The balance sheet of chase industries included the following shareholders’ equity section at december 31, 2018 ($ in millions): common stock ($1 par value, authorized 100m shares, issued and outstanding 90m shares) $ 90 paid-in capital—excess of par 540 retained earnings 280 total shareholders’ equity $910 on january 5, 2019, chase purchased and retired 1 million shares for $10 million. immediately after the purchase of the shares, the balances in the paid-in capital—excess of par and retained earnings accounts are:

Aceramics manufacturer sold cups last year for $7.50 each. variable costs of manufacturing were $2.25 per unit. the company needed to sell 20,000 cups to break even. net income was $5,040. this year, the company expects the price per cup to be $9.00; variable manufacturing costs to increase 33.3%; and fixed costs to increase 10%. how many cups (rounded) does the company need to sell this year to break even?

P11.2a (lo 2, 4) fechter corporation had the following stockholders’ equity accounts on january 1, 2020: common stock ($5 par) $500,000, paid-in capital in excess of par—common stock $200,000, and retained earnings $100,000. in 2020, the company had the following treasury stock transactions. journalize and post treasury stock transactions, and prepare stockholders’ equity section. mar. 1 purchased 5,000 shares at $8 per share. june 1 sold 1,000 shares at $12 per share. sept. 1 sold 2,000 shares at $10 per share. dec. 1 sold 1,000 shares at $7 per share. fechter corporation uses the cost method of accounting for treasury stock. in 2020, the company reported net income of $30,000. instructions a. journalize the treasury stock transactions, and prepare the closing entry at december 31, 2020, for net income. b. open accounts for (1) paid-in capital from treasury stock, (2) treasury stock, and (3) retained earnings. (post to t-accounts.) c. prepare the stockholders’ equity section for fechter corporation at december 31, 2020.

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.