Make a sketch of the region and its bounding curves. Find the area of the region. The region inside the rose r=4 sin 2

$$\theta$$

and inside the circle r=2

The financial statements at the end of Palo Duro Realty’s first month of operations are shown at the top of the next page.

$$\begin{array}{cl} \textbf{Palo Duro Realty}\\ \textbf{Income Statement}\\ \textbf{For the Month Ended November}\ \bm{30, 2010}\\ {\textcolor{#4257b2}{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \end{array}$$

$$\begin{array}{lrr} \text{Fees earned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . } && \$ \hspace{16pt} \left(\text{a}\right)\\ \text{Expenses:}\\ \hspace{10pt}\text{Wages expense. . . . . . . . . . . . . . . . . . . . . . . . . . . . } & \$ 51,000\\ \hspace{10pt}\text{Rent expense. . . . . . . . . . . . . . . . . . . . . . .. . . . . . .} & 19,200\\ \hspace{10pt}\text{Supplies expense.. . . . . . . . . . . . . . . . . . . . . . . . . .} & \hspace{16pt} \left(\text{b}\right)\\ \hspace{10pt}\text{Utilities expense.. . . . . . . . . . . . . . . . . . . . . . . . . . } & 10,800\\ \hspace{10pt}\text{Miscellaneous expense. . . . . . . . . . . . . . . . . . . . . .} & \underline{\ \ \ \ 6,600}\\ \hspace{20pt}\text{Total expenses. . . . . . . . . . . . . . . . . . . . . . . . . .} && \underline{\ 105,600}\\ \text{Net income. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .}&& \underline{\underline{\$ \hspace{3pt}74,400}} \end{array}$$

$$\begin{array}{cl} \textbf{Palo Duro Realty}\\ \textbf{Statement of Owner’s Equity}\\ \textbf{For the Month Ended November}\ \bm{30, 2010}\\ {\textcolor{#4257b2}{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \end{array}$$

$$\begin{array}{lrr} \text{Laura Biddle, capital, November $1$, $2010$. . . . . . . . . . . . . . . } && \$ \hspace{16pt} \left(\text{c}\right)\\ \text{Investment on November $1$, $2010$. . . . . . . . . . . . . . . . . . . . .} & \$ 240,000\\ \text{Net income for November. . . . . . . . . . . . . . . . . . . . . . . . . . . } & \underline{\hspace{20pt} \left(\text{d}\right)}\\ & \left(\text{e}\right)\\ \text{Less withdrawals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .} & \underline{\hspace{10pt}6,000}\\ \text{Increase in owner’s equity . . . . . . . . . . . . . . . .. . . . . . . . . . .} && \underline{\hspace{20pt}\left(\text{f}\right)}\\ \text{Laura Biddle, capital, November $31$, $2010$. . . . . . . . . . . . . . } && \underline{\underline{\hspace{22pt}\left(\text{g}\right)}} \end{array}$$

$$\begin{array}{cl} \textbf{Palo Duro Realty}\\ \textbf{Balance Sheet}\\ \textbf{November}\ \bm{30, 2010}\\ {\textcolor{#4257b2}{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \end{array}$$

$$\begin{array}{lrclr} \hspace{65pt}\textbf{Assets} &&& \hspace{65pt}\textbf{Liabilities}\\ \text{Cash . . . . . . . . . . . .} & \$ \hspace{5pt}26,700 && \text{Accounts payable. . . . . . . . . . . . . .} & \$ \hspace{5pt} 9,600\\ \text{Supplies. . . . . . . . . .} & 21,300 && \hspace{65pt}\textbf{Owner’s Equity}\\ \text{Land . . . . . . . . . . . .}& \underline{240,000} && \text{Laura Biddle, capital . . . . . . . . . . .} & \underline{\hspace{24pt}\left(\text{i}\right)}\\ \text{Total assets. . . . . . . }& \underline{\underline{\hspace{24pt}\left(\text{h}\right)}} && \text{Total liabilities and owner’s equity.} & \underline{\underline{\hspace{20pt}\left(\hspace{4pt}\text{j}\right)}} \end{array}$$

$$\begin{array}{cl} \textbf{Palo Duro Realty}\\ \textbf{Statement of Cash Flows}\\ \textbf{For the Month Ended November}\ \bm{30, 2010}\\ {\textcolor{#4257b2}{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}} \end{array}$$

