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gfds - Name Section ‘ Math 110 EXAM 1A Show All Work For...

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Unformatted text preview: Name Section ‘ Math 110, EXAM 1A, 2/20/04 Show All Work! For Problem #5, round answers to 3 decimal places. (3) 1a.Find the slope of the line through the points (-3, 6) and (2,-1). (6)b. Find the x and y-intercepts of -2x - 3y = 17. y —- intercept x — intercept_~ (3)c. Find an equation of the line passing through (12,9) and parallel to the line y = -17. (3)d. Find an equation of the vertical line through (39,51). 2. The number of annual sales of new, in-ground swimming pools in the United States increased from 125 thousand in 1997 to 155 thousand in 2001. (10)a. Find a linear model for the number y, of sales of in-ground swimming pools in the year x, with x = 0 corresponding to 2000. (4)b. Use your model to predict the number of in-ground-pool sales in 2010. 3. Barbara’s Bonnets sells straw hats for $5.00 each. It costs Barbara $1.50 to produce each hat and $7000 per month in fixed costs. (4) a. Find the linear equation for total cost, C, in terms of x, the number of hats produced. (2)b. Find the linear equation for revenue, R, in terms of x, the number of hats sold. (4)c. How many hats must be produced and sold to break-even? (4)d. What is Barbara’s profit (loss) if she produces and sells 2600 hats? (l2)4. Solve the following systems of linear equations algebraically. lf there is no solution, so state. a. 2x+3y=13 b. 2x+y=5 3x+5y=23 -10x=5y-25 5.The following table shows the number of spring bouquets sold at varying prices. Price (in $) 7 5 20 6 2 9 8 21 Number of Bouquets Sold 15 18 3 14 30 12 14 2 (5)a. Create a stem-and-leaf plot of the number of bouquets sold. (5)b. What is the median of the prices? (5)c. What is the mean of the number of bouquets sold? (5)d. Using least—squares linear regression, find the best-fit-line for the data (let x be price, y be number of bouquets sold). Line: (4)e. According to the model found in part (d) how many more (fewer) bouquets can you expect to sell if you increase the price by one dollar? (4)f. According to the model found in part (d), how many bouquets would you expect to sell if they are priced at $l0 each? (4)g. According to the model found in part (d), at what price per bouquet would you expect to sell 20 bouquets? (13) 6. Donna is ordering sandwich platters and dessert platters for her dorm’s leap—year party. Each sandwich platter costs $18.50 and each dessert platter costs $12.75. Donna has ordered 3 times as many sandwich platters as dessert platters. If Donna spent a total of $887.25 on her order, how many platters of each type did she buy? (Define variable(s), set up equation(s) and solve.) HONOR PLEDGE: I pledge on my honor that l have not given or received any unauthorized assistance on this examination or assignment. Please write the exact wording of the pledge, followed by your signature, in the space below: Signature ...
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