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Welcome back!
1/6/2015
Let’s review some of the topics we have discussed so
far this year…
7.3a
The table below lists the amounts of leading farm products that the
United States exported to other countries in the year 2000.
Product
Amount in millions of
metric tons
Corn
50.5
Cotton
6.8
Rice
2.8
Soybeans
26.5
Wheat
30.0
50.5 + 6.8 + 2.8 + 26.5 + 30 =
116.6
What is the total amount, in millions of metric tons, of farm products
the United States exported in the year 2000?
A
79.6
B
89.6
C
114.6
D
116.6
7.4b
Haley bought 1.6 pounds of almonds for $13.20. How much
did she pay per pound for the almonds?
13.20 ÷ 1.6 =
$8.25 per pound
$13.20
1.6 𝑙𝑏𝑠
=
$?
1 𝑙𝑏
7.4d
Thomas observed that his friend blinked an average of three
times every 15 seconds. How many times should his friend
blink in 65 seconds?
3 x 65 = _____
15x = 195
X = 13
3 𝑏𝑙𝑖𝑛𝑘𝑠
15 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
=
𝑥 𝑏𝑙𝑖𝑛𝑘𝑠
65 𝑠𝑒𝑐𝑜𝑛𝑑𝑠
7.4e
Gordon went mountain biking and rode 23 miles in 4 hours. At this
rate, what was the approximate number of miles he can ride in 30
minutes?
23 x .5 = ______
4x = 11.5
X = 2.875
A
B
C
D
5 miles
4 miles
3 miles
2 miles
23 𝑚𝑖𝑙𝑒𝑠
4 ℎ𝑜𝑢𝑟𝑠
=
𝑥 𝑚𝑖𝑙𝑒𝑠
.5 ℎ𝑜𝑢𝑟𝑠
7.4e
Bell Ringer
1/7/2015
A 3.2 pound package of ground beef costs $8.16. What is the
price per pound?
8.16 ÷ 3.2 =
$ 2.55
$8.16
3.2 𝑙𝑏𝑠
=
$𝑥
1 𝑙𝑏
Great ournals
(Your notes should
look like this)
1. Your pages should be full (No
wasted space).
2. You should write the question,
the answer, and the work showing
how to solve it.
3. You should be able to read it (If
you give your notebook to the
person next to you, can they read
it? If not, we have a problem)
7.11a
Consider the inequality:
3x + 2 > –1
Use the model to of the inequality to find the solution.
3x + 2 > –1
–2 –2
A
B
x > –1
x>1
3x + 0 > – 3
C
1
x>
3
3x > – 3
3
3
D
1
x>–
5
X > –1
7.13b
The table below shows a portion of the planned budget for the
Jones family. Their monthly income is $6,500.
BUDGET ITEM
Retirement Savings
Emergency Savings
Housing Expenses
AMOUNT
$700
$550
$1,300
Which of the following shows the percentage of income used for
housing expenses?
1,300
A
20%
= .2 = 20%
B
18%
6,500
C
23%
D
10%
7.13a
Bell Ringer
1-8-15
Kevin is an employee at Good Electronics. The electricity is not working
one day after a thunderstorm, but Kevin still has to charge customers for
their purchases. He writes up the following sales ticket by hand.
Good Electronics
972-555-5555
Wireless Router
$89.00
Ethernet Cable
$15.00
Wire Cutters
$6.00
Subtotal
Tax (8.25%)
$110.00
$9.075 = $9.08
Total
$119.08
How much should Kevin charge the customer for their total?
A
$110.00
B
$9.08
C
$118.25
D
$119.08
Decimal Rules
When Adding and Subtracting: Line up the decimals.
When Multiplying: Do NOT line up the decimals.
When Dividing: Remember the dog and cat move
together.
Review is done!
