When Alfred Nobel died, he left the majority of his estate to fund five prizes, each to be awarded annually in perpetuity starting one year after he died. (a) If he wanted the cash award of each of the five prizes to be $48,000 and his estate could earn 11% per year, how much would he need to fund his prizes? (b) If he wanted the value of each prize to grow by 5% per year (perhaps to keep up with inflation), how much would he need to leave? Assume that the first amount was still $48,000. (c) His heirs were surprised by his will and fought it. If they had been able to keep the amount of money you calculated in (b), and had invested it at 11% per year, how much would they have in 2014, 118 years after his death?

When color is used on a topographical drawing, black is used to represent what?

Lavage rapide is a canadian company that owns and operates a large automatic car wash facility near montreal. the following table provides data concerning the company’s costs: fixed cost per month cost per car washed cleaning supplies $ 0.70 electricity $ 1,400 $ 0.07 maintenance $ 0.15 wages and salaries $ 4,900 $ 0.30 depreciation $ 8,300 rent $ 1,900 administrative expenses $ 1,400 $ 0.03 for example, electricity costs are $1,400 per month plus $0.07 per car washed. the company expects to wash 8,000 cars in august and to collect an average of $6.50 per car washed. the actual operating results for august appear below. lavage rapide income statement for the month ended august 31 actual cars washed 8,100 revenue $ 54,100 expenses: cleaning supplies 6,100 electricity 1,930 maintenance 1,440 wages and salaries 7,660 depreciation 8,300 rent 2,100 administrative expenses 1,540 total expense 29,070 net operating income $ 25,030 required: calculate the company's revenue and spending variances for august.

Find the zeros of the polynomial 5 x square + 12 x + 7 by factorization method and verify the relation between zeros and coefficient of the polynomials