Your target variable is δf, the magnitude of the difference in frequency between the waves emitted from the sonar device and the waves received by the device after reflecting off the whale. write an expression for δf in terms of the relevant frequencies using the subscript notation introduced above. express your answer in terms of some or all of the variables fle, flr, fse, and fsr.

You are head of the schwartz family endowment for the arts. you have decided to fund an arts school in the san francisco bay area in perpetuity. every 5 years, you will give the school $ 1 comma 000 comma 000. the first payment will occur 5 years from today. if the interest rate is 5.9 % per year, what is the present value of your gift?

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Transactions on april 1 of the current year, andrea byrd established a business to manage rental property. she completed the following transactions during april: opened a business bank account with a deposit of $45,000 from personal funds. purchased office supplies on account, $2,000. received cash from fees earned for managing rental property, $8,500. paid rent on office and equipment for the month, $5,000. paid creditors on account, $1,375. billed customers for fees earned for managing rental property, $11,250. paid automobile expenses for month, $840, and miscellaneous expenses, $900. paid office salaries, $3,600. determined that the cost of supplies on hand was $550; therefore, the cost of supplies used was $1,450. withdrew cash for personal use, $2,000. required: 1. indicate the effect of each transaction and the balances after each transaction: for those boxes in which no entry is required, leave the box blank. for those boxes in which you must enter subtractive or negative numbers use a minus sign. (example: -300)