If a company reports positive net income for the year, can it also show a net cash outflow from operating activities? Explain.

(a) A weighted coin has probability of $\frac{2}{3}$ of showing heads and $\frac{1}{3}$ of showing tails. Find the probabilities of hh, ht, th and tt in two tosses of the coin. Set up the sample space and the associated probabilities. Do the probabilities add to 1 as they should? What is the probability of at least one head? What is the probability of two heads if you know there was at least one head? (b) For the coin in (a), set up the sample space for three tosses, find the associated probabilities, and use it to answer the questions.

Find the indicated derivatives and simplify. $f^{\prime}(x)$ for $f(x)=\frac{3 x^{2}}{2 x-1}$

A clerk in Kentucky is responsible for issuing marriage licenses in her county. Several same-sex couples have applied for marriage licenses and the clerk has refused to issue them, claiming it would violate her religious beliefs and rights. Based on the Establishment Clause of the First Amendment, how would you rule?

Simplify each power of i. $\frac{1}{i^{-12}}$

A baseball approaches home plate at a speed of 45.0 m/s, moving horizontally just before being hit by a bat. The batter hits a pop-up such that after hitting the bat, the baseball is moving at 55.0 m/s straight up. The ball has a mass of 145 g and is in contact with the bat for 2.00 ms. What is the average vector force the ball exerts on the bat during their interaction?

Find each indefinite integral and check the result by differentiating. $\int \frac{e^{x}}{1+e^{x}} d x$

A photon having energy $E_{0}$ is scattered by a free electron initially at rest such that the scattering angle of the scattered electron is equal to that of the scattered photon. Determine the angle $\theta$.

Use the intermediate value theorem to show that each polynomial function has a real zero between the numbers given. $f(x)=2 x^{2}-7 x+4$; 2 and 3

Use synthetic division to decide whether the given number k is a zero of the polynomial function. If it is not, give the value of f(k). $f(x)=x^{2}-3 x+5$; k=1-2i

An object of mass m = 5.00 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.00 m. (a) When the vibrator is set to a frequency of 150 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord? (b) How many loops (if any) will result if m is changed to 45.0 kg? (c) How many loops (if any) will result if m is changed to 10.0 kg?

Compute the following limit for each function $\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{h}$. f(x)=|x+1|

Simplify each complex fraction. $\frac{1+\frac{1}{1-b}}{1-\frac{1}{1+b}}$

Sketch or computer plot a graph of the function $y=e^{-x^{2}}$