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$100 $100 $100 $100 $100
$200
$300
$400
$500
$200 $200 $200 $200
$300 $300 $300 $300
$400 $400 $400 $400
$500 $500$500 $500
Properties Theoretical
Probability
+, -, *, /
Rational #’s
Experimental
ProbabilityVocabulary
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Properties for $100
Name the Property shown below:
b + 0 = b
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Answer
Identity Property of Addition
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Properties for $200
Name the Property shown below:
7 + (3 + C) = (7 + 3) + C
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Answer
Associative Property of Addition
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Properties for $300
Name the Property shown below:
2*b = b*2
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Answer
Commutative Property of Multiplication
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Properties for $400
Name the Property shown below:
5(1/5) = 1
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Answer
Inverse Property of Multiplication
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Properties for $500
Simplify the expression. Justify each step.
6x + 4(3 + 9x)
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Answer
6x + 4(3 + 9x)
6x + 4*3 + 4 *9x => Distributive Property
6x + 12 + 36x => Multiplication
6x + 36x + 12 => Commutative Property of addition
(6 + 36)x + 12 => Distributive Property
42x + 12 => Addition
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Theoretical Probability for $100
If I roll a dice one time, what is the probability of rolling a one or a three?
i.e. P(1 or 3) = ?
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Answer
Number of Items in Sample Space = 6
Sample Space {1 2 3 4 5 6}
Probability = 2/6 or 1/3
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Theoretical Probability for $200
If I flip a coin 4 times, what is the probability of the same face showing up all 4 times?
i.e. Either H-H-H-H or T-T-T-T
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Answer
Elements in Sample Space = 2*2*2*2 = 16
P(H-H-H-H) = 1/16
P(T-T-T-T) = 1/16
P(H-H-H-H OR T-T-T-T)
= (1/16) + (1/16) = 2/16= 1/8
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Theoretical Probability for $300
Suppose you choose an m&m from a bag containing 5 blue m&m’s, 4 red m&m’s and 7 yellow m&m’s. You then pick another m&m. Find P(red then yellow)
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Answer
P(red then yellow)
Number of Items in Sample Space: 16
Sample Space {b b b b b r r r r y y y y y y y}
Event 1: P(red) = 4/16 = ¼
New Sample Space {b b b b b r r r y y y y y y y}
Event 2: P(yellow) = 7/15
P(red then yellow) = ¼ * 7/15 = 7/60
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Theoretical Probability for $400
Draw the sample space for the following event:
You flip a coin, and then spin the spinner shown below.
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Answer
{Back
}H-O
H-P
H-Y
H-G
H-R
T-O
T-P
T-Y
T-G
T-R
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Theoretical Probability for $500
I spin the spinner shown below, and then roll a dice. Find P(Red and 2)
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Answer
Number of elements in sample space:
5 * 6 = 30
P(Red) = 1/5
P(2) = 1/6
P(Red and 2) = (1/5) * (1/6) = 1/30
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Experimental Probability for $100
If I draw 35 cards out of a bag, and 7 or them are hearts, what is the experimental probability of drawing a heart?
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Answer
7/35 = 1/5
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Experimental Probability for $200
What is the experimental probability of thinking Mr. Paul is funny if out of 98 randomly chosen students, 2 thought he was funny?
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Answer
2/98 = 1/49 = 2.04%
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Experimental Probability for $300
I rolled a dice 12 times, and the results are shown below. What is the experimental probability of rolling a 6?
3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3
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Answer
Items in Sample Space: 12
Sample Space:
{3, 5, 1, 5, 4, 6, 6, 3, 6, 3, 5, 3}
Favorable outcomes in sample space: 3
Experimental Probability= 3/12 = ¼ = 25%
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Experimental Probability for $400
If I randomly pick 24 of the 66 eighth graders at AIS and find that 8 of them are eating pizza for lunch, how many of the 66 total eighth graders would we expect to be eating pizza?
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Answer
Experimental Probability = 8/24 = 1/3
Total 8th graders = 66
Total Students Eating Pizza Expected
= (1/3) * 66 = 22 Students
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Experimental Probability for $500
There are 452 dogs that live in district 1. If I randomly select 69 of the dogs, and find that 29 are small dogs, what is the experimental probability of a dog being small AND how many of the 452 dogs in district 1 would we expect to be small dogs?
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Answer
Experimental Probability = 29/69
Total Dogs in District 1 = 452
Total Small Dogs Expected
= (29/69) * 452 = 190 Dogs
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Vocabulary for $100
Define the following word:
Coefficient
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Answer
Coefficient – The numerical factor of a term (a number, a variable, or the product of a number and one or more variables)
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Vocabulary for $200
Define the following word:
Matrix
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Answer
Matrix – a rectangular arrangement of numbers in rows and columns
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Vocabulary for $300
Define the following word:
Like Terms
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Answer
Like Terms – Terms (a number, a variable, or the product of a number and one or more variables) that have exactly the same variable factors
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Vocabulary for $400
Define the following word:
Sample Space
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Answer
Sample Space – The set of all possible outcomes of an event
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Vocabulary for $500
Define the following word:
Complement of an Event
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Answer
Complement of an Event – All of the possible outcomes not in the event.
i.e. all of the items in the sample space that do not satisfy the given event
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Operations on of Rational #’s for $100
Solve:
5 - -3 + 9*3
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Answer
5 - -3 + 9*3
= 5 - -3 + 27
= 8+27
= 35
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Operations on of Rational #’s for $200
Solve:
-3 *|3-5|
-2
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Answer
-3 *|3-5| = -3 * 2 = -6 = 3
-2 -2 -2
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Operations on of Rational #’s for $300
Evaluate the following expression
for b = -2.1
|3 – b| - 2(b + 6) + |b|
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Answer
|3 – b| - 2(b + 6) + |b|
= |3 - -2.1| - 2(-2.1 + 6) + |-2.1|
= |5.1| - 2(3.9) + |-2.1|
= 5.1 – 7.8 + 2.1
= -0.6
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Operations on of Rational #’s for $400
Add the following two Matrices:
-2.3 3.0 -5.3 2.1 9
1.2 5.4 -7.2 3.2 10.2
6.7 -0.3 -1.5 9.8 7.7
6.4 6.6 -1.6 3.3 -1
7.6 5.0 -7.1 0.1 2.5 3.4 -1.2 3.97.6 -4.3 -6.1 -2.7 4.4 4.6 -10 8.3-7.9 -8.2 -1.1 5.6
+
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Answer
The matrices can not be added because they are not the same size. The first is a 4x5, the second is a 5x4
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Operations on of Rational #’s for $500
Add the following three Matrices:
-2 7
5 -1
0 6
6 -4
2 -6
-4 -8
9 7
7 -3
3 9
+ + =
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Answer
Back
13 10
14 -10
-1 7