Find a logic statement involving p and q that generates each of the following truth tables .

$$\left[\begin{array}{lll} p & q & ?\\ \hline T & T & T\\ T & F & F\\ F & T & T\\ F & F & T \end{array}\right]$$

$$10 \times \$ 3.65$$

Write the number in scientific notation and perform the operations. Give an answer in scientific notation and in standard notation.

$$\frac { 0.00000128 } { 0.0004 }$$

A dock is 6 feet above water. Suppose you stand on the edge of the dock and pull a rope attached to a boat at the constant rate of 2 ft/s. Assume that the boat remains at water level. At what speed is the boat approaching the dock when it is 20 feet from the dock? 10 feet from the dock? Isn’t it surprising that the boat’s speed is not constant?

The ratio of the corresponding linear measures of two similar solids is 3:5. The volume of the smaller solid is 108 cubic inches. Describe and correct the error in finding the volume of the larger solid.

$$\begin{array} { l } { \frac { 108 } { V } = \left( \frac { 3 } { 5 } \right) ^ { 2 } } \\ { \frac { 108 } { V } = \frac { 9 } { 25 } } \\ { 300 = V } \end{array}$$

The volume of the larger solid is 300 cubic inches.

Use $\frac{22}{7}$ for $\pi$ to approximate each circumference. $d=\frac{49}{2} \mathrm{in.}$

A rigid, insulated tank having a volume of $50 \: ft^3$ initially contains a two-phase liquid–vapor mixture of ammonia at $100^{\circ}F$ and a quality of 1.9%. Saturated vapor is slowly withdrawn from the tank until a two-phase liquid–vapor mixture at $80^{\circ}F$ remains. Determine the mass of ammonia in the tank initially and finally, each in lb.

Choose the word or phrase that best answers the question. What is the name for the smallest blood vessels? A. arteries, B. capillaries, C. atria, D. veins

The handicap differential (HCD) for a round of golf is calculated from the formula: $$ H C D = \frac { ( \text {Score} - \text {Course Rating } ) } { \text {Course Slope} } \times 113 $$ The course rating and the slope are measures of how difficult a particular course is. A golfers handicap is calculated from a certain number N of their best (lowest) handicap scores according to the following table. $$ \begin{matrix} \text{# Rounds played} & \text{N} & \text{# Rounds played} & \text{N}\\ \text{5-6} & \text{1} & \text{15-16} & \text{6}\\ \text{7-8} & \text{2} & \text{17} & \text{7}\\ \text{9-10} & \text{3} & \text{18} & \text{8}\\ \text{11-12} & \text{4} & \text{19} & \text{9}\\ \text{13-14} & \text{5} & \text{20} & \text{10}\\ \end{matrix} $$ For example, if 13 rounds have been played, only the best five handicaps are used. A handicap cannot be computed for fewer than five rounds. If more than 20 rounds have been played, only the 20 most recent results are used. Once the lowest N handicap differentials have been identified, they are averaged and then rounded down to the nearest tenth. The result is the player's handicap. Write a program in a script file that calculates a person's handicap. The program asks the user to enter the golfers record in a three columns matrix where the first column is the course rating, the second is the course slope, and the third is the player's score. Each row corresponds to one round. The program displays the person's handicap. Execute the program for players with the following records. $$ (a) $$ $$ \begin{matrix} \text{Rating} & \text{Slope} & \text{Score}\\ \text{71.6} & \text{122} & \text{85}\\ \text{72.8} & \text{118} & \text{87}\\ \text{69.7} & \text{103} & \text{83}\\ \text{70.3} & \text{115} & \text{81}\\ \text{70.9} & \text{116} & \text{79}\\ \text{72.3} & \text{117} & \text{91}\\ \text{71.6} & \text{122} & \text{89}\\ \text{70.3} & \text{115} & \text{83}\\ \text{72.8} & \text{118} & \text{92}\\ \text{70.9} & \text{109} & \text{80}\\ \text{73.1} & \text{132} & \text{94}\\ \text{68.2} & \text{115} & \text{78}\\ \text{74.2} & \text{135} & \text{103}\\ \text{71.9} & \text{121} & \text{84}\\ \end{matrix} $$ $$ (b) $$ $$ \begin{matrix} \text{Rating} & \text{Slope} & \text{Score}\\ \text{72.2} & \text{119} & \text{71}\\ \text{71.6} & \text{122} & \text{73}\\ \text{74.0} & \text{139} & \text{78}\\ \text{68.2} & \text{125} & \text{69}\\ \text{70.2} & \text{130} & \text{74}\\ \text{69.6} & \text{109} & \text{69}\\ \text{66.6} & \text{111} & \text{74}\\ \end{matrix} $$

Complete parts a-c for each quadratic equation. a. Find the value of the discriminant. b. Describe the number and type of roots. c. Find the exact solutions by using the Quadratic Formula.

$$3x^2-3x+8=0$$

(a) Find constant ${4 \times 1}$ vectors ${a}$ and ${b}$ such that the solution of the initial value problem

$$\begin{gather*} x' = \left(\begin{array}{cccc}-2 & -1 & 4 & 2 \\ -19 & -6 & 6 & 16 \\ -9 & -1 & 1 & 6 \\ -5 & -3 & 6 & 5\end{array}\right) \ x, \,\,\, x(0) = x_{0} \in S, \end{gather*}$$

is a closed curve lying entirely in ${S}$, where

$$\begin{gather*} S = {u : u = a_{1}a + a{2}b, -\infty < a_{1}, a_{2} < \infty}. \end{gather*}$$

Describe the long-time behavior of any solutions for which ${x_{0} \notin S}$.

List ten non-native and five native human food sources produced in Canada.

Assume that a, b, and c are integers and $a \neq 0$. a. Prove that the solution of the linear equation ax - b = c must be a rational number. b. Describe the values of a, b, and c for which the solutions of ax^2 + b = c are rational.

Compare two methods of plant propagation used by humans.