Quiz 4: Application Problems, REVIEW, Test: Job Related Services

16 cans

A #10 can yields 120 oz. of pineapple. A restaurant plans to give each guest an 8-oz. portion. They estimate there will be 240 guests. How many #10 cans will be needed?

1728 cubic cm

A rectangular solid has sides 16 cm, 12 cm, and 9 cm. What is its volume?

478 square centimeters

A rectangular solid has sides of 7 cm, 9 cm, and 11 cm. What is its surface area?

640 square feet

Choose the right answer. Mr. Klampett has been asked to partition some space in a garage for storage. He estimates 8 square feet of storage space per individual will be required to meet the needs of 12 people. If the storage space takes up 15% of the garage, what is the size of the garage?

56 cm²

Compute the area of a triangle with the following measurements: h = 8 cm b = 14 cm

49 m²

Determine the area of the following triangle: A right triangle has two perpendicular sides measuring 7 meters and 14 meters.

510 sq. km

Find the area of a rectangle if one side is 20 km and other side is 25.5 km.

120 cm³

Find the area of a trapezoid with the following measurements: a = 8 cm b = 16 cm h = 10 cm

113.04 square yards

Find the area of the following circle. Use π=3.14. r = 6 yd

175.9 sq. in.

Find the area of the following ellipse. Use π=3.14 and round to nearest tenth. a = 8 in ; b = 7 in

45

How large is an angle whose supplement is three times its complement? The measure of the angle is _____ degrees.

15.0

The boy is 4' 9" tall and his shadow is 6 ft. If the shadow of the flagpole is 19 ft., determine the height of the flagpole (to the nearest tenth).

40 ft.

A contractor is pouring a concrete driveway. The perimeter of the driveway is 108 ft. What is the length of the driveway if the width is 14 ft.? The driveway is _____ feet long.

28.6 lbs

A diner is serving boneless chicken to 100 guests. How many pounds of chicken does the diner need to buy? Calculate your answer to the nearest tenth of a pound. To calculate the pounds of meat needed to feed diners do the following: for poultry or meat with bones, divide the number to be served by 2.5; for meat with little or no bone, divide the number to be served by 3.5; and for fish fillets divide the number to be served by 3.5.

15 pounds

An alloy of copper is 10% copper and weighs 25 pounds. A second alloy is 18% copper. How much (to the nearest lb.) of the second alloy must be added to the first alloy to get a 13% mixture.

10 lbs 20 lbs

An alloy weighing 30 lbs. is 11% tin. The alloy was made by mixing a 15% tin alloy and a 9% tin alloy. How many pounds of each alloy were used to make the 11% alloy? ____ lbs. of the 15% alloy and _____ lbs. of the 9% alloy.

11.4 lbs. 28.6 lbs.

An alloy weighing 40 lbs. is made of 10% tin. The alloy was made by mixing a 15% tin alloy and an 8% tin alloy. How many pounds of each alloy (to the nearest tenth) were used to make the 10% alloy?

40° and 50°

An angle is 10° more than the measure of its complement. What are the measurements of both angles?

81 in²

Choose the best answer. A square measures 9 inches on each side. What is it's area rounded off to the nearest whole number.

no

Choose the right answer. If you have a rectangular space with dimensions of 180 ft. x 75 ft., and 20,000 square feet is required by 45 cars, do you have sufficient space for 45 cars?

480 sq. ft.

Choose the right answer. Mr. Thompson has been asked to add storage space to a garage. He estimates 6 square feet per individual will be required to meet the needs of 12 people. If the storage space is 15% of the total amount of space required, how much total space does Mr. Thompson have?

4

Choose the right answer. The Marrieds are planning to serve 380 guests at a breakfast event. They plan to serve tomato juice, which comes in 46 oz. cans. Assuming they plan to serve each guest a 5 oz. portion and that there are 12 cans in a case, how many cases of tomato juice will they need? Number of cases needed = ___ cases

43 lbs.

Choose the right answer. To calculate the number of pounds of meat required to feed diners do the following: for poultry or meat with bones, divide the number to be served by 2.5; for meat with little or no bone, divide the number to be served by 3.5; and for fish fillets divide the number to be served by 3.5. You are negotiating with a caterer on a plan to serve ground round steak. You estimate you will have 150 guests. How many pounds of round steak should you be charged for? Number of pounds of meat = _____ lbs.

