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Name _______________ Honors Brief Calc.

Period ____ Semester 1 Review #1

1. The school yearbook costs $15 per book to produce with an overhead (storage, etc.) of $5500. The yearbook sells for $40. What is the break-even point?

2. For a certain commodity the supply equation is given by [pic]. At a price of $1, 19 units of the commodity are demanded. If the demand equation is linear and the market price is $4, find the demand equation.

Solve the following systems of equations:

3. [pic] 4. [pic] 5. [pic]

6. Advertising vs. Sales: A business would like to determine the relationship between the amount of money spent on advertising and its total weekly sales. Over a period of 5 weeks it gathers the following data.

Find the best line to represent the data.

7. A factory manufactures 2 products each requiring the use of 3 machines. The first machine can be used at most 70 hours; the second machine at most 40 hours; and the third machine at most 90 hours. The first product requires 2 hours on machine 1, 1 hour on machine 2 and 1 hour on machine 3. The second product requires 1 hour each on machines 1 and 2, and 3 hours on machine 3. If the profit is $40 per unit for the first product and $60 per unit for the second product, find the maximum profit.

8. A brewery manufactures three types of beer – lite, regular, and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barley, 3 bags of sugar, and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar, and 4 bags of hops. Each day the brewery has 800 bags of barley, 600 bags of sugar, and 300 bags of hops available. The brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer. How many vats of lite, regular, and dark beer should be brewed in order to maximize profits? What is the maximum profit?

9. Katy wants to buy a bicycle that costs $175 and will purchase it in 9 months. How much should she put in her savings account each month for this if she can get 10% per annum compounded monthly?

10. House Mortgage: A $152,400 loan is taken out at 9.5% for 25 years for the purchase of a house. The loan requires monthly payments. Find the amount of each payment.

11. Determine the total amount repaid over the life of the loan.

12. Brian deposited $100 a month into an account paying 9% interest per annum compounded monthly for 40 years. What is the largest amount he may withdraw monthly for the next 25 years?

13. Find the total amount (interest plus principal) on $12,000 invested for 8 months at 7% compounded monthly.

14. Five people are to line up for a group photo. If 2 of them refuse to stand next to each other, in how many ways can the photo be taken?

15. In a marketing survey, consumers are asked to give their first three choices, in order of preference, of 9 different drinks. In how many ways can they indicate their choices?

16. If the class consists of 10 girls and 5 boys, how many different groups of 4 are made up of 2 boys and 2 girls?

17. A survey of freshman calculus students at a certain university showed the following graphics calculator use:

21 use TI 13 use TI and Casio

45 use Casio 14 use HP and TI

24 use HP 15 use Casio and HP

1 uses none of these 8 use all three

How many students were surveyed?

18. If [pic], [pic], and [pic] form a partition of a sample space S and [pic], [pic], [pic] and if E is an event of S for which [pic], [pic], and [pic]. Find [pic].

19. Four percent of the items coming off an assembly line are defective. If the defective items occur randomly and ten items are chosen for inspection, what is the probability that exactly two items are defective?

20. A man claims to be able to distinguish between scotch and bourbon 80% of the time. A test of 15 samples is given to him and, if he is correct at least 12 times, he proves his claim. What is the probability his claim is justified, but he does not pass?

21. In a lottery, 1000 tickets are sold at $0.25 each. There are 3 cash prizes: $100, $50, and $30. Alice buys 5 tickets. What would have been a fair price for a ticket?

22. An experimental test to detect a particular type of cancer indicates the presence of cancer in 90% of the individuals known to have this type of cancer and in 15% of the individuals known to be cancer-free. One hundred individuals volunteer to take the test. Of the 100, 60 are known to have cancer and 40 are known to be cancer-free. If the test indicates that a randomly chosen individual has the cancer, what is the probability that he or she is cancer-free?

23. Use the normal approximation to the binomial distribution to find the probability that at least 70 of 100 sick people will be cured by a new drug, when the probability is 0.75 that any one of them will be cured by the new drug.

24. The time spent in a waiting line at a supermarket is known to be normally distributed with a mean of five minutes and a standard deviation of 30 seconds (0.5 minutes). Determine the probability that a randomly chosen customer will spend between 4.5 and 6.5 minutes in line.

25. Find a Z-score such that 10% of the area under the curve is to the left of the score.

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