Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #5 : Mean
Peter was paid $4000 for editing a 3200-page encyclopedia. What was his rate earned per page?
This question is really just asking for the average dollar per page. This could be easily calculated:
However, you might also think of this as a rate problem:
Using the information from the question, we can see that 
This comes out to what we solved above:
Example Question #7 : Mean
A group of five candles are burning. Each candle is 1.5 inches taller than the one to its left. The smallest candle is 5 inches tall. What is the mean height of the group?
To solve this, you should first calculate the size of the candles. Based on the description, the group would be:
The sum of this group is:
The average is then found by dividing this total by 5:
Example Question #102 : Data Properties
A bank has 100 accounts established. The smallest account contains $1000. Each account after this one is $100 more than the one previous. For instance, the next account is $1100, then the next $1200, and so forth. What is the mean value of the accounts in the bank?
The easiest way to think of this problem is to make a list of the accounts (though not all 100, of course).
The largest account will be:
So, our list looks like this:
1000, 1100, 1200, . . ., 9700, