The table shows regulation distances between hurdles in woman'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.

$$\begin{matrix} \text{Event} & \text{Distance of Race} & \text{Distance from Start to First Hurdle} & \text{Distance Between Hurdles} & \text{Distance from last Hurdle to Finish}\\ \text{Women's} & \text{100 m} & \text{13.00 m} & \text{8.50 m} & \text{ }\\ \text{Men's} & \text{110 m} & \text{13.72 m} & \text{9.14 m} & \text{ }\\ \end{matrix}$$

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

Find the LCM, the add or subtract. Write your answer in simplest form. $\frac { 5 } { x ^ { 2 } y ^ { 3 } } - \frac { 7 } { x y ^ { 2 } }$

The coordinate of M is 2.5, and MN=4. What are the possible coordinates for N?

Simplify the expression.

$$\left( -\frac{3}{4}c \right )^3$$

Determine the number of real solutions for each equation. Then solve each equation that has one or more real solutions by using the quadratic formula. $3 x^{2}-9=7 x^{2}-12 x$ _____.

How can your write general rules involving properties of exponents?

Use an equation to find the probability of the event. rolling a number less than 4 on two number cubes-and a coin landing on heads

Use the definitions of functions $f$ and $g$ below.

$$f(x) = 3x - 7$$

$$g(x) = \dfrac{x + 7}{3}$$

Find each value. a. $f(10)$ b. $g(23)$
c. $f(f(0))$ d. $g(g(-28))$
e. $f(g(172))$ f. $g(f(0.27))$
g. $f(g(f(g(1000))))$

A commercial developer hires a market research company to determine the mean household income of those who live within a 10 mi radius of the site of a proposed upscale shopping center. a. Explain why the commercial developer would do this. b. How might the market research company get the information?

A transparent film (n = 1.43) is deposited on a glass plate (n = 1.52) to form a nonreflecting coating. The film has a thickness that is

$$1.07 \times 10 ^ { - 7 } \mathrm { m }$$

What is the longest possible wavelength (in vacuum) of light for which this film has been designed?

Silicon tetrachloride

$$(\mathrm{SiCl_4})$$

can be prepared by heating Si in chlorine gas:

$$\mathrm{Si}(s)+2\mathrm{Cl_2}(g)\rightarrow\mathrm{SiCl_4}(l)$$

In one reaction, 0.507 mol of

$$\mathrm{SiCl_4}$$

is produced. How many moles of molecular chlorine were used in the reaction?

Let $G$ act on the set $A$. Prove that if $a,b\in A$ and $b=g\cdot a$ for some $g\in G$, then $G_b =g G_a g^{-1}$ ($G_a$ is the stabilizer of $a$). Deduce that if $G$ acts transitively on $A$ then the kernel of the action is $\cap_{g\in G}gG_ag^{-1}$.

Solve each inequality and graph the solutions.

$$\frac { 4 + x } { 3 } > - 4$$

A toy rocket blasts off from ground level. After 0.5 s it is 8.8 ft high. It hits the ground after 1.6 s. Write an equation in factored form to model the height of the rocket as a function of time.