OWare- Consumer Math 9. Job Related Services

Refer to the graphic above to answer the question (to the nearest tenth). From your answers in the previous problems, what is the entire area covered by panels of all types?

292

The person casts a shadow ___ feet long. The building casts a shadow ___ feet long. The ratio of the person's shadow to the building's shadow is ___ to ___. If the other side of the building is ___ feet tall, the person will be ___ feet tall

3 15 3 15 2

An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin. How much (to the nearest tenth lb.) of the second alloy must be added to the first alloy to get a 12% mixture.

30

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

30 and 60

Perform the following food service calculation. Meat to be served = fish fillet Amount of stock = 86 lb. How many customers can be served fish?

301

Compute the number of vinyl tiles, measuring 28 inches on each side, needed to tile a kitchen measuring 102 ft. by 18 ft.

338

a = 4 in.; b = 7 in

35.54 (wrong)

Solve this problem in your notebook using the four steps. An angle is 14° more than the measure of its complement. Find the number of degrees in each angle. The angles measure and ___ degrees.

38 and 52

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?

4

Use the formula to solve the problem. Round to the nearest hundredth. Volume of a sphere: V = 4/3r3Surface area of a sphere: A = 4r2 Find the volume of a sphere with a radius of 1 inch.

4.19

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?

43

Perform the following application. Use 3.14 for and round to the nearest tenth. A culvert has a circumference of 280 cm. You wish to seal off both of its ends. What is the culvert's radius? ___ cm. How much material will you need? ___ sq. cm.

44.6 6,246.0

You are going to convert a bedroom in your home to an office. You wish to cover the four walls with panel board (standard size 4' × 8') halfway up each wall. Each wall measures 8 feet in height and 12 feet in length. Assuming no loss, how many panels will you need

5 (wrong)

200/4 = x/1 In the proportion above, what is the value of x?

50

Refer to the graphic above to answer the question (to the nearest tenth). How much area is covered by all the roof panels? Be sure to include the roof panels on the other side of the shed (not shown)

50 (wrong)

The capacity of an automobile cooling system is 16 quarts. It is half full of 15% antifreeze solution. The owner is adding 2 gallons of 90% solution. When he is finished, what will the solution's percentage value be? A gallon is 4 quarts.

52.5%

Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle. The first and second angles measure ___ degrees, and the third angle measures ___ degrees.

54 72

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? I (to the nearest hundredth) = ___ amperes.

54.55

Circumference = 280 cm. (Hint: Find r from C = 2πr (round r to tenths); then find area).

6,246

If the three angles of a triangle have equal measures, find that measure. The measure of each angle is ___ degrees.

60

Find the area and circumference of the following circle. (Round answer to the nearest hundredth.) r = 4.5 cm area = circumference =

63.59 28.26

Perform the following food service calculation. Guests = 160 Meat served = chicken with a bone How many pounds of chicken required?

64

Perform the following food service calculation. Guests = 320 Portions of beets served = 8 oz.\ Size of beet can = 40 oz. How many cans of beets required?

64

Volume of a pyramid: V = 1/3(area of base) x (altitude)Surface area of a pyramid: A = 1/2(perimeter of base) x (slant height) A pyramid has a rectangular base measuring 6' x 4'. If its altitude is 8', what is its volume?

64

Refer to the graphic above to answer the question (to the nearest tenth). How much area is covered by the enclosed end including its gable, and the gable at the open end?

72

a = 4.5 m; b = 5.5 m

77.72

How many roof panels are required?

8

Work the following pricing problems for services rendered. (Round to hundredths.) Labor rate = $8.50 per hour Labor time = 4 3/4 hours Overhead rate = 85% Retail price for parts = $17.75 Total job cost?

92.45

In the figure below, a surveyor put stakes at the lettered points. He used string to determine lengths of line segments and a transit to check that the angles at D and B were both right angles. If CD = 3, CE = 5, DE = 4 and DB = 18, and:

AB= 20

Which of the following are aspects of the building and construction trades?

Electrical work Plumbing

Context does not dictate when to overestimate and when to underestimate. Always round down.