We start probability tomorrow…
- A grocery store flyer this week included the
7.3b
#13
following sale price information:
Product
Prices
Red grapes
5 lbs for $5.50
Soft drink 12-packs
3 for $9.99
Snack mix bag
Buy two at $1.50
Lunch meat package
$4.25 each
Susan needs to buy 2 lbs of grapes, five 12-packs of soft drinks, 3
packages of lunch meat, and four bags of snack mix. How much will
Susan spend on her items, not including tax?
A
B
C
D
$61.46
$35.15
$40.90
$34.60
7.4d
#14
There are 36 students in Mr. Barrett's math class. If 25% of
the students are boys, how many students are girls?
36 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
100%
X = 36 x .75
X=
=
𝑥 𝑔𝑖𝑟𝑙𝑠
75%
7.5c #15
For an activity in class, students used pieces of string to measure
roads on a map. They used a map scale to determine the distance
between two cities. One group measured the distance between
Fort Myers and Miami on a Florida state map. The string distance
was 7.75 inches, which represents a real-life distance of about 155
miles. Another group measured the distance between Tampa and
Orlando on the same map and found that distance to be 4.25
inches. What is the real-life distance to the nearest mile between
Tampa and Orlando?
7.75 𝑖𝑛
4.25 𝑖𝑛
A
B
C
D
44 miles
85 miles
152 miles
282 miles
155 𝑚𝑖𝑙
=
? 𝑚𝑖𝑙𝑒𝑠
7.4d
If Lewis can make 2 pies with 6 apples. How many pies can he
make with 15 apples?
2 X 15 = _____
6x = 30
X=5
A
B
C
D
3 pies
5 pies
45 pies
2 pies
2 𝑝𝑖𝑒𝑠
6 𝑎𝑝𝑝𝑙𝑒𝑠
=
𝑥 𝑝𝑖𝑒𝑠
15 𝑎𝑝𝑝𝑙𝑒𝑠
7.4e
A car wash sells a special package of 12 car washes for
$95.40. What is the cost per car wash?
95.40 ÷ 12 =
$ 7.95
12 𝑤𝑎𝑠ℎ𝑒𝑠
$95.40
=
1 𝑤𝑎𝑠ℎ
$?
7.5c
Jasmine enlarged a drawing she made in art class.
2.5 𝑙𝑒𝑛𝑔𝑡ℎ 𝑥 𝑙𝑒𝑛𝑔𝑡ℎ
What is the value of x?
=
3.75 𝑤𝑖𝑑𝑡ℎ 60 𝑤𝑖𝑑𝑡ℎ
A
B
C
D
16
40
58.75
90
Addition
14.3 + 2.75 = _______
15.05 + 197.3 = ________
Subtraction
191.27 - 13.52 = _______
4,201 – 79.55 = _______
Multiplication
191.27 x 13.52 = ________ 201.1 x 9.55 = ________
Division
67.2 ÷ 22.4= ________
500.4 ÷ 7.2 = _________
7.10a
Which equation fits the situation?
Mike’s test score was 20 points lower than Mark’s. If Mark scored a
95 on the test which equation would give Mike’s score?
A
B
C
D
95 = p + 20
p-20 = 95
90 = p +5
p-95=20
7.11b
Ana tells her friends that her sister Mary is 4 less than twice her
age. The friends know that Ana is 12 years old. The equation 2x –
4 = 12 represents the relationship between the sisters' ages. Each
friend calculates Mary's age.
Friend
Answer
Caleb
X = 16
Which friend is correct?
A
Caleb
B
Henry
C
Melissa
D
Jeff
Henry
X=8
Melissa
X=9
Jeff
X=4
7.13f
Four different stores are offering incentives to purchase
headphones as shown below.
Noisy Music
Regular Price
$250
Clearance 15% off
Loud N Sharp
Regular Price
$200
$5 off for every
$100 spent
Music Mart
Regular Price
$300
Mail-in rebate
for $115
Which store offers the lowest price?
