MAT 115 – Basic Mathematics

Week #6 Checkpoint Chapters 6 and 7

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Instructions: For each assigned problem show your complete solution in the left column under each problem. Show all work for each problem (using either MathType or Equation Editor) in order to receive credit. Be sure to reduce all fractions to lowest terms. If there is no work to show then explain in words how you solved the problem. Points will be deducted if there is insufficient explanation or work.

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Problems
(Enter your work and answer in this column) / Instructor’s comments
Section 6.1 – p. 441, # 58 a & c
58 (1 pt) Find the decimal and fractional notation:
a.  9%



c. 6%





Section 6.2 – p. 448, # 34
34. (1 pt) Write as a percent:
Convert to a decimal
= 1.2
Multiply by 100%
= 120%
Section 6.3 – pp. 456–457, # 12, 18
12. (1 pt) Identify the rate, base and amount. Do not solve:
150 is 75% of what number?
Rate: the percentage = 75%
Base: the number we’d have to solve for
Amount: 150, since that is 75% of something
18. (1 pt) Identify the rate, base and amount. Do not solve:
Business and finance. In a shipment of 750 parts, 75 were found to be defective. What percent of the parts were faulty?
Rate: the unknown percentage
Base: 750, the total number of parts
Amount: 75, the defective parts
Section 6.4 – p. 465, #46, 50
46. (1 pt) Solve: 6.5% of what number is 325?
0.065x = 325
Divide by 0.065:
x = 5000
50. (1 pt) Estimate the amount:
What is 48.3% of 1,500?
That is about half of 1500:
750
Section 6.5 – pp. 477–485, #6, 26, 42, 56, 68, 70
6. (1 pt) Business and finance. Ms. Jordan has been given a loan of $2,500 for 1 year. If the interest charged is $275, what is the interest rate on the loan?
Divide to get the rate:
275/2500
= 0.11
Multiply by 100%
= 11%
26. (1 pt) Social science. A school had 900 students at the start of a school year. If there is an enrollment increase of 7% by the beginning of the next year, what is the new enrollment?
Multiply:
7% times 900
7% = 0.07
0.07 times 900
= 63
That is the increase, so add to the original amount:
900 + 63
= 963
42. (1 pt) Business and Finance. A virus scanning program is checking every file for viruses. It has completed checking 40% of the files in 300 seconds. How long should it take to check all the files?
40% = 0.4
Divide the 300 by that:
300/0.4
= 750 seconds
56. (1 pt) Social science. Gasoline accounts for 85% of the motor fuel consumed in the United States every day. If 8,882 thousand barrels (bbl) of motor fuel is consumed each day, how much gasoline is consumed each day in the United States? Round to the nearest bbl.
85% = 0.85
Multiply by the total:
0.85*8882
= 7549.7
Rounds to:
7550 bbl
68. (1 pt) Business and finance. Jerry earned $18,500 one year and then received a 10.5% raise, What is his new yearly salary?
The increase is: 0.105 times 18500 = 1942.5
Add that to the original amount:
1942.5+18500
= $20442.50
70. (1 pt) Business and finance. Yi Chen made a $6,400 investment at the beginning of a year. By the end of the year, the value of the investment had decreased by 8.2%. What is its value at the end of the year?
The new percentage is:
100-8.2 = 91.8%
Multiply that by the 6400:
6400 times 0.918
= $5875.20
Section 7.1 – pp. 508–509, # 50, 54, 74
50. (1 pt) Add and simplify

Add the hours:
3+4+5 = 12
Add the minutes:
20 + 25 + 35 = 80 min = 1 hr 20 min
Total:
13 hr 20 min
54. (1 pt) Subtract:

Subtract the pounds: 9-5 = 4
Subtract the oz: 15-8 = 7
4 lb 7 oz
74. (1 pt) Crafts. Mark uses 1 pt 9 fl oz and then 2 pt 10 fl oz from a container of film developer that holds 3 qt. How much of the developer remains?
3 quarts = 6 pints
1 pint = 16 oz
3 quarts = 96 oz
96 oz – (16+9) – (32+10)
= 29 oz left over
Section 7.2 – p. 520, # 50
50. (1 pt) What units in the metric system would you use to measure each of the following quantities?
a)  Distance from Los Angeles to New York.
Very far -- kilometers
b)  Your waist measurement.
I’m not “too” big, so centimeters
c)  Width of a hair
Very tiny, so millimeters
d)  Your height.
I’m normal height, so meters
Section 7.3 – p. 528, # 70
70. (1 pt) Science and medicine. The United States emitted 19.5 million t of nitrogen oxides (NO) into the atmosphere in 1987. One metric ton (1 t) equals 1,000 kg. How many kilograms of NO were emitted to the atmosphere in the United States during 1987?
19.5 million = 19500000
Multiply by 1000 kg:
19500000000 kg
Section 7.4 – p. 533, # 6, 12, 18
6. (1 pt) Complete the statement. (Round to the nearest hundredth.)
72 in. = cm
1 in = 2.54 cm, so 72 times 2.54
= 182.88 cm
12. (1 pt) Complete the statement. (Round to the nearest hundredth.)
7 L = qt
1 L = 1.05668821 qt
Multiply by 7:
= 7.39681747 qt
Rounds to:
7.40 quarts
18. (1 pt) Science and medicine. Samantha’s speedometer reads in kilometers per hour. If the legal speed limit is 55 mi/h, how fast can she drive in kilometers per hour?
1 mi/hr = 1.609344 km/hr
55 times 1.609344
= 88.51392 km/hr
Round:
88.51 km/hr
Section 7.5 – pp. 546–550, # 6, 26, 52
6. (1 pt) Identify as a line or line segment and explain your answer.

It is a line, since it goes infinitely in each direction (assuming that you aren’t asking specifically about the part between u and v)
26. (1 pt) Give an appropriate name for the indicated angle:

It is acute, since it is less than 90 degrees.
52. (1 pt) Find mÐa, mÐb, mÐc:

mÐa = 56
because of alternate exterior angles
mÐb = 124
because straight lines add to 180, so: 180-56 = 124
mÐc = 124
because straight lines add to 180, so: 180-56 = 124
Section 7.6 – pp. 557–563, # 2, 10, 24, 26, 44
2. (1 pt) Label the triangle as acute or obtuse, explain your answer

It is obtuse, since the upper left angle is larger than 90 degrees
10. (1 pt) Label as equilateral, isosceles, or scalene, explain your answer

It is scalene, since the sides are not the same length.
24. (1 pt) Assume the given triangle is isosceles:
Find mÐD and mÐF:

mD = mF = (180-72)/2 = 54 degrees
They have to be equal, and the whole thing must add to 180 degrees
26. (1 pt) Which two triangles are similar? Explain how you know they are similar.



Triangles “a” and “b” are similar since they are both 30-60-90 triangles. The angles must add to 180 degrees, and the non right angle in triangle C is not 30 or 60.
44. (1 pt) A tree casts a shadow that measures 5 m. At the same time, a meter stick casts a shadow that is 0.4 m long. How tall is the tree?

Set up a proportion:

Cross multiply:
0.4x = 5
Divide by 0.4:
x = 12.5 meters
Section 7.7 – p. 570, # 4, 16
4. (1 pt) Find the square root:

What number multiplied by itself equals 196?
14 times 14 = 196
= 14
16. (1 pt) Find the missing length:

Use the Pythagorean Theorem:





Mat 115 Week #6 Checkpoint