With the discrete model, choosing the unit to illustrate given equivalent fractions takes some thought. Just any number of objects may not fit the fractions well; a set of Four objects would not work for showing $\frac{2}{4}=\frac{3}{6}$, e.g. Describe a usable unit for showing that each of the following pairs of fractions is equivalent. Then show each fraction on a separate sketch of the unit, in such a way that the equivalence is visually clear. If a context is given, make your sketch to fit that context. a. $\frac{4}{5}=\frac{8}{10} \quad$ Context: popsicle sticks b. $\frac{6}{9}=\frac{4}{6} \quad$ Context: marbles (Do you have the smallest unit?) c. $\frac{2}{3}=\frac{4}{6} \quad$ Context: children d. $\frac{2}{3}=\frac{12}{18}$ Context: Choose your own.

Convert the angle measure to decimal degree. If applicable, round to the nearest thousandth of a degree. $-70^{\circ} 48^{\prime}$

Convert the angle measure to decimal degree. If applicable, round to the nearest thousandth of a degree. $82^{\circ} 30^{\prime}$

Evaluate the absolute value expression. $\left|2\left(-\frac{7}{2}\right)\right|$

Evaluate the definite integral. $\int_{1}^{95} \frac{x}{\ln e^{x}} d x$

Rewrite the following paragraph, adding, deleting, or changing any end marks and commas to correct the numbered word groups that are incorrectly punctuated.

EXAMPLE: In looking through a United States atlas have you cver been tempted to use it, as a menu to create a meal of places named for foods. In looking through a United States atlas, have you ever been tempted to use it as a menu to create a meal of places named for foods?*

For an appetizer, that will take the edge off your family's hunger, without filling them up why not serve a relish tray assembled from Pickleville in Utah. Olive in Montana, and Pepperton in Georgia, along with Rolls from Arizona and Indiana and Butters from North Carolina

Find the Jacobian J of the transformation $x=u \cos \left(e^{v}\right), y=u \sin \left(e^{v}\right)$

Find exact values of the six trigonometric functions of each angle. Rationalize denominators when applicable. $-1020^{\circ}$

Simplify the expression.

$$\left( s ^ { 5 } \right) ^ { 2 } \left( s ^ { 3 } \right) ^ { 8 }$$

Find each definite integral. $\int_{3}^{0}(-\pi) d t$.

Simplify the expression.

$$\left(7^{0} n^{-3}\right)^{2}\left(n^{5}\right)^{2}$$

A finite number of terms are deleted from a divergent series. Determine whether the new series will still diverge. Explain your reasoning.

Evaluate the definite integral. $\int_{0}^{2} x \sqrt{x^{2}+1} d x$

Subtract.

$$\left( - 8.9 p ^ { 3 } - 2.4 p \right) - \left( 2.1 p ^ { 3 } + 0.8 p ^ { 2 } - p \right)$$