Imagine that you are a menu planner for a restaurant. You decide to create a nutritious salad. Write down the factors you must consider. Describe your salad, and include an ingredient list. Explain what makes your salad nutritious. Describe the type of customers who might be interested in your salad.

According to physicist Peter Brancazio, the key to a successful foul shot in basketball lies in the arc of the shot. Brancazio determined the optimal angle of the arc from the free-throw line to be 45 degrees. The arc also depends on the velocity with which the ball is shot. If a player shoots a foul shot, releasing the ball at a 45-degree angle from a position 6 feet above the floor, then the path of the ball can be modeled by the function $h(x)=-\frac{44 x^{2}}{v^{2}}+x+6$ where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot in feet per second. Suppose a player shoots a ball with an initial velocity of 28 feet per second. Determine the height of the ball after it has traveled 8 feet in front of the foul line.

A local organic farm sells your restaurant asparagus at $2 per pound, plus a flat$5 fee for delivery. Write an algebraic equation that shows the relationship between the total order price and the number of pounds ordered. Then, graph this equation.

A height of a rhombus divides its base into two equal segments. What are the angles of the rhombus?

Solve the linear inequality. Express the solution using interval notation and graph the solution set. $5-3 x \geq 8 x-7$

Solve for h.

$$V=\pi r^2 h$$

For the given functions f and g, find the following. Also find the domain. $(f \cdot g)(2)$, $f(x)=x-1 ; \quad g(x)=2 x^{2}$

Which of the following is a possible density for the buoys floating in the lake? a. 0.9 $g/cm^3$, b. 9 $g/cm^3$, c. 90 $g/cm^3$, d. 900 $g/cm^3$

Hypothesize why this might be the case.

Find the following for each function: f(1) $f(x)=|x|+4$

Describe bioplastics and list their positive and negative qualities.

Let $T$ and $U$ be positive definite operators on an inner product space V. Prove the following results. $\\$ (a)$T+U$is positive definite.$$(b) If$c>0,$then$c \top$is positive definite.$$(c)$T^{-1}$ is positive definite.

What factors are likely to make consumers in the United States prefer small, fuel-efficient cars to large vehicles?

A firm has been experiencing low profitability in recent years. Perform an analysis of the firm’s financial position using the DuPont equation. The firm has no lease payments but has a $2 million sinking fund payment on its debt. The most recent industry average ratios and the firm’s financial statements are as follows:$ $$ \begin{matrix} \text{Industry Average Ratios}\\ \text{Current ratio} & \text{3 }{\times} & \text{Fixed assets turnover} & \text{6 }{\times}\\ \text{Debt-to-capital ratio} & \text{20\\%} & \text{Total assets turnover} & \text{3 }{\3 times}\\ \text{Times interest earned} & \text{7 }{\times} & \text{Profit margin} & \text{3\\%}\\ \text{EBITDA coverage} & \text{9 }{\times} & \text{Return on total assets} & \text{9\\%}\\ \text{Inventory turnover} & \text{10}{\times} & \text{Return on common equity} & \text{12.86\\%}\\ \text{Days sales outstanding} & \text{24 days} & \text{Return on invested capital} & \text{11.50\\%}\\ \end{matrix} $$ $$ $\begin{matrix} \text{Balance Sheet as of December 31, 2016 (millions of Dollars)}\\ \text{Cash and equivalents} & \text{\$ 78} & \text{Accounts payable} & \text{\$ 45}\\ \text{Accounts receivable} & \text{66} & \text{Other current liabilities} & \text{11}\\ \text{Inventories} & \text{159} & \text{Notes payable} & \text{29}\\ \text{Total current assets} & \text{\$ 303} & \text{Total current liabilities} & \text{\$ 85}\\ \text{ } & \text{ } & \text{Long-term debt} & \text{50}\\ \text{ } & \text{ } & \text{Total liabilities} & \text{\$ 135}\\ \text{Gross fixed assets} & \text{225} & \text{Common stock} & \text{114}\\ \text{Less depreciation} & \text{78} & \text{Retained earnings} & \text{201}\\ \text{Net fixed assets} & \text{\$ 147} & \text{Total stockholders' equity} & \text{\$ 315}\\ \text{Total assets} & \text{\$ 450} & \text{Total liabilities and equity} & \text{\$ 450}\\ \end{matrix} $$ $$ \begin{matrix} \text{Income Statements for Year Ended December 31, 2016 (millions of dollars)}\\ \text{Net sales} & \text{\$ 795.0}\\ \text{Cost of goods sold} & \text{660.0}\\ \text{Gross profit} & \text{\$ 135.0}\\ \text{Selling expenses} & \text{73.5}\\ \text{EBITDA} & \text{\$ 61.5}\\ \text{Depreciation expense} & \text{12.0}\\ \text{Earnings before interest and taxes (EBIT)} & \text{\$ 49.5}\\ \text{Interest expense} & \text{4.5}\\ \text{Earnings before taxes (EBT)} & \text{\$ 45.0}\\ \text{Taxes (40\\%)} & \text{18.0}\\ \text{Net income} & \text{\$ 27.0}\\ \end{matrix} $$ a. Calculate the ratios you think would be useful in this analysis. b. Construct a DuPont equation, and compare the company’s ratios to the industry average ratios. c. Do the balance sheet accounts or the income statement figures seem to be primarily responsible for the low profits? d. Which specific accounts seem to be most out of line relative to other firms in the industry? e. If the firm had a pronounced seasonal sales pattern or if it grew rapidly during the year, how might that affect the validity of your ratio analysis? How might you correct for such potential problems?