General Term of Arithmetic Sequence that Models the Potential Annual Salaries

Problem
A job posted at jobstreet.com offered a starting salary of \$40,000 per year and guaranteeing a raise of \$1600 per year for the rest of 5 years. Write the general term for the arithmetic sequence that models potential annual salaries.

A.   an = 38,400 + 1600n
B.   an = 33,400 + 2600n
C.   an = 36,400 + 1400n
D.   an = 34,400 +1800n

Weight of Copper and Tin to Produce an Alloy of 30% Copper and 10% of Tin

Problem
A given alloy contains 20% copper and 5% tin. How many pounds of copper and of tin must be melted with 100 lb of the given alloy to produce another alloy analyzing 30% copper and 10% tin? All percentages are by weight.

A.   20.5 lb copper and 4.5 lb tin
B.   17.5 lb copper and 7.5 lb tin
C.   19.5 lb copper and 5.5 lb tin
D.   18.5 lb copper and 6.5 lb tin
2016-may-math-mixture-problem-copper-tin-alloy.gif

 

Nutrition: Amount of food A, B and C to Meet the Nutrient Requirements

Problem
A nutritionist in a hospital is arranging special diets that consist of a combination of three basic foods. It is important that the patients on this diet consume exactly 310 units of calcium, 190 units of iron, and 250 units of vitamin A each day. The amounts of these nutrients in one ounce food are given in the following table.

  Units Per Ounce
Calcium Iron Vitamin A
Food A 30 10 10
Food B 10 10 30
Food C 20 20 20

How many ounces each food must be used to satisfy the nutrient requirements exactly?

A.   6 ounces of Food A, 5 ounces of Food B and 3 ounces of Food C
B.   3 ounces of Food A, 5 ounces of Food B and 6 ounces of Food C
C.   6 ounces of Food A, 3 ounces of Food B and 5 ounces of Food C
D.   5 ounces of Food A, 3 ounces of Food B and 6 ounces of Food C

Samuel Pepys Wrote Isaac Newton Asking Which Event is More Likely to Occur

Problem
Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (a) at least 1 six when 6 dice are rolled (b) at least two sixes when 12 dice are rolled, or (c) at least 3 sixes when 18 dice are rolled. What is the answer?

A.   (a) is more likely than (b) and (c)
B.   (b) is more likely than (a) and (c)
C.   (c) is more likely than (a) and (b)
D.   (a), (b), and (c) are equally likely

Strength of Temporary Earth Retaining Wall Made from Wooden Planks

Situation
A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Given the following:
Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick
Allowable bending stress of the plank = 10.4 MPa
Allowable shear stress of the plank = 0.8 MPa
Unit weight of retained soil = 17.3 kN/m3
Active earth pressure coefficient = 1/3

1.   Calculate the maximum flexural stress.

A.   12.7 MPa C.   8.6 MPa
B.   14.2 MPa D.   10.1 MPa

2.   Calculate the maximum shear stress.

A.   1.11 MPa C.   0.99 MPa
B.   0.33 MPa D.   0.77 MPa

3.   Calculate the minimum thickness of the plank to prevent failure.

A.   90 mm C.   110 mm
B.   80 mm D.   100 mm

Burning Bale from Catapult to Travel 150 ft and Clear Over 35 ft Castle Wall

Problem
A catapult is placed 100 ft from the castle wall, which is 35 feet high. The soldier wants the burning bale of hay to clear the top of the wall and land 50 feet inside the castle wall. If the initial velocity of the bale is 70 feet per second, then at what angle should the bale of hay be launched so that it travel 150 feet and pass over the castle wall. Use g = 32 ft/sec2.
 

2016-may-math-catapult.jpg

 

A.   49.8° C.   39.2°
B.   50.8° D.   40.2°

 

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