| № |
Condition |
free/or 0.5$ |
| m67037 | Americans own a total of about 355 million fish, cats, and dogs as pets. The number of fish owned is 11 million more than the total number of cats and dogs owned, and 16 million more cats are owned than dogs. (Source: American Pet Products Manufacturers Association) How many of each type of pet do Americans own? |
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| m67041 | An 18-oz jar of peanut butter in the shape of a right circular cylinder is 5 in. high and 3 in. in diameter and sells for $2.89.
In the same store, a 28-oz jar of the same brand is 5 1/2 in. high and 3 1/4 in. in diameter. If the cost is directly proportional to volume, what should the price of the larger jar be? If the cost is directly proportional to weight, what should the price of the larger jar be? |
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| m67052 | An airline with two types of airplanes, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 2000 first-class, 1500 tourist-class, and 2400 economy-class passengers. For a certain trip, airplane P1 costs $12 thousand to operate and can accommodate 40 first-class, 40 tourist class, and 120 economy-class passengers, whereas airplane P2 costs $10 thousand to operate and can accommodate 80 first-class, 30 tourist-class, and 40 economy-class passengers. How many of each type of airplane should be used in order to minimize the operating cost? |
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| m67053 | An airplane is flying at an altitude of 3700 ft. The slanted distance directly to the airport is d feet. Express the horizontal distance h as a function of d. |
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| m67054 | An airplane is flying at an altitude of 3700 ft. The slanted distance directly to the airport is 14,200 ft. How far horizontally is the airplane from the airport? |
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| m67055 | An airplane that can travel 375 mph in still air is flying with a 25-mph tailwind. How long will it take the plane to travel 700 mi with the wind? |
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| m67056 | An airplane that travels 450 mph in still air encounters a 30-mph headwind. How long will it take the plane to travel 1050 mi into the wind? |
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| m67057 | An All-Star baseball player earning $25,000,000 per year plays 162 games per year. If you divide the salary by the number of games, does that baseball player reach this year s maximum taxable income in the first game of the year? |
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| m67061 | An American roulette wheel contains 38 slots numbered 00, 0, 1, 2, 3, c, 35, 36. Eighteen of the slots numbered 1-36 are colored red and 18 are colored black. The 00 and 0 slots are considered to be uncolored. The wheel is spun, and a ball is rolled around the rim until it falls into a slot. What is the probability that the ball falls in each of the following?
1. A red slot
2. A black slot
3. The 00 slot |
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| m67063 | An animal feed to be mixed from soybean meal and oats must contain at least 120 lb of protein, 24 lb of fat, and 10 lb of mineral ash. Each 100-lb sack of soybean meal costs $15 and contains 50 lb of protein, 8 lb of fat, and 5 lb of mineral ash. Each 100-lb sack of oats costs $5 and contains 15 lb of protein, 5 lb of fat, and 1 lb of mineral ash. How many sacks of each should be used to satisfy the minimum requirements at minimum cost? |
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| m67078 | An automobile radiator contains 16 L of antifreeze and water. This mixture is 30% antifreeze. How much of this mixture should be drained and replaced with pure antifreeze so that the final mixture will be 50% antifreeze? |
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| m67083 | An electronics store is selling car chargers for cell phones. The expense function is E = -300p + 13,000 and the revenue function is R = -32p2 + 1,200p.
a. At what price would the maximum revenue be reached?
b. What would that maximum revenue be? Round to the nearest cent.
c. Graph the expense and revenue functions. Circle the breakeven points.
d. Determine the prices at the breakeven points. Round to the nearest cent.
e. Determine the revenue and expense amounts for each of the breakeven points. Round to the nearest cent. |
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| m67084 | An elite private college receives large donations from successful alumni. The account that holds these donations has $955,000,000 currently.
a. How much would the account earn in one year of simple interest at a rate of 5.33%?
b. How much would the account earn in one year at 5.33% if the interest was compounded daily? Round to the nearest cent.
c. How much more interest is earned by compounded daily as com- pared to simple interest?
d. If the money is used to pay full scholarships, and the price of tuition is $61,000 per year to attend, how many more students can receive full four-year scholarships if the interest was com- pounded daily rather than using simple interest? |
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| m67088 | An engineer designs a satellite dish with a parabolic cross section. The dish is 15 ft wide at the opening, and the focus is placed 4 ft from the vertex.
a) Position a coordinate system with the origin at the vertex and the x-axis on the parabola s axis of symmetry and find an equation of the parabola.
b) Find the depth of the satellite dish at the vertex. |
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| m67090 | An equilateral triangle is shown below.
(a) Find an expression for its height h in terms of a.
(b) Find an expression for its area A in terms of a. |
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| m67095 | An experiment was conducted by the authors to determine the relative occurrence of various letters of the English alphabet. The front page of a newspaper was considered. In all, there were 9136 letters. The number of occurrences of each letter of the alphabet is listed in the table below.
a) Complete the table of probabilities with the percentage, to the nearest tenth of a percent, of the occurrence of each letter.
b) What is the probability of a vowel occurring?
c) What is the probability of a consonant occurring? |
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| m67131 | An online job seeking service allows job seekers to post their resumes for free. The service charges employers looking for applicants a fee to look through the resumes. The fee is based on how long the employer wants access to the resumes, and how many miles from the workplace address the employer wants to consider. The fees are $585 for a 100-mile radius for 3 weeks and $675 for a 150-mile radius for 3 weeks.
a. If there are 98 resumes within a 100-mile radius, what is the average cost to the nearest cent to the employer for looking at each resume?
b. If there are 208 resumes within a 150-mile radius, what is the average cost to the employer for looking at each resume?
c. Under the 150-mile radius option, an employer would see the same 98 resumes from part a that he would have seen under the 100-mile radius option. What is the average cost to the employer for looking at the extra resumes he would see if he opted for the more expensive plan? Explain.
d. Give an advantage and a disadvantage of opting for the more expensive plan. |
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| m67133 | An open box is made from a 10-cm by 20-cm piece of tin by cutting a square from each corner and folding up the edges. The area of the resulting base is 96 cm2. What is the length of the sides of the squares? |
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| m67134 | An open box is made from a 10-cm by 20-cm piece of aluminum by cutting a square from each corner and folding up the edges. The area of the resulting base is 90 cm2. What is the length of the sides of the squares? |
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| m67148 | Andrew and Meghan moved into an apartment in the city and pay $2,700 rent per month. The landlord told them the rent has increased 11.1% per year on average.
a. Express the rent y as an exponential function of x, the number of years they rent the apartment. Show.
b. Suppose the rent has increased $200 each year. Express the rent y as a function of the number of years x.
c. Graph the functions from parts and b on the same axes.
d. Describe the difference between how the two graphs show the increase in rent. |
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