Evaluate the function at the indicated values.

$$f ( x ) = x ^ { 3 } + 2 x ; \quad f ( - 2 ) , f ( - 1 ) , f ( 0 ) , f \left( \frac { 1 } { 2 } \right)$$

Consider the following game: A player throws a fair die repeatedly until he rolls a 2, 3, 4, 5, or 6. In other words, the player continues to throw the die as long as he rolls 1s. When he rolls a “non-1,” he stops. What is the expected number of rolls needed to obtain the first non-1?

Given the coordinates of two points and the equation of a line, how can you check that one point is the image of the other point reflected across the line?

(a) What type of bond joins neighbouring amino acids together? (b) How is this bond formed? (c) Circle this bond in the dipeptide above: (d) How are di- and polypeptides broken down?

Solve the equation.

$$c^2+5c+4=0$$

Write an equation for a direct variation with a graph that passes through each point. (-5, -3)

Use transformations of

$$f ( x ) = \frac { 1 } { x } \ or \ f ( x ) = \frac { 1 } { x ^ { 2 } }$$

to graph each rational function.

$$g ( x ) = \frac { 1 } { x + 2 } - 2$$

A water-skier is moving at a speed of 12.0 m/s . When she skis in the same direction as a traveling wave, she springs upward every 0.600 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.500 s in response to the crests. The speed of the skier is greater than the speed of the wave. Determine (a) the speed and (b) the wavelength of the wave.

Ammonia forms hydrogen-bonding intermolecular forces resulting in an unusually high boiling point for a substance with the small size of $\mathrm { NH } _ { 3 } .$ Can hydrazine $\left( \mathrm { N } _ { 2 } \mathrm { H } _ { 4 } \right)$ also form hydrogen-bonding interactions?

Which of the following is an example of how economics can affect science? F. Limited funding may lead scientists to research one topic instead of another. G. Legislators may create new laws about the use of natural resources based on the recommendations of scientists. H. A health crisis may drive scientists to prioritize research on new medications or vaccines. I. Community leaders may use scientific data to support a recommendation for costly pollution clean-ups.

Find the quotient.

$$\left( 10 a ^ { 3 } - 20 a ^ { 2 } + 5 a \right) \div 5 a$$

A steady current of 1 ampere flowing through a solution of silver nitrate will deposit

$$1.12 \times 10 ^ { - 3 }$$

g of silver in one second. How much silver will be deposited by a current of 12.0 amperes in one hour?

Write an exponential decay function to model each situation. Then find the value of the function after the given amount of time. The population of a town is 18,000 and is decreasing at a rate of 2% per year; 6 years.

Simplify.

$$\frac { 1 } { 4 } ( z + 4 )$$