solve the problem using inductive reasoning. - blinn · pdf filesolve the problem using...

Solve the problem using inductive reasoning.
1) In how many ways can you exactly cover the last two diagrams with "dominoes" that are just the size of two
small squares?
2) Find the number of games played in a round robin tournament for the given numbers of teams. In a round
robin tournament every team plays every other team once.
Number of teams Number of games played
3 teams 3 games
4 teams 6 games
5 teams 10 games
6 teams __ games
7 teams __ games
Look for a pattern. Find the number of games played in a round robin tournament involving n teams. Find the
number of games played in a round robin tournament involving 16 teams.
Draw the next figure in the pattern.
3)
4)
5)
1

Use inductive reasoning to predict the next line in the pattern.
6) 9 9 = 81
99 99 = 9801
999 999 = 998,001
7) 40 - 9 = 31
400 - 89 = 311
4000 - 789 = 3211
Use inductive reasoning to predict the next number in the sequence.
8) 0, 4, 4, 0, -4, ...
9) 3, 5, 6, 10, 12, 20, ...
Solve the problem using inductive reasoning.
10) Find the next term in the following sequence.
F, S, S, M, T
11) Find the 4th triangular number that corresponds to the following dot sequence.
Estimate the answer from the table or graph.
12) The number of students at Alder High School who studied foreign languages in different years is shown in the
bar graph. What is the total number of students who studied a foreign language in 2012? (Assume no student
studied two foreign languages).
2006 2008 2010 2012
Year
A) 150 students B) 130 students C) 90 students D) 170 students
2

13) In a shop that sells a variety of nuts, the prices of some items are as given below. If Sarah buys 2 lb of cashews, 1
lb of walnuts, and 2 lb of raisins, how much did she have to pay?
Item Cost/lb
Almonds $4.30
Walnuts $3.80
Cashews $4.80
Pecans $3.80
Raisins $3.50
14) The graph shows the average monthly cost of a wireless phone service for the years 2005 through 2012. Estimate
the average monthly cost of this wireless phone service in 2006.
x2005 2006 2007 2008 2009 2010 2011 2012
y70
60
50
40
30
20
10
Year
Cost (dollars)
x2005 2006 2007 2008 2009 2010 2011 2012
y70
60
50
40
30
20
10
Year
Cost (dollars)
A) $37 B) $44 C) $34 D) $31
Solve the problem.
15) One gallon of a driveway sealant covers an area of 180 ft2. How many gallons of the sealant are needed to cover
a 900 ft2 driveway?
16) To make orange juice from concentrate powder, you need to mix 2.5 teaspoons of the concentrate in 16 ounces
of water. How much concentrate powder do you need for 1 gallon of water?
17) The cost of gasoline is $4.40 per gallon. Jane's car gives a mileage of 35 miles per gallon. Approximately how
much did Jane pay for gasoline for a trip of 491 miles?
18) An airport parking lot charges $4.50 for the first two hours of parking and $1.00 for each additional half hour or
part thereof. If Sam parks his car for 7 hours, how much does he pay for parking?
19) A small farm field is a square measuring 350 ft on a side. What is the perimeter of the field? If you double the
length of each side of the field, what is the new perimeter?
20) A boxer takes 3 drinks of water between each round for the first four rounds of a championship fight. After the
fourth round he starts to take his three drinks plus one additional drink between each of the remaining rounds.
If he continues to increase his drinks by 1 after each round, how many drinks will he take between the 14th and
15th round?
3

21) Missy and Adam work at different jobs. Missy earns $7 per hour and Adam earns $5 per hour. They each earn
the same amount per week but Adam works 2 more hours. How many hours a week does Adam work?
22) An average newspaper contains at least 16 pages and at most 87 pages. How many newspapers must be
collected to be certain that at least two newspapers have the same number of pages?
Use the table or graph to answer the question.
23) Amy graphed her utility bills for the last year for her records. Estimate the total amount Amy paid for her
utilities for the month of January.
24) The following chart shows an appliance store's average percent profit margin on certain items:
Product category Average profit margin,%
Washer/Dryer 17
Refrigerator 13
Stove 16
Microwave 40
What is the average profit for the store if it lists the price of a particular refrigerator at $800?
Complete the magic (addition) square.
25) Use each number 26, 27, 28, 29, 30, 31, 32, 33, and 34 once.
31
30 28
27 34
26) Use each number 20, 21, 22, 23, 24, 25, 26, 27, and 28 once.
22 23
24 28
21
4

Solve the problem.
27) A die is rolled 50 times with the following results.
Outcome 1 2 3 4 5 6
Frequency 11 2 24 8 0 5
Compute the empirical probability that the die comes up a 5.
28) Three coins are tossed 80 times and the number of heads is observed.
Outcome no heads one head two heads three heads
Frequency 9 15 33 23
Compute the empirical probability that at most two heads occur.
29) This spinner is spun 36 times. The spinner landed on A 17 times, on B 11 times, and on C 8 times. Compute the
empirical probability that the spinner will land on B.
30) A die is rolled 100 times with the following results.
Outcome 1 2 3 4 5 6
Frequency 12 12 28 28 11 9
Compute the empirical probability that the die comes up 2 or 3.
31) Two coins are tossed 20 times and the number of tails is observed.
Outcome 2 tails 1 tail 0 tails
Frequency 6 8 6
Compute the empirical probability that exactly one tail occurred.
Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low.
32) Four of a kind (4 cards of the same value)
33) Full house (3 cards of one value, 2 of another value)
34) Straight (5 in a row, but not a straight flush)
35) Flush (5 in same suit, but not a straight flush)
36) Royal flush (5 highest cards of a single suit)
5

Find the probability. Round to the nearest ten-thousandth when necessary.
37) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random. Find
the probability that you have all cherry candies.
the probability that you have 1 cherry candy and 2 lemon candies.
39) A bag contains 6 cherry, 3 orange, and 2 lemon candies. You reach in and take 3 pieces of candy at random.
What is the probability that you have at least 2 cherry candies?
the probability that you have 2 orange candies and 1 lemon candy.
What is the probability that you have at least 2 orange candies?
What is the probability that you have at least 1 lemon candy?
the probability that you have all lemon candies.
the probability that you have one candy of each flavor.
45) A coin is biased to show 42% heads and 58% tails. The coin is tossed twice. What is the probability that the coin
turns up heads on the second toss?
46) A coin is biased to show 39% heads and 61% tails. The coin is tossed twice. What is the probability that the coin
turns up heads once and tails once?
47) A fair coin is tossed 5 times. What is the probability of exactly 2 head(s)?
Find the probability.
48) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly four fives? Round to the
nearest ten-thousandth.
49) A child rolls a 6-sided die 6 times. What is the probability of the child rolling exactly three sixes? Round to the
nearest ten-thousandth.
50) A child rolls a 6-sided die 6 times. What is the probability of the child rolling no more than three twos? Round
to the nearest ten-thousandth.
51) A die is rolled 20 times and the number of twos that come up is tallied. Find the probability of getting more
than three twos. Round to the nearest thousandth when necessary.
52) In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 physics majors is
chosen. Find the probability that 2 or less are ethnic minorities. Round to the nearest ten-thousandth.
6

53) In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 physics majors is
chosen. Find the probability that 7 or more are ethnic minorities. Round to the nearest ten-thousandth.
54) In a certain college, 33% of the physics majors are ethnic minorities. A random sample of 10 phys

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