Exam 1: Review of Basic Concepts

Use these sets to find the following. Identify any disjoint sets. -Let $U = \{ 1,2,3,4,5,6,7,8,9,10,11 \} , M = \{ 1,3,5,7 \} , N = \{ 2,4,6,8,10 \} , Q = \{ 1,3,5,7,9,11 \}$ , and $R = \{ 1,2,3,4 \}$ . $Q \cap R ^ { \prime }$

Round to two decimal places unless otherwise indicated. If the average cost per unit C(x) to produce x units of plywood is given by C(x) , what is the -In the following formula, $\mathrm { y }$ is the minimum number of hours of studying required to attain a test score of $\mathrm { x } : \mathrm { y } = \frac { 0.48 \mathrm { x } } { 100.5 - \mathrm { x } }$ . How many hours of study are needed to score 91 ?

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 2 } } { 2 \sqrt { 5 } - \sqrt { 2 } }$

Factor the trinomial, if possible. - $u ^ { 2 } - 4 u v - 45 v ^ { 2 }$

Solve the problem. -The radius of a sphere is given by the formula $r = \sqrt { \frac { S } { 4 \pi } }$ , where $S$ is the surface area. If the surface area is 7614 square inches, what is the radius? Use $3.14$ for $\pi$ , and round your answer to the nearest tenth of an inch.

Tell whether the statement is true or false. - $5 \in \{ - 1,6,7,10 \}$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } + n ^ { - 1 } } { ( m n ) ^ { - 1 } }$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 17 , \sqrt { 7 } , - 23,0 , \frac { 0 } { 9 } , \sqrt { 9 } \right\}$ Natural numbers

Evaluate the expression. - $\left( 9 - 4 ^ { 2 } \right) ( - 2 + \sqrt { 49 } )$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 50 } { x } }$

Solve the equation - $\frac { x ^ { 2 } - 11 x + 18 } { x - 9 }$

Insert $\in$ or $\notin$ in the blank to make the statement is true. -0 {1, 3, 0, 5, 4}

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { n ^ { - 3 / 8 } } { x ^ { - 2 / 7 } } \right) ^ { 3 } \left( \frac { x ^ { 1 / 6 } } { n ^ { 1 / 5 } } \right) ^ { - 1 }$

Provide an appropriate response. -The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$ , where $\mathrm { b }$ is the length of the base, $\mathrm { a }$ is the length of the top, and $\mathrm { h }$ is the height. Try to visualize the figure if $a = b = h$ . Calculate the volume if $a = 296$ feet, $b = 296$ feet, and $h = 296$ feet.

Find the distance between two points given their coordinates. -Find the distance between points P and Q on a number line, with coordinates 3 and 10, respectively.

Evaluate the expression. - $( - 2 ) ^ { 3 } - ( - 2 ) ^ { 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 8 } { 5 } }$

Solve the problem. - $( 2 x - 9 y ) ^ { 2 }$

Factor the trinomial, if possible. - $2 x ^ { 2 } - 6 x y - 8 y ^ { 2 }$

Evaluate the expression. - $\text { Let } x = 9 , y = 8 \text {. Evaluate } | 6 x - 7 y | \text {. }$