A sequence is defined by

$$u _ { n } = \frac { 71 - 7 n } { 2 }$$

. a. Show that the sequence is arithmetic. b. Find

$$u_1$$

and d. c. Find

$$u_{75}$$

. d. For what values of n are the terms of the sequence less than -200?

Write the ratio as a fraction in simplest form. 15. 16 dogs to 12 cats

Perform the indicated calculation.

$$_ { 8 } P _ { 6 }$$

Determine the best method to solve the system of equation. Then solve the system. 6x + 5y = 9, -2x + 4y = 14

Square ABCD has vertices at (0, 0), (0, 2), (2, 2), and (2, 0). Perform the indicated transformation. Then give the coordinates of figure

$$A ^ { \prime } B ^ { \prime } C ^ { \prime } D ^ { \prime }$$

.

$$( x , y ) \rightarrow ( x + 3 , y )$$

(a) Prove that there exist unique scalars $c_0,c_1,\dots,c_n$ such that

$$f(-1)+f(-2)=c_0f(0)+c_1f(1)+\dots+c_nf(n)$$

for every polynomial $f(x)$ in $\mathcal{P}_n$. (b) Find the scalars $c_0,c_1,c_2,c_3,$ and $c_4$ such that

$$f(-1)+f(-2)=c_0f(0)+c_1f(1)+c_2f(2)+c_3f(3)+c_4f(4)$$

for every polynomial $f(x)$ in $\mathcal{P}_4$.

Juanita runs every third day and swims every fifth day. If Juanita runs and swims today, in how many days will she run and swim again on the same day?

Simplify: 8 1/3 · 1 4/5

Fill in the blanks. Given a relation in x and y, if to each value of x in the domain there corresponds exactly one value of in the range, y is said to be a _____ of x. We call x the independent _____ and y the _____ variable.

Find the: a. smallest multiple of 6 that is greater than 200 b. greatest multiple of 11 that is less than 500.

We now have $5,000 in assets and are given a choice between investment 1 and investment 2. With investment 1, 80% of the time weincrease our asset position by$295,000, and 20% of the time we increase our asset position by $95,000. With investment 2, 50% of the time we increase our asset position by$595,000, and 50% of the time we increase our asset position by $5,000. Our utility function for final asset position x is u(x). We are given the following values for u(x): u(0) = 0, u(640,000) = .80, u(810,000) = .90, u(0) = 0, u(90,000) = .30, u(1,000,000) = 1, u(490,000) = .7. a. Are we risk-averse, risk-seeking, or risk-neutral? Explain. b. Will we prefer investment 1 or investment 2?

Convert each rectangular equation to a polar equation that expresses f in terms of

$$\theta.$$

$$2 x + 3 y = 8$$

Evaluate the expression when a=16, b=8, and c=7. 3a+2.1(4)

The region below the curve y=1/sqrt(4+x^2) from x=0 to x=2 is revolved avbout the x-axis. Find the volume of the resulting solid