461 tiles

Compute the number of vinyl tiles, measuring 10 in. each side, needed to tile a kitchen measuring 20 ft. by 16 ft.

similar flagpole flagpole

If we want to find the height of an object like a flagpole, we can use ________ triangles. In the graphic above, triangle ABE is similar to triangle ACD. In the graphic line segment DC is the height of the _______. Using the length of BE (your height), AB (your shadow), and AC (shadow of flagpole), we can use a proportion to determine the height of the _______.

1250 r.p.m.

In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; it usually runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Suppose an engine is running 2,000 r.p.m. in second gear. How fast is the drive shaft running? Drive shaft rotation = ________ r.p.m.

5 ft.

In this fulcrum, the weights are perfectly balanced. How far must the fulcrum be located from the 40 lb. weight if the bar is 9 feet long? x = ____ ft.

117 calories

The number of calories used per mile of jogging is determined both by an individual's weight and speed of running. Individuals of the same approximate weight running 6 mph or 1 mile every ten minutes have a calorie use factor of 62% of their weight; i.e. calories burned = (weight)(0.62). If a person runs an 8-minute mile, the factor is 65%. A man weighs 180 lb. He runs a mile in 8 minutes. How many calories does he use? Round to the nearest calorie.

12.8

To reduce 16 ounces of a 18% saline solution to a 10% solution, how much distilled water (to the nearest tenth oz.) should a nurse add? The nurse should add _______ oz. of distilled water.

54.55

Use the following equation to answer the question: I=ER A car has a 12-volt battery. The engine has a resistance of 0.22 ohms. How many amps will be drawn from the battery when the key is turned? Round your answer to the nearest hundredth.

144 lb.

Use the formula to answer the question. x/y = 45/100 This proportion can be changed to (0.45)y = x, where x represents the person's weight in kilograms and y represents the person's weight in pounds. The recommended protein intake in grams is numerically equal to the person's weight in kilograms. If a man intakes 65 g of protein daily, his recommended intake, how much does he weigh in pounds? Round to the nearest pound.

15 m

Use the formula to solve the problem. Area of a trapezoid = (1/2)(a + b)h, where a and b are the lengths of the two parallel sides and h is the altitude. The area of a trapezoid is 375 m². If the two parallel sides are 20 m and 30 m, respectively, what is the altitude of the trapezoid?

176 cm²

Use the formula to solve the problem. Volume of a cone: V = 1/3πrh² Lateral surface area of a cone: A = πrs, where s equals slant height. Find the lateral surface area of a cone whose base is a circle with a 5 cm radius and whose altitude is 10 cm. Round to the nearest cm².

64 cubic ft.

Use the formula to solve the problem. Volume of a pyramid: V = 1/3(area of base) × (altitude) Surface area of a pyramid: A= 1/2(perimeter of base) × (slant height) A pyramid has a rectangular base measuring 6′×4′. If its altitude is 8′, what is its volume?

$121.50

Your heavy-duty mechanics earn $30.00 per hour. Your light-duty servicemen earn $10.50 per hour. Assume a customer wants his engine tuned, oiled, and greased. If the job takes 1 1/2 hours of a mechanic's time, 1 1/2 hours of a serviceman's time, and the overhead rate is 100%, what are the total charges (to the nearest cent)?

113.0 sq. inches

A circle has a radius of 6 inches. What is its area? Use 3.14 for π and round to the nearest tenth.

$213.75

A mason's assistant's rate of pay is $0.95 per cubic foot of earth moved. He digs a trench 1.5 ft. wide by 1 ft. deep by 150 ft. in length. What is his pay for this job?

55 ohms

Calculate the resistance for this automotive-services problem. Voltage = 220 v Current = 4 amps

1130.4 cm³

Find the volume of a cylinder with an elliptical base that has a major semiaxis of 6 cm, a minor semiaxis of 5 cm, and an altitude of 12 cm. Use 3.14 for pi. Round your answer to the nearest tenth.

50 r.p.m

If pulley A rotates at 500 r.p.m., then how fast must pulley D be rotating? r.p.m. of pulley D = _____ r.p.m.

88 ft.