A
Noisy Music
B
Loud N Sharp
C
Music Mart
D
Head Jamz
Head Jamz
Regular Price
$225
Owner Special 25% off
Bell Ringer
3x + 2x = 150
Combine like terms:
3x + 2x = 5x
5x = 150
X = 30
Bell Ringer
2x + 4 = 3x + 1
X=?
A
B
C
D
1
2
3
4
Bell Ringer
3x = 33
5x – 10 = 40
3x + 2x = 100
5x + 7x – 2x = 500
2x + 4 = 3x + 1
Bell Ringer
1-9-15
Convert the following into a decimal and a percent:
4
= .8 = 80%
5
3
= .375 = 37.5%
8
Multiply the following:
1
3
x
3
3
=
7
21
3
3
÷ =
1
7
Unit 6
1-9-15
Real World Video’s
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TH_RW_V7.12
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FFWVHKCAE8imrbkVx9hD5imXE&bctid=ref:TXGOM
TH_RW_V7.13
Cloudy with a chance of…
If you listen to weather forecasts you could hear
expressions like these:
‘There is a strong likelihood of rain tomorrow.’
‘In the afternoon there is a possibility of thunder.’
‘The rain will probably clear towards evening.’
Weather forecasts are made by studying charts and
weather data to tell us how likely it is, for example, that it
will rain tomorrow.
Definitions
Probability – a ratio between the number of desired
outcomes to the total possible outcomes, 0 ≤ p ≤1
Probability (event) =
Desired outcomes
Total possible outcomes
Probability tells you how likely something is to happen.
Probability does not tell you what exactly will happen,
it is just a guide.
Decimals, Fractions, Percents
Probability can use decimals, fractions, or percents so you
must know the following:
Probabilities are written
as:
1
1 = 100% =
1
Fractions from 0 to 1
3
.75 = 75% =
4
Decimals from 0 to 1
1
.5 = 50% =
2
Percents from 0% to 100%
1
.25 = 25% =
4
Bell Ringer
1-12-15
Write each fraction in simplest form.
6
10
45
54
=
9
15
=
30
33
=
14
42
=
=
48
72
=
Probability Scale:
If an event is CERTAIN to happen, then the
probability of the event is 1 or 100%.
If an event will NEVER happen, then the probability
of the event is 0 or 0%.
If an event is just as LIKELY as UNLIKELY to happen,
then the probability of the event is considered to
𝟏
have an EQUAL CHANCE and is , 0.5 or 50%.
𝟐
Probability Scale:
Impossible
Unlikely
Equal Chances
0
0.5
0%
50%
𝟏
𝟐
Likely
Certain
1
100%
Definitions
Sample Space: A set of all possible outcomes for an event.
Ex. 2 outcomes when a coin is flipped or 6 when
rolling a number cube (die)
Probability (event) = Desired outcomes
Total possible outcomes
Complement: The set of all outcomes in the sample space
that are not included in the event.
Ex. In the event of rolling a 3 on a die, the complement
is rolling any number other than 3. (1, 2, 4, 5, 6)
P(event) + P(complement) = 1
𝟏
𝟓
+
= 1
𝟔
𝟔
Lawrence is the captain of his track team. The team is
deciding on a color and all eight members wrote their
choice down on equal size cards. If Lawrence picks
one card at random, what is the probability that he
will pick blue?
Desired outcomes
Total possible outcomes
Number of blues = 3
Total cards = 8
3/8 or 0.375 or 37.5%
blue
yellow
red
blue
green
blue
black
black
Flipping a Coin
When a fair coin is flipped, there are two possible
outcomes:
Heads (H) or Tails (T)
We can say that the probability of the coin landing on
1
H is .
2
We can say that the probability of the coin landing on
1
T is .
2
Flipping a coin
When flipping a fair coin twice, the following are all
the possible outcomes, or sample space:
HH, HT, TT, TH
What is the probability of landing on tails both
times?
Desired outcomes
Total possible outcomes
Probability =
1
4
Flipping a coin
When flipping a fair coin twice, what is the probability
of landing on heads and then tails?
