Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)

Pettijohn inc. the balance sheet and income statement shown below are for pettijohn inc. note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during the next 5 years, and the notes payable will be rolled over. balance sheet (millions of $) assets 2016 cash and securities $ 1,554.0 accounts receivable 9,660.0 inventories 13,440.0 total current assets $24,654.0 net plant and equipment 17,346.0 total assets $42,000.0 liabilities and equity accounts payable $ 7,980.0 notes payable 5,880.0 accruals 4,620.0 total current liabilities $18,480.0 long-term bonds 10,920.0 total debt $29,400.0 common stock 3,360.0 retained earnings 9,240.0 total common equity $12,600.0 total liabilities and equity $42,000.0 income statement (millions of $) 2016 net sales $58,800.0 operating costs except depr'n $54,978.0 depreciation $ 1,029.0 earnings bef int and taxes (ebit) $ 2,793.0 less interest 1,050.0 earnings before taxes (ebt) $ 1,743.0 taxes $ 610.1 net income $ 1,133.0 other data: shares outstanding (millions) 175.00 common dividends $ 509.83 int rate on notes payable 1. what is the firm's current ratio? (points : 6) 0.97 1.08 1.20 1.33 2. what is the firm's quick ratio? (points : 6) 0.49 0.61 0.73 0.87 3. what is the firm's total assets turnover? (points : 6) 0.90 1.12 1.40 1.68 4. what is the firm's inventory turnover ratio? (points : 6) 4.38 4.59 4.82 5.06 5. what is the firm's debt ratio? (points : 6) 45.93% 51.03% 56.70% 70.00% 6. what is the firm's roa? (points : 6) 2.70% 2.97% 3.26% 3.59% 7. what is the firm's roe? (points : 6) 8.54% 8.99% 9.44% 9.91%

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.

Lin corporation has a single product whose selling price is $136 per unit and whose variable expense is $68 per unit. the company’s monthly fixed expense is $32,400. required: 1. calculate the unit sales needed to attain a target profit of $5,000. (do not round intermediate calculations.) 2. calculate the dollar sales needed to attain a target profit of $8,400.