The "grad" is a unit of angle measure that is sometimes used in France. One grad is the measure of an angle that cuts off an arc that is $\frac{1}{400} \mathrm{th}$ of a circle's circumference. An angle that rotates a circle's circumference is 400 grads. (Recall that one degree is an angle with vertex at the origin that cuts off an are that is $\frac{1}{360} \mathrm{th}$ of a circle's circumference and every circle's circumference is 360 degrees.) a. Using measures of circumference and arc length, explain how to make a protractor that measures an angle's openness in grads. b. If the protractor has a radius of 4.3 inches, determine the arc length in inches of: i. grad ii. 10 grads iii. 200 grads iv. 400 grads. c. An angle measuring 50 grads subtends what percent (or fractional part) of a circle's circumference? Explain your answer. d. How many degrees are equivalent to 50 grads? 100 grads? 10.2 grads? e. Define a function that converts a number of grads to a number of degrees. Explain how you determined this function.

Write each degree measure in radians as a multiple of $\pi$ and each radian measure in degrees. $225^{\circ}$

Find the sum of the geometric series, if possible. $1+\frac{2}{3}+\frac{4}{9}+\dots+\frac{32}{243}$

Determine the inverse of the given matrix if possible. Otherwise state that the matrix is singular.

$$A=\left[\begin{array}{rr}5 & -2 \\ 1 & 2\end{array}\right]$$

What effect does doubling the radius of a circle have on each of the following measures? Explain your reasoning. the area of a sector of the circle with a central angle that measures $\theta$ radians

Evaluate each expression. $3^{\log _{3} 9}$

An augmented matrix is given. Determine the number of solutions to the corresponding system of equations.

$$\left[\begin{array}{rrr|r}{1} & {0} & {2} & {5} \\ {0} & {1} & {4} & {-2} \\ {0} & {0} & {0} & {-1}\end{array}\right]$$

Use the Venn diagram to find each of the following. $A \cap B$

Solve each system of equations by graphing.

$$\begin{aligned} &xy=-2\\ &3 x-and=10 \end{aligned}$$

Write the domain of the function in interval notation.

$$q(x)=\sqrt{4 x^{2}+7 x-2}$$

Determine whether each pair of vectors are parallel. $\mathrm{g}=\langle 3,4,-6\rangle, \mathrm{h}=\langle 9,12,-18\rangle$

Draw a diagram to illustrate why the area of a square with side length, s = 4 kilometers, is computed using the formula $A=s^{2}$. What is the unit of the answer? Explain.

Given the sequence defined by $a_{n}=n^{2}-2 n,$ find the fifth partial sum.

Consider an experiment where a single 10 -sided die is rolled with the outcomes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Determine the probability of each event. A number between 2 and 7 , inclusive, is rolled.