Probability =
Probability =
Desired outcomes
Total possible outcomes
1 x 1
2
2
Landing on H
Landing on T
Landing on H and then T
=
1
4
Bell Ringer
1-13-15
Find each probability. Write your answer in simplest form.
Spinning a spinner that has 5 equal sections marked one
through 5 and landing on an even number.
__________
There are 4 aces and 4 kings in a standard deck of 52 cards.
You pick one card at random. What is the probability of
selecting an ace or a king?
__________
How many sides are on a single die?
6 sides (1, 2, 3, 4, 5, 6)
How many sides on a single die have an even number?
3 sides (2, 4, 6)
How many sides have a number larger than 4?
2 sides (5 and 6)
Which letters of the alphabet are vowels?
A, E, I, O, U, and sometimes Y
What prime numbers are between 1 & 10?
2, 3, 5, 7
Find each probability. Write your answer in simplest form.
A bag contains 8 blue coins and 6 red coins. A coin is
removed at random and replaced by three of the other color.
a. What is the probability that the removed coin is blue?
______________
b. If the coin removed is blue, what is the probability of
drawing a red coin after three red coins are put in the bag to
replace the blue one?
______________
c. If the coin removed is red, what is the probability of
drawing a red coin after three blue coins are put in the bag
to replace the red one?
______________
Bell Ringer
1-14-15
Find each probability. Write you answer in simplest form.
There are 12 pieces of fruit in a bowl. Seven of the pieces are
apples and two are peaches. What is the probability that a
randomly selected piece of fruit will not be an apple or a peach?
𝟏
𝟑
=
=
_______________
𝟏𝟐 𝟒
For breakfast, Clarissa can choose from oatmeal, cereal, French
toast, or scrambled eggs. She thinks that if she selects a
breakfast at random, it is likely that it will be oatmeal. Is she
correct?
𝟏
= ; 𝑵𝒐
𝟒
_______________
And in Probability
P (A and B) =
𝒏(𝑨 𝒂𝒏𝒅 𝑩)
𝒏(𝒔)
n(A and B) means the number of outcomes in both A and B.
n(S) means the total number of possible outcomes.
And in Probability
Needing 2 specific events to happen in probability decreases
the chances of getting your desired outcome. “And” means
that the outcome has to satisfy both conditions at the same
time. Remember: And = Multiplication. How this works:
A die is rolled. What is the probability that the number is
even and less than 3?
There is only one
Even numbers on a die: 2, 4, 6 = 𝟑
𝟔
𝟐
Numbers less than 3: 1, 2 =
𝟔
number (2) that is
in both events A
and B.
Even numbers less than 3: 2
Probability =
Desired outcomes
Total possible outcomes
=
𝟏
𝟔
Rolling dice examples
With a single die being rolled twice, what is the
probability that the outcome is a 2 and then a 6?
Probability =
Probability =
Desired outcomes
Total possible outcomes
1
1
6 x 6
=
1
36
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
And in Probability
Fazio is selecting a jersey. His choices are shown below.
Fazio chooses a jersey at random and then replaces it. He
then selects a second jersey at random. What is the
probability that Fazio selects a striped jersey both times?
A.
B.
C.
1
100
1
16
1
25
2
10
x
2
10
=
4
100
÷
4
4
=
1
25
And in Probability
Two fair six-sided number cubes are rolled 36 times.
Which of the following predicts and explains the
number of times a 2 and an even number are likely
to be rolled?
Number 2: There is one 2; so
1
6
Even Numbers on a die: 2, 4, 6 =
1
6
x
3
6
=
3
36
÷
3
3
=
1
12
x
36
1
=
3
6
36
12
1
2
or ( )
= 3 times
Rolling dice
When a single die is rolled, there are six possible
outcomes:
1, 2, 3, 4, 5, 6
The probability of rolling any of those numbers is
1
.
6
Rolling dice examples
With a single die being rolled, what is the probability that
an even number will be the outcome?
