result under a variety of different circumstances is its __________.

Parallelogram ABCD has vertices

$$A \left( - 2 , - 5 \frac { 1 } { 2 } \right) , B \left( - 4 , - 5 \frac { 1 } { 2 } \right)$$

, C(-3, -2), and D(-1, -2). Find the vertices of parallelogram

$$A ^ { \prime } B ^ { \prime } C D ^ { \prime }$$

after a transformation of

$$2 \frac { 1 } { 2 }$$

units down.

Write the decimal as a percent or the percent as a decimal. 0.1