A contractor is building a circular swimming pool. The radius of the circle is 14 feet. He needs to know the circumference in order to buy tile to put around the edge of the pool. What is the circumference if he uses π=22/7?

7 inches

A cube has a surface area of 294 sq. in. What is the length of its sides?

8

Bob is cooking hamburgers. If he serves each guest an 8 oz. portion, how many people can he serve from a package of hamburger that weighs 70 oz.? ____ people

23

Brine is a solution of salt and water. If a tub contains 70 pounds of a 5% solution of brine, how much water (to the nearest whole lb.) must evaporate to change it to an 7.5% solution? ______ lbs. of water must evaporate.

50.4 grams

Calculate the protein intake of Miss Exercise who weighs 112 lb. Remember: (0.45)(w−lb)=(w−kg) and the recommended protein in grams is numerically equal to the person's weight in kilograms.

60 lb.

Given the axle in the figure, how much force must be used to lift the weight? Force = ___ lb.

6,000 24

If a rectangular lot measures 120ft. x 80ft., and 10 foot set backs are required from each lot line, how much area is left? If a kennel for 50 dogs requires 12,500 square feet, how many dogs can be accommodated in the small rectangle? Use whole numbers. There will be ______ square feet in the smaller lot. The number of dogs allowed is ________.

24.8 ft.

If the boy is 5' 6" tall, his shadow is 4 ft., and the shadow of the flagpole is 18 ft., determine the height of the flagpole. Round your answer to the nearest tenth.

44.6 cm 12492.0 sq. cm

Perform the following application. Use 3.14 for π and round to the nearest tenth. A culvert has a circumference of 280 cm. You wish to seal off both of its ends. Find the radius of the culvert and calculate how much material you will need to cover the culvert on both ends. Radius = ______ cm Material Needed = _____ sq. cm

1167 r.p.m.

Solve the following automotive-services problem. In first gear, or low gear, an automobile's engine runs about three times as fast as the drive shaft. In second gear, the engine does not have to run as fast; usually, it runs about 1.6 times faster than the drive shaft. Finally, in third, or high gear, the engine runs at the same speed as the drive shaft. Engine speed = 3,500 r.p.m. Transmission in first gear What is the drive-shaft speed (to nearest r.p.m.)?

33 and 55

Solve this problem. Two angles are complementary. One contains 20° more than the other. Find both angles. The measures of the angles are ______and _____ degrees.

30 and 60

Solve this problem. Two angles are complementary. One contains 30° more than the other. Find both angles. The measures of the angles are ___ and ___ degrees.

152

The diagram shows the floor plan of a one-bedroom apartment. Find the area of the bedroom in square feet. Round to nearest square foot.

85 sq. ft.

The diagram shows the floor plan of a one-bedroom apartment. Find the area of the dining room in square feet. Round your answer to the nearest square foot.

48 cm²

Use the formula to solve the problem. A=(1/2)bh Determine the area of a triangle whose base is 12 cm and whose altitude is 8 cm.

30.2 sq. ft.

Use the formula to solve the problem. Area of an ellipse: A = πab, where a and b are the semiaxes of the ellipse. You must cover a hole that is elliptical in shape. You measure the major and minor axes and find them to be 6 ft. and 4.5 ft. respectively. If you want a 6 inch overhang around the hole, how much covering will you need? (Round to the tenth.)

4.19 cubic in.

Use the formula to solve the problem. Round to the nearest hundredth. Volume of a sphere: V=4/3πr³ Surface area of a sphere: A=4πr² Find the volume of a sphere with a radius of 1 inch.

$10.90

What is the hourly rate for labor? (For all calculations use hundredths.) Labor time = 8 hours Overhead rate = 65% Retail price of parts = $98.70 Total cost of job = $242.58

$60.19

You must give an estimate to service an automobile. The hourly rate for labor is $7.50. You estimate the job will take 2 1/2 hours. The overhead rate at your shop is 85%. You also figure that parts to be used total $25.50 retail. How much is the job estimate (to the nearest cent)?

155520 cubic inches 3240 bricks

You plan to construct a brick wall measuring 15 ft. in length, 6 ft. high, and 1 ft. in width. If a brick measures 6 in. x 4 in. x 2 in., how many bricks will you need to make the wall? (Remember to round up.) Total volume (to the nearest cubic inch) = ____ cubic inches Number of bricks needed = _____