Find each product. Look for patterns. a. $\left(\dfrac{10}{13}\times54\right)\times13$
b. $\left(\dfrac{10}{13}\times81\right)\times13$
c. $\left(\dfrac{10}{13}\times1113\right)\times13$
d. Describe a pattern.

Find the vertex and the axis of symmetry of the graph of the function. $f ( x ) = 5 ( x - 2 ) ^ { 2 }$

Explain why cos $\theta=\cos \left(\theta+n \cdot 360^{\circ}\right)$ for any angle $\theta$ and any integer n.

Change the order of integration by integrating first with respect to z, then x, then y. $\int _ { - 1 } ^ { 2 } \int _ { 1 } ^ { 3 } \int _ { 0 } ^ { 4 } \left( x ^ { 2 } z + \frac { 1 } { y } \right) d x d y d z$

Convert the polar equation to rectangular form and sketch its graph. $r=4 \sin \theta$

Determine the angular momentum ${H}_{P}$ of the 6-lb particle about point P .

Indicate whether each nerve tract is ascending or descending. a. rubrospinal b. corticospinal c. spinothalamic d. fasciculus gracilis e. reticulospinal f. spinocerebellar

Use the numbers 19, 21, and 399 to write two multiplication facts and two division facts.

Write a counterexample for the conditional statement. If a number is divisible by 2, then it is divisible by 4.

Identify and graph each polar equation. $r=1-2 \sin \theta$

Let $X$ and $Y$ be i.i.d. $\text{Expo}(1)$, and $L = X − Y$ . The Laplace distribution has PDF

$$f ( x ) = \frac { 1 } { 2 } e ^ { - | x | }$$

for all real $x$. Use MGFs to show that the distribution of $L$ is Laplace.

Simplify.

$$b^2\cdot b^4$$

Write each Hindu-Arabic numeral as a Roman numeral. 4578

Let

$$s ( x ) = 2.5 x ^ { 3 } - 3.6 x ^ { 2 } + 1.1 x$$

a. s(-10) b. s(10)