$$\begin{array}{lrr} \text{Cash flows from operating activities:}\\ \hspace{10pt}\text{Cash received from customers. . . . . . . . . . . . . . . . . . . . . . . . . . . .} & \$ \hspace{20pt}\left(\text{k}\right)\\ \hspace{10pt}\text{Deduct cash payments for expenses and payments to creditors. .} & \underline{117,300}\\ \hspace{10pt}\text{Net cash flow from operating activities. . . . . . . . . . . . . . . . . . . . .} && \$ \hspace{20pt}\left(\text{l}\right)\\ \text{Cash flows from investing activities:}\\ \hspace{10pt}\text{Cash payments for acquisition of land. . . . . . . . . . . . . . . . . . . . . .} && \left(\text{m}\right)\\ \text{Cash flows from financing activities:}\\ \hspace{10pt}\text{Cash received as owner’s investment. . . . . . . . . . . . . . . . . . . . . . .} & \left(\text{n}\right)\\ \hspace{10pt}\text{Deduct cash withdrawal by owner. . . . . . . . . . . . . . . . . . . . . . . . .} & \underline{\hspace{22pt}\left(\text{o}\right)}\\ \hspace{10pt}\text{Net cash flow from financing activities. . . . . . . . . . . . . . . . . . . . . .} && \underline{\hspace{20pt}\left(\text{\hspace{5pt}p}\right)}\\ \hspace{10pt}\text{Net cash flow and November $30$, $2010$, cash balance. . . . . . . . . . . . . . . .} && \underline{\underline{\hspace{20pt}\left(\text{\hspace{5pt}q}\right)}}\\ \end{array}$$

$\textsf{\textcolor{#4257b2}{Instructions}}$
By analyzing the interrelationships among the four financial statements, determine the proper amounts for (a) through (q).

For this exercise, the domains were determined in the previous exercises. Use a graph to (a) find the range, (b) give the largest open interval over which the function is increasing, (c) give the largest open interval over which the function is decreasing, and (d) solve the equation $f(x)=0$ by observing the graph.

$$f(x)=-\sqrt[4]{6-x}$$

For this exercise, the domains were determined in the previous exercises. Use a graph to (a) find the range, (b) give the largest open interval over which the function is increasing, (c) give the largest open interval over which the function is decreasing, and (d) solve the equation $f(x)=0$ by observing the graph.

$$f(x)=\sqrt{49-x^2}$$

Write each ratio in lowest terms. 3 yd:48 in.

For the given functions f and g, find: $f \circ f$, $f(x)=x^{2}+1 ; \quad g(x)=\sqrt{x-1}$

The income statement of Booker T Industries Inc. for the current year ended June 30 is as follows:

$$\begin{array}{lrr} \text{Sales}&&\$\hspace{10pt}{511,000}\\ \text{Cost of merchandise sold}&&\underline{\hspace{15pt}{290,500}}\\ \text{Gross profit}&&{\$\hspace{10pt}{220,500}}\\ \text{Operating expenses:}\\ \hspace{10pt}\text{Depreciation expense}&\$\hspace{10pt}{39,200}\\ \hspace{10pt}\text{Other operating expenses}&\underline{{\hspace{10pt}105,000}}\\ \hspace{20pt}\text{Total operating expenses}&&\underline{\hspace{15pt}144,200}\\ \text{Income before income tax}&&\$\hspace{15pt}{76,300}\\ \text{Income tax expense}&&\underline{{\hspace{20pt}21,700}}\\ \text{Net income}&&\underline{\underline{\$\hspace{15pt}{54,600}}}\\ \end{array}$$

Changes in the balances of selected accounts from the beginning to the end of the current year are as follows:

a. Prepare the Cash Flows from Operating Activities section of the statement of cash flows, using the direct method.

Find the centroid of a homogeneous solid hemisphere of radius a.

A local petting zoo had a total of 98,464 visitors last year. The zoo was open every day except Thanksgiving, Christmas, and New Year's Day. Estimate the average number of visitors per day. -There were 365 days last year. How many days was the petting zoo open?

(a) Suppose f is twice differentiable on an open interval I and $f^{\prime \prime}(x)=0$ for all $x \in I$. Show f has the form f(x)=ax+b for suitable constants a and b. (b) Suppose f is three times differentiable on an open interval I and $f^{\prime \prime \prime}=0$ on I. What form does f have? Prove your claim.

Write the equations in standard form for two quadratic functions that have the same vertex but open in different directions.

Write each ratio in simplest form. 2 m:5 cm

Sally spent $36 and had$12 left. What percent of her money did she spend?

Solve each open sentence and graph each solution set. 3(2x-1)=4x+7