1. (4 POINTS) Earth vs. Sun. The mass of Earth is about 6 x 1021 metric tons. The mass of the sun is about 1.998 x 1027 metric tons. About how many times the mass of Earth is the mass of the sun? Express the answer in scientific notation.
Answer: 3.313 x 105
2. (4 POINTS) Perimeter of a Baseball Diamond. The perimeter P of a square of side x is given by the polynomial equation: P=4x A baseball diamond is a square 90 ft on a side. Find the perimeter of a baseball diamond.
Answer :360 ft
3. (4 POINTS) Total Revenue. Hadley Electronics is marketing a new kind of plasma TV. The firm determines that when it sells x TVs, its total revenue R (the total amount of money taken in) will be R = 280x - 0.4x2 dollars. What is the total revenue from the sale of 75 TVs?
Answer: $18, 750
4. (4 POINTS) Lung Capacity. The polynomial equation C = 0.041h - 0.018A - 2.69 can be used to estimate the lung capacity C, in liters, of a female of height h, in centimeters, and age A, in years. Find the lung capacity of a 20-year-old woman who is 165 cm tall.
Answer: 3.715
5. ( 4 POINTS) Handshakes. A researcher wants to investigate the potential spread of germs by contact. She knows that the number of possible handshakes within a group of x people, assuming each person shakes every other person’s hand only once, is given by the following formula. Use this formula for the following exercises. N = ½(x2 – x). a. There are 100 people at a party. How many handshakes are possible? b. Everyone at a meeting shook hands with each other. There were 300 handshakes in all. How many people were at the meeting?
Answer: a) 4950 handshakes b) 25 people
1. (4 POINTS) Construction. It takes Mandy 4 hrs to put up paneling in a room. Omar takes 5 hrs to do the same job. How long would it take them, working together, to panel the room?
Answer: 20/9 hours
2. (4 POINTS) Train Speed. The speed of a B & M freight train is 14 mph slower than the speed of an Amtrak passenger train. The freight train travels 330 mi in the same time that it takes the passenger train to travel 400 mi. Find the speed of each train.
Answer: freight train’s speed 66mph, passenger train’s speed: 80mph
3. (4 points) Tractor Speed. Manley’s tractor is just as fast as Caledonia’s. It takes Manley 1 hr more than it takes Caledonia to drive to town. If Manley is 20 mi from town and Caledonia is 15 mi from town, how long does it take Caledonia to drive to town?
Answer: 3 hours
4. (4 POINTS) Protein Needs. A 120-lb person should eat a minimum of 44 g of protein each day. How much protein should a 180-lb person eat each day?
Answer: 66 g of protein
5. (4 POINTS) Estimating Trout Population. To determine the number of trout in a lake, a conservationist catches 112 trout, tags them, and throws them back into the lake. Later, 82 trout are caught; 32 of them are tagged. Estimate the number of trout in the lake.
Answer: 287 trout
1. (4 POINTS) Hang Time. One of the most exciting plays in basketball is the dunk shot. The amount of time T that passes from the moment a player leaves the ground, goes up, makes the shot, and arrives back on the ground is called the hang time. A function relating an athlete’s vertical leap V, in inches, to hang time T, in seconds, is given by ??????? is given by what???
a. Carl Landry, of Purdue University, has a hang time of about 0.835 sec. What is his vertical leap?
b. The record for the greatest vertical leap in the NBA is held by Darryl Griffith of the Utah Jazz. It was 48 in. What was his hang time?
Answer:
2. (4 POINTS) Falling Distance. An object that is tossed downward with an initial speed (velocity) of????will travel a distance of s meters, where????? and t is measured in seconds. Solve for t.
3. (4 points) Page Numbers. A student opens a literature book to two facing pages. The product of the page numbers is 812. Find the page numbers.
Answer: pages 28 and 29
4. (4 POINTS) Architecture. An architect is designing the floors for a hotel. Each floor is to be rectangular and is allotted 720 ft of security piping around walls outside the rooms. What dimensions of the atrium will allow an atrium at the bottom to have maximum area?
Answer: 180 ft by 180 ft
5. (4 POINTS) Minimizing Cost. Aki’s Bicycle Designs has determined that when x hundred bicycles are built, the average cost per bicycle is given by , ?????
where ????is in hundreds of dollars. How many bicycles should the shop build in order to minimize the average cost per bicycle?
- (4 POINTS) Pendulums. The period of a pendulum is the time it takes to complete one cycle, swinging to and fro. For a pendulum that is L centimeters long, the period T is given by the function
T(L) =???????????
where T is in seconds. Use 3.14 for and find, to the nearest hundredth of a second, the period of a pendulum of length (a) 65 cm; (b) 98 cm;
- (4 POINTS) Musical Performances. The group *NSYNC regularly performed outdoors for large audiences. A scientific instrument at one of their concerts determined that the sound of the group was traveling at a rate of 1170 ft/sec. What was the air temperature at the concert?
Use the formula ….. what formula?? Type it here!
3. (4 POINTS) Ramps for the Disabled. Laws regarding access ramps for the disabled state that a ramp must be in the form of a right triangle, where every vertical length (leg) of 1 ft has a horizontal length (leg) of 12 ft. What is the length of a ramp with a 12-ft horizontal leg and a 1-ft vertical leg? Give an exact answer and an approximation to three decimal places.
Answer: square root of 145 = 12.0416 ft
- (8 POINTS) Wind Chill Temperature. Because wind enhances the loss of heat from the skin, we feel colder when there is wind than when there is not. The wind chill temperature is what the temperature would have to be with no wind in order to give the same chilling effect as with the wind. A formula for finding the wind chill temperature, Tw, is ,
Tw=?????????????????????????????
where T is the actual temperature given by a thermometer, in degrees Fahrenheit, and v is the wind speed, in miles per hour.* Use a calculator to find the wind chill temperature in each case. Round to the nearest degree.