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

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

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

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

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.

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

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)

Solve each equation mentally.

$$d \div 3 = 6$$

If left untreated, all STDs: (a) can lead to serious health problems. (b) will eventually cure itself. (c) will become asymptomatic. (d) lead to infection by HIV/AIDS.

A 2575-kg van runs into the back of an 825-kg compact car at rest. They move off together at 8.5 m/s. Assuming that the friction with the road is negligible, calculate the initial speed of the van.

List the numbers in

$$\left\{ - 5,0 , - \sqrt { 3 } , 2.4,7 , - \frac { 2 } { 3 } , - 3.\overline {6} , \pi , \frac { 15 } { 4 } , 0.13242368 \dots \right\}$$

that belong to the following sets. a. Natural numbers b. Whole numbers