False

Houses can be either domed or octagonal.

False

Knowing how to estimate the amount of food to buy for a meal is not important.

False

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.

N/A

Perform the following food service calculation. No. of diners = 240 Meat served = meat with little bone Amount of meat required?

N/A

Costs related to rent, utilities, administration, equipment use and/or depreciation are called overhead.

True

Which of the following could be costs in calculating overhead?

Utilities Equipment use Rent

Total Price = Labor ___ Overhead

plus

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 (the shadow of flagpole), we can use a proportion to determine the height of the ___.

right flagpole person

Many professions require mixtures of various materials to be precisely formed.

true

The purpose of this lesson is to review concepts from this unit.

true

1. circle 2. ellipse

1. a plane figure bounded by a line, every point of which is equally distant from a point within called the center 2. a plane figure bounded by a line formed by the path of a point that moves so that the sum of its distances from two fixed points remains the same

A mixture of 30 lbs. of candy sells for $1.10 a pound. The mixture consists of chocolates worth $1.50 a pound and chocolates worth 90¢ a pound. How many pounds of each kind were used to make the mixture?

10 20

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 they run an 8-minute mile the factor is 65%. A man weighs 180 lb. He jogs a mile in 8 minutes. How many calories has he used up?

117

Work the following pricing problems for services rendered. (For all calculations use hundredths.) Labor time = 4 1/2 hours Overhead rate = 95% Retail price of parts = $134.75 Total cost of job = $241.98 Hourly rate?

12.22

Refer to the graphic above to answer the question (to the nearest tenth). How much area is covered by all the side panels? Be sure to include the side panels on the opposite side of the shed (not shown).

120

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 labor plus overhead charges?

121.50

A telephone pole has a shadow of 16 ft. when a person 5 ft. tall has a shadow of 6 ft. How tall is the pole? Write answer as a fraction.

13 1/3

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?

15

Work the following pricing problems for services rendered. (Round to hundredths.) Labor rate = $7.00 per hour Labor time = 15 hours Overhead rate = 110% Retail price of parts = $38.75 Total job cost?

154.25 (wrong)

2a = 10 cm; 2b = 20 cm.

157

How many panels are required to cover the sides and end (including the triangular gables)?

16

If 400 bricks measuring 81" by 31" are required to build a wall 42 ft. high, how long is the wall?

166

Use the formula to solve the problem. Volume of a cone: V = 1/3 r2 hLateral Surface area of cone: A = r s, where s= 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.

176

Find the area of the following circle. (Round answer to the nearest hundredth.) d = 15 in area = circumference =

176.63 47.1

Brine is a solution of salt and water. If a tub contains 50 pounds of 5% solution of brine, how much water (to the nearest tenth lb.) must evaporate to change it to an 8% solution?

18.8

Perform the following food service calculation. No. of diners = 240 Portions of juice served = 4 oz. per diner Size of juice can = 48 oz. How many cases of juice required if there are 8 cans in a case and you must buy a whole case?

2 (wrong)

If the boy is 5 ft. tall and his shadow is 4 ft. and the shadow of the flagpole is 16 ft., determine the height of the flagpole.

20

Work the following pricing problems for services rendered. (Round to tenths.) Labor rate = $8.00 per hour Labor time = 6 hours Retail price of parts = $0 Total job cost = $86.00 Overhead rate?

20.8% (wrong)

Work the following pricing problems for services rendered. (Round to hundredths.) Hourly rate, worker A = $15.00 Hourly rate, worker B = $8.00 Hourly rate, worker C = $5.25 Labor time, worker A = 2 1/2 hours Labor time, worker B = 1 hour Labor time, worker C = 3/4 hour Overhead rate = 75% Retail price of goods = $125.50 Total cost of job?

212.02

Perform the following food service calculation. Size of juice can = 54 oz. Portions of juice served = 6 oz. Number of cases used = 2 Number of cans per case = 12 How many guests can be served?

216

To reduce 16 ounces of a 25% solution of antiseptic to a 10% solution, how much distilled water (to the nearest oz.) should a nurse add?

24