Use the following information for this exercise .

The table shows regulation distances between hurdles in women's and men's races. In both the women's and men's events, the race consists of a straight track with 10 equally spaced hurdles.

Event	Distance of Race	Distance from Start to First Hurdle	Distance Between Hurdles	Distance from Last Hurdle to Finish
Women's	$100 \mathrm{~m}$	$13.00 \mathrm{~m}$	$8.50 \mathrm{~m}$
Men's	$110 \mathrm{~m}$	$13.72 \mathrm{~m}$	$9.14 \mathrm{~m}$

Find the distance from the last hurdle to the finish line for the men's race.

$\overrightarrow{B D}$ bisects $\angle A B C,$ m$\angle A B C=(4 x+5)^{\circ}$, and m$\angle A B D=(3 x-1)^{\circ}$. What is the value of $x$?

(A) 2.2

(B) 3

(C) 3.5

(D) 7

Draw $\overline{A B}$. Then construct point C so that it is not on $\overline{A B}$ and is the same distance from A and B. Construct $\overline{A C}$ and $\overline{B C}$. Compare $\mathrm{m} \angle C A B$ and $\mathrm{m} \angle C B A$ and compare AC and CB. Make a conjecture.

In a report issued by the Economist Intelligence Unit in 2013, the number of commercial vehicle registrations in the United States (in thousands) by year from 2010 through 2015 is approximated by the function $N(t)=1.3926 t^{3}-9.2873 t^{2}+74.719 t+228.3$ $(0 \leq t \leq 5)$ where t is measured in years with t = 0 corresponding to 2010. If the projection holds up, what would the approximate average commercial vehicle registration per year be in the period from 2010 through 2015?

Mohs' scale is used to identify minerals. A mineral with a higher number is harder than a mineral with a lower number. Use the table and the statements below.

Write each conditional and find its truth value.

$$\begin{array}{c|c} \text { Hardness } & \text { Mineral } \\ \hline 1 & \text { Tälc } \\ 2 & \text { Gypsum } \\ 3 & \text { Calcite } \\ 4 & \text { Fluorite } \\ 5 & \text { Apatite } \\ 6 & \text { Orthoclase } \\ 7 & \text { Quartz } \\ 8 & \text { Topaz } \\ 9 & \text { Corundum } \\ 10 & \text { Diamond } \end{array}$$

$$\begin{array}{ll}p: \text { calcite } & q: \text { not apatite } \\ r: \text { a hardness of } 3 & s: \text { a hardness less than } 5\end{array}$$

$$p \rightarrow r$$

Use the following information for this exercise .

The table shows regulation distances between hurdles in women's and men's races. In both the women's and men's events, the race consists of a straight track with 10 equally spaced hurdles.

Find the distance from the last hurdle to the finish line for the women's race.

Rob is training for the President's Challenge physical fitness program. During his first week of training, Rob does 15 sit-ups each day. He will add 20 sit-ups to his daily routine each week. His goal is to reach 150 sit-ups per day.

a. Make a table of the number of sit-ups Rob does each week from week 1 through week 10.

b. During which week will Rob reach his goal?

c. Write a conjecture for the number of sit-ups Rob does during week $n$.

Find a counterexample to show that the converse of each conditional is false.

If you use sunscreen, then you will not get sunburned.

Presidential elections are held every four years. U.S. senators are elected to b-year terms, but only $\frac{1}{3}$ of the Senate is up for election every two years. If $\frac{1}{3}$ of the Senate is elected during a presidential election year, how many years must pass before these same senate seats are up for election during another presidential election year?

A, D, N, and X are collinear points. D is between N and A. NA + AX = NX. Draw a diagram that represents this information.

HJ is twice JK . J is between H and K. If HJ=4x and HK=78, find JK.

Use a protractor to draw a $70^{\circ}$ angle. Then use a compass and straightedge to bisect the angle. What do you think will be the measure of each angle formed? Use a protractor to support your answer.

Make a table of values for the rule x$^2+x+11$ when x is an integer from 1 to 8. Make a conjecture about the type of number generated by the rule. Continue your table. What value of x generates a counterexample?

Find a counterexample to show that the converse of each conditional is false.

If two angles are adjacent, then they share a vertex.