Solve the inequality. Check your solutions. -5 ≤ 11 + 4j

Suppose the height of a triangle is tripled. How does this affect the area of the triangle? Explain.

Find the value of the expression when a = 8, a = 16, and c = 64. $\sqrt { c }$

If g(x) + x sin g(x) = x^2, find g’(0)

Relate the structure of water molecules to water's unique properties.

When $b ^ { 2 } - 4 a c = 0$ there is only one real root. Give an example showing why this is so.

Write the logarithmic equation in exponential form.

$$\log _ { \pi } \pi = 1$$

A nonprofit institution collects the savings of its members and invests those funds in a wide variety of assets in order to provide its members with income after retirement. This describes a A. mutual fund. B. bank. C. savings and loan. D. pension fund. E. life insurance company.

Use the following experiment. A state lottery game consists of choosing one card from each of the four suits in a standard deck of playing cards. (There are 13 cards in each suit.) Count the number of elements in the event that an ace, a king, a queen, and a jack are chosen.

A physicist wants to find the kinetic energy of a ball that has a mass of 2.5 kg and travels a distance of 5.8 meters in 2.5 seconds. The formula for kinetic energy is $E _ { K } = \frac { 1 } { 2 } m v ^ { 2 } ,$ where m is the mass of the object and v is the object's velocity. The formula for velocity is $v = \frac { d } { t } ,$ where d is distance traveled and t is the amount of time. What are the velocity and the kinetic energy of the ball?

Consider the sequence given by $b _ { n } = n - \sqrt { n ^ { 2 } + 2 n } .$ Taking $( 1 / n ) \rightarrow 0$ as given, and using the Algebraic Limit Theorem show $\lim b _ { n }$ exists and find the value of the limit.

Joe buys a ticket in his state's Pick 3 lottery game very week; is the number of times in a year that he wins a prize. In this situation, is it reasonable to use a binomial distribution for the random variable X? Give reason for your answer.

Find the critical points of the function and classify them as local maxima or minima or neither. f(x) = sin x + cos x

A hill of gravel (sedimentary particles) is composed primarily of rounded pebbles. What series of events would most likely transform this material into a sedimentary rock? (1) heating and melting followed by slow crystallization (2) water washing in clay followed by compression (3) weathering by exposure to rain, snow and wind (4) transportation by water to a new gravel location