Determine whether each statement makes sense or does not make sense, and explain your reasoning. Even if I'm not sure how mathemat icians define irrational and complex numbers, telling me how these sets are related, I can construct a Venn diagram illustrating their relationship.

(This logic problem dates back to the eighth century.) A farmer needs to take his goat , wolf, and cabbage across a stream. His boat can hold him and one other passenger (the goat , wolf, or cabbage). If he takes the wolf with him , the goat will eat the cabbage. If he takes the cabbage, the wolf will eat the goat. Only when the farmer is present are the cabbage and goat safe from their respective predators. How does the farmer get everything across the stream?

For a polygon to be convex means that all of its interior angles are less than 180 degrees. Use mathematical induction to prove that for all integers

$$n \geq 3$$

, the angles of any n-sided convex polygon add up to 180(n-2) degrees.

Simplify the complex fraction.

$$\frac { \frac { 3 } { b ^ { 2 } } - \frac { 4 } { b } + 1 } { 1 - \frac { 1 } { b } - \frac { 6 } { b ^ { 2 } } }$$

Mike dove to an elevation of -40 feet, and Julio dove to an elevation of -50 feet. Mike says that because -40 is greater than -50, he dove farther than Julio. Use absolute value to explain Mike's error.

Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

$$\left. \begin{array} { l } { y = \frac { 4 } { 3 } x - 2 } \\ { 3 y - 4 x = - 6 } \end{array} \right.$$

Choose the best answer. Rhonda earns 5.5% commission when she sells a house. The amount of commission she receives from a sale is $18,700. What is the sale price of the house? A.$1028.50 B. $321,300 C.$340,000 D. $358,700

Solve each equation. 4 b-3=17

What is a prodigy?

Graph each equation in a rectangular coordinate system. If two functions are indicated, graph both in the same system. Then use your graphs to identify each relation's domain and range.

$$f ( x ) = x ^ { 2 } - 1 , x \geq 0 , \text { and } f ^ { - 1 }$$

The A locus and the D locus are so tightly linked that no recombination is ever observed between them. If Ad/ Ad is crossed with aD/aD and the

$$F_1$$

is intercrossed, what phenotypes will be seen in the

$$F_2$$

and in what proportions?

Is the number of prospective occupants an important consideration in the design of heating and cooling systems of classrooms? Explain.

What are two ways to measure the obligation for postretirement benefits other than pensions? Define these measurement approaches.

The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select passengers for an extra security check prior to boarding. One such flight had 76 passengers - 12 in first class and 64 in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class. We can use a simulation to see if this result is likely to happen by chance. In 100 repetitions of the simulation, there were 15 times when none of the 10 passengers chosen was seated in first class. What conclusion would you draw?