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# Algebra and Geometry Notation

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MAT115

Solve all problems and attach your solutions Remember to show all steps and check your work carefully.
Problem Remember to simplify all answers Solutions
1 Name the property that is illustrated.

a) 7  6  6  7

b) 7  (1  9)  (7 1)  9

2 Give the place value for the indicated digit.

a) 8 in the number 138,350

b) 6 in the number 51, 761

3 Find the prime factorization of the number 117.

5 Find the least common multiple of 18, 27, and 45.
6 Four buttons have diameters of , , , and inches. Which button is smallest?

9 Find the circumference of the figure. Use 3.14 for and round your answer to one decimal place.

10 Determine whether the pair of fractions is proportional:

11 Write the following as a common fraction or mixed number, then simplify

0.76
12 Use percent notation to name the shaded portion of the drawing.

8 gal 7 qt
+ 3 gal 2 qt

14 a) Identify the base in the following statement
b) Solve for the amount.

What is 81% of 285?

15 a) Find the supplement of A.
b) Find the compliment of A.

mA  72

16 a) Find m2.

b) Find m1.

17 Label the triangle as equilateral, isosceles, or scalene, then justify your answer.

18 The following scores were recorded on a 100-point examination:
95, 75, 76, 86, 96, 71, 68, 81, 95, 76, 69, 82, 93, 88, 94

Find the mean and median final examination scores.
19 a) Find the mode of the following set of numbers.

b) Find the range of the following set of numbers.

11, 13, 13, 12, 11, 12, 13, 10, 14

20 Find the five-number summary of the following set of numbers.

341, 233, 181, 368, 247, 551, 286, 223, 313

21 Which of the following numbers are integers?

22 Evaluate
a)

b) | -45| + | 33|
23 Evaluate the expressions below.

a)

b)

24 Evaluate the expression, then simplify.

25 Use the bar graph, showing the attendance at a circus for 7 days in September, to find the median attendance over the 7 days.

26 The following pie chart shows the budget for a local company. The total budget is \$520,000. Find the actual amount budgeted in the category of Taxes.

Real World Applications
(Remember to show all steps.)
27 Approximately 5 out of every 10 students at Reye's college live on campus. The college has 8,000 students. How many of them live on campus?

28 Carlos works 8.25 h and receives \$102.30 pay. What will he receive at the same rate if he works 14 h?

29 A circular path around a lake has a diameter of 1,500 feet (ft). Pranotti jogs around the path 3 times for her morning run. How far does she run? Use 3.14 for and round your answer to the nearest foot.

30 Automobiles and small trucks account for 84% of the travel to and from work in the United States. What fraction represents all other means of travel to and from work in the United States?

31 A state sales tax is levied at a rate of 7.5%. How much tax would one pay on a purchase of \$550?

32 If a salesman is paid a \$2,100 commission on the sale of a \$35,000 sailboat, what is his commission rate?

33 The two triangles are similar. Find the indicated side.

Find x.

34 Find the missing length of the right triangle.

35 An airline had 122, 138, 114, and 133 passengers on four flights from San Diego to San Jose during 1 day. What was the total number of passengers?

36 A train traveled 1,176 mi in 21 h. What was the speed of the train? Hint: Speed is the distance traveled divided by the time.

37 A plate glass window measures 5 ft by 7 ft. If glass costs \$7 per square foot, how much will it cost to replace the window?

38 The gas tank in Giorgio's car holds 23 gal when full. The car gets 25 mi/gal. How far can he travel on 4 full tanks?

39 Kristi jogged for of an hour, swam for of an hour, and rode her bicycle for of an hour. How long did she exercise?

40 Jacque earns \$8.60 per hour (h). For overtime (each hour over 40 h) he earns \$12.90 per h. If he works 55.5 h in a week, what pay should he receive?

41 Let's reflect on our resources for this course:
1. Do you feel that the text has good examples?
2. Did you find the extra materials on our topics in Course Materials helpful?
3. If so, how were they helpful?
4. If not, what suggestions can you make so that this material might be more helpful?
What other resources (MathZone, other websites) would you suggest to benefit someone taking this course
42 Now, let's reflect on the entire course:

2.Two things I would change in this class are:

3. I felt frustrated in this class when:

4. I felt good in this class when:

5. If I were Teacher for a Week, I would _________________.
(complete this thought)