Find the distance between the two points. If necessary, you may draw graphs but you shouldn't need to use the distance formula.

$(0,0)$ and $(3,4)$

Let X={a, b, c}. Define a function S from $\mathcal{P}$(X) to the set of bit strings of length 3 as follows. Let Y$\subseteq$X. If a$\in$Y, set $s_1=0$; If a$\notin$Y, set $s_1=1$; If b$\in$Y, set $s_2=0$; If b$\notin$Y, set $s_2=1$; If c$\in$Y, set $s_3=0$; If c$\in$Y, set $s_3=1$. Define S(Y)=$s_1s_2s_3$.

Prove that S is onto.

Phoenix Industries has pulled off a miraculous recovery. Four years ago it was near bankruptcy. Today, it announced a $1 per share dividend to be paid a year from now, the first dividend since the crisis. Analysts expect dividends to increase by$1 a year for another 2 years. After the third year (in which dividends to increase by $1 a year for another 2 years. After the third year (in which dividends are$3 per share) dividend growth is expected to settle down to a more moderate long-term growth rate of 6%. If the firm's investors expect to earn a return of 14% on this stock, what must be its price?

What are the properties that identify a rotation?

Find the time requested, to the nearest 0.1 year. The time it would take $6,000 to grow to$10,000 at 4.75% simple annual interest

In 1975, an airplane carrying an atomic clock flew back and forth for $15 \mathrm{~h}$ at an average speed of $140 \mathrm{~m} / \mathrm{s}$ as part of a time-dilation experiment. The time on the clock was compared to the time on an atomic clock kept on the ground. How much time did the airborne clock "lose" with respect to the clock on the ground?

(Printing a String) Write a program that defines and uses macro PRINT to print a string value.

Find the distance from the

(b). origin to the plane $2=z-x$.

Given are five observations collected in a regression study on two variables.

$$\begin{array}{r|rrrrr} \boldsymbol{x}_{\boldsymbol{i}} & 2 & 6 & 9 & 13 & 20 \\ \hline \boldsymbol{y}_i & 7 & 18 & 9 & 26 & 23 \end{array}$$

c. Use the estimated regression equation to predict the value of $y$ when $x=6$.

Determine whether the statement is true or false. Use the following sets of numbers.

$N=$ set of natural numbers.

$Z=$ set of integers

$I=$ set of irrational numbers

$Q=$ set of rational numbers

$\mathbb{R}=$ set of real number

$$-1 \in Z$$

In a pulse power circuit, the voltage of a 10$\mu$F capacitor is zero for t<0 and $v=5(1-e^{-4000t})$ V for t>0. Determine the capacitor current and the energy stored in the capacitor at t=0ms and t=10ms.

Write the correct word in the space next to each definition.

random $\rule{2cm}{0.15mm}$

Determine if each of the following statements are true or false. Provide a brief explanation to justify each of your answers. a. The roots of a polynomial function are rational numbers. b. The process of finding zeros of a polynomial function is also referenced as finding the roots of the polynomial function. c. We can apply the zero-product property to determine the zeros of a polynomial function in factored form. d. The function used to model the box problem in Module 3 has two roots, at x = 0 and x = 4.25. e. The zeros of any function f represent the value(s) of x that when input into the function f return a value of 1 for the output variable f(x). f. The graph of a polynomial function is always a smooth curve, g. Polynomial functions are not always continuous.

Find the distance between the points.

$$(1,12),(6,0)$$