Cheyenne is the manager of a local small hotel. just today cheyenne received word that a major convention will be coming to town next month, and the demand for hotel rooms is expected to skyrocket. in a conversation with the owner, she asked, "what should our approach to pricing be for the week of the convention

The leading producer of cell phone backup batteries, jumpstart, has achieved great success because they produce high-quality battery backups that are not too expensive. even so, another company that produces lower-quality batteries at the same price has also achieved some success, but not as much as jumpstart. also, in general, the price of backup batteries has declined because of economies of scale and learning. in addition, jumpstart has added complementary assets, such as a carrying case. considering all of these factors, the backup battery industry is most likely in the introduction stage. growth stage. shakeout stage. maturity stage.

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.

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.