Probability =
Desired outcomes
Total possible outcomes
Probability =
3
6
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
Bag of marbles
A bag contains different color marbles; 3 red, 4 blue, and
2 green. What is the probability of grabbing a red
marble?
Probability =
Desired outcomes
Total possible outcomes
Probability =
3
9
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
Rolling dice examples
With a single die being rolled, what is the probability that
the outcome is a number larger than 2?
Probability =
Desired outcomes
Total possible outcomes
Probability =
4
6
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
Bell Ringer
1-15-15
Two fair six-sided number cubes are rolled 36 times.
What is the probability a 2 and an even number are
likely to be rolled?
Number 2: There is one 2; so
1
6
Even Numbers on a die: 2, 4, 6 =
1
6
x
3
6
=
3
36
÷
3
3
=
1
12
x
36
1
=
3
6
36
12
1
2
or ( )
= 3 times
Independent Example
Independent Event: The result of the second event is
not affected by the result of the first event.
If A and B are independent events, the probability
of both events occurring is the product of the
probabilities of the individual events
If A and B are independent events,
P(A and B) = P(A) • P(B).
Independent Example
A drawer contains 3 red paperclips, 4 green paperclips, and 5
blue paperclips. One paperclip is taken from the drawer and
then replaced. Another paperclip is taken from the
drawer. What is the probability that the first paperclip is red
and the second paperclip is blue?
3
First Paperclip =
12
1
4
x
5
12
=
𝟓
𝟒𝟖
=
1
4
5
Second Paperclip =
12
Bag of marbles
A bag contains different color marbles; 3 red, 4 blue,
and 2 green. When grabbing one marble at a time and
then putting it right back in the bag, what is the
probability of grabbing two green marbles?
Probability =
Desired outcomes
Total possible outcomes
Probability =
2
9
x
2
9
=
1st green marble
2nd green marble
Grabbing both green marbles
4
81
Why is this 9 ?
Bell Ringer
1-16-15
Answer’s must be in %’s
What is the probability of getting a blue marble?
4
= .8 = 80%
5
What is the probability of getting a purple marble?
1
= .2 = 20%
5
What is the probability of getting a blue or purple
marble?
5
= 1 = 100%
5
Dependent Example
Dependent Event: The result of one event IS affected
by the result of another event.
If A and B are dependent events, the probability of
both events occurring is the product of the probability
of the first event and the probability of the second
event once the first event has occurred.
If A and B are dependent events, and A occurs first,
P(A and B) = P(A) • P(B,once A has occurred)
... and is written as ...
P(A and B) = P(A) • P(B|A)
Dependent Example
A drawer contains 3 red paperclips, 4 green paperclips, and 5
blue paperclips. One paperclip is taken from the drawer and
is NOT replaced. Another paperclip is taken from the
drawer. What is the probability that the first paperclip is red
and the second paperclip is blue?
3
First Paperclip =
12
1
4
x
5
11
=
𝟓
𝟒𝟒
=
1
4
5
Second Paperclip =
11
Bag of marbles
A bag contains different color marbles; 3 red, 4 blue, and
2 green. When grabbing one marble at a time without
putting the first one back in the bag, what is the
probability of grabbing two green marbles?
Probability =
Desired outcomes
Total possible outcomes
Probability =
2
9
x
1
8
=
1st green marble
2nd green marble
Grabbing both green marbles
2
1
72 = 36
Why is this now 8 ?
Or in Probability
Having the choice of “or” in probability increases the
chances of getting your desired outcome. Remember:
Or means to ADD. How this works:
What is the probability of picking a red marble?
Probability =
Desired outcomes
Total possible outcomes
=
1
3
What is the probability of picking a red or a purple
1
2
1
Desired outcomes
marble?
Total possible outcomes
3
+
3
=
3
Bag of marbles
A bag contains different color marbles; 3 red, 4 blue, and
2 green. What is the probability of not grabbing a red
marble?
