Compute the nun1ber of (a) five-digit binary numbers.

Convert $\text{F}111_{\text {sixteen }}$ to binary.

Why is it important to only change one experimental variable at a time in an experiment?

If you have a friend in an abusive relationship, you may be tempted to "rescue" her or him. You may try to persuade your friend to leave the relationship by criticizing the abuser. However, criticizing the abuser may simply make the victim less willing to confide in you. Ask your friend how she or he feels. Express your concerns in a way that focuses on the abusive behavior rather than on the abuser. You might say, "I'm worried that you're getting hurt," rather than "That jerk doesn't deserve you." Let your friend know that she or he can always count on you for sympathy and support. That way, when your friend does feel ready to leave the relationship, she or he will be more likely to turn to you for help. The purpose of this piece is (a) to describe the consequences of abuse. (b) to discuss ways to prevent abuse. (c) to let teens know how to help a friend in an abusive relationship. (d) to list sources of help for abused teens.

Which of the following is true about the graph of the linear equation y = 2? A. The graph is a vertical line that passes through (2, 0). B. The graph is a vertical line that passes through (0, 2). C. The graph is a horizontal line that passes through (2, 0). D. The graph is a horizontal line that passes through (0, 2).

The vectors $(8, k)$ and $(9,6)$ are perpendicular. Find the value of $k$.

Find the relative extreme values of the function.

f(x, y) = x$^3$ + y$^3$ - 3xy

Evaluate the sum: $\sum_{k=1}^{13} k^2$

Use your results above to complete these statements: The quotient of two integers with the same sign is ______. The quotient of two integers with different signs is ______.

The purpose of this exercise is to develop a formula for the monthly payment P that is required to repay a loan of A dollars in n monthly installments, with the interest on the unpaid balance equal to a monthly rate r. Let $A_k=$ amount still owed after paying k installments. Then interest for the (k+1) st month is $r A_k$, and the principal paid off in the (k+1) st payment is $P-r A_k$. Thus,

$$A_{k+1}=A_k-\left(P-r A_k\right)=(1+r) A_k-P .$$

a. Use the equation above and the fact that $A_0=A$ to find $A_1, A_2$, and $A_3$ in terms of A, r, and P.

b. Generalizing from $A_1, A_2$, and $A_3$, you get $A_n=(1+r)^n A-\left[(1+r)^{n-1}+(1+r)^{n-2}+\cdots+(1+r)+1\right] P$.

Since the bracketed quantity above is a geometric series, show that the equation can be rewritten

$$A_n=(1+r)^n A-\left[\frac{(1+r)^n-1}{r}\right] P .$$

c. Since $A_n=0$ (why?), use the last equation in part (b) to show that

$$P=\frac{A r(1+r)^n}{(1+r)^n-1} \text {. }$$

Find the Taylor series at x = 0 for each function by modifying one of the Taylor series from this section.

sin x + cos x

Find exact values for the given expression.

$$\sin 15^{\circ}$$

Compare the average reaction rate measured over an initial, short time interval to one measured over a long time interval.

Use the $\epsilon=\delta$ definition of limit to verify the limit statements given.

$$\lim _{(x, y) \rightarrow(0,0)}\left(x+y^{2}\right)=0$$