The following data relate to the direct materials cost for the production of 10,000 automobile tires: Actual: 145,000 lbs. at $2.80 per lb. Standard: 150,000 lbs. at $2.75 per lb. a. Determine the direct materials price variance, direct materials quantity variance, and total direct materials cost variance. Enter a favorable variance as a negative number using a minus sign and an unfavorable variance as a positive number.

Balance sheet the assets of dallas & associates consist entirely of current assets and net plant and equipment. the firm has total assets of $2 5 million and net plant and equipment equals $2 million. it has notes payable of $150,000, long-term debt of $750,000, and total common equity of $1 5 million. the firm does have accounts payable and accruals on its balance sheet. the firm only finances with debt and common equity, so it has no preferred stock on its balance sheet. a. what is the company's total debt? b. what is the amount of total liabilities and equity that appears on the firm's balance sheet? c. what is the balance of current assets on the firm's balance sheet? d. what is the balance of current liabilities on the firm's balance sheet? e. what is the amount of accounts payable and accruals on its balance sheet? [hint: consider this as a single line item on the firm's balance sheet.] f. what is the firm's net working capital? g. what is the firm's net operating working capital? h. what is the explanation for the difference in your answers to parts f and g?

Grant, inc., acquired 30% of south co.’s voting stock for $200,000 on january 2, year 1, and did not elect the fair value option. the price equaled the carrying amount and the fair value of the interest purchased in south’s net assets. grant’s 30% interest in south gave grant the ability to exercise significant influence over south’s operating and financial policies. during year 1, south earned $80,000 and paid dividends of $50,000. south reported earnings of $100,000 for the 6 months ended june 30, year 2, and $200,000 for the year ended december 31, year 2. on july 1, year 2, grant sold half of its stock in south for $150,000 cash. south paid dividends of $60,000 on october 1, year 2. before income taxes, what amount should grant include in its year 1 income statement as a result of the investment?

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.