Probability =
Desired outcomes
Total possible outcomes
Probability =
6
9
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
Rolling dice examples
With a single die being rolled, what is the probability that
the outcome is a 1 or a 6?
Probability =
Desired outcomes
Total possible outcomes
Probability =
1
6
+
1
6
=
2
6
If you do not see your answer right away you might have
to:
• Reduce
• Convert into a decimal or percent
A number is chosen at random from 1 to 25. Find
the probability of selecting an odd number or
multiple of 5.
Odd Numbers:
13
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 =
25
Multiple of 5:
5
5, 10, 15, 20, 25 =
25
Same Number in both events A and B.
3
5, 15, 25 =
25
13
Answer:
25
5
+
25
-
3
25
=
15 5
÷
25 5
=
3
5
Experimental vs. Theoretical probability
Example: toss a coin 100 times, how many Heads will
come up?
Theoretical probability:
1
2
Probability says that Heads have a chance, so we
can expect 50 Heads.
Experimental probability:
But when we actually try it we might get 48 heads, or 55
heads ... or anything really, but in most cases it will be a
number near 50.
Experimental vs. Theoretical probability
Experimental data – the data collected or observed from
the outcomes of an experiment
Experimental probability – the likelihood of an event
occurring from the outcomes of an experiment
Theoretical data – the possible outcomes of an event
without conducting an experiment
Theoretical probability – the likelihood of an event
occurring without conducting an experiment
Definitions
Random sample – a subset of the population selected
without bias in order to make inferences about the entire
population
Sample – a subset of the population selected in order to
make inferences about the entire population
Sample space – a set of all possible outcomes of one or
more events
Simple event – an event that consists of a single outcome
Simulation – an experiment or model used to test the
outcomes of an event
Outcome – the result of an action or event
Bell Ringer
Which of the following numbers are prime?
1 , 2, 3, 4, 5, 6, 7, 8, 9, 10
Which letters in the alphabet are vowels?
A, E, I, O, U, & sometimes Y
What is the probability of choosing the letter i from
the word probability?
A bag contains 5 green shirts, 9 blue shirts, and 10 red
shirts and you ask a friend to pick one without
looking. What is the probability that the shirt will be
green?
Mark rolls a number cube that has sides labeled 1 to 6
and then flips a coin. What is the probability that she
rolls an even number and flips heads?
A.
1
8
B.
1
4
C.
1
2
D.
3
4
The experimental probability that Pedro will hit a hole
2
in one at the golf course is . If Pedro goes golfing 40
5
times in a year, how many times can he expect
to hit a hole in one?
A. 16
B. 24
C. 25
D. 40
Wendy noticed that out of 345 cars that passed by
her house 56 were SUVs. About how many SUVs
could she expect to see pass by if 2,100 cars were to
pass her house?
A. 200
B. 300
C. 400
D. 500
Maurico conducted an experiment in
which he drew marbles out of a bag and
recorded the color. The results of the
experiment are shown to the right. What
is the probability that Mauricio drew a
yellow marble?
A.
1
12
B.
3
10
C.
7
30
D.
4
15
The probability of an event is 0.001. Which of the
following best describes the event?
A. The event will never occur.
B. There is a small chance that the event will occur.
C. The event is likely to occur.
D. The event will definitely occur.
The experimental probability that Josie’s dad gets
home from work between 5 P.M. and 6 P.M. is equal
5
to . About what percent of the time will Josie’s dad
8
get home from work between 5 P.M. and 6 P.M.?
A. 37.5%
B. 58%
C. 62.5%
D. 85%
Kathleen rolled a number cube that has sides labeled 1
to 6. What is the probability that she rolled a 2 or a 4?
A.
1
6
B.
1
4
C.
1
3
D.
3
4
Tyler recorded the hair color and eye
color of students walking in the hallway
outside her homeroom. What is the
experimental probability that the next
student she sees will have blue eyes?
A.
15
45
B.
19
20
C.
5
19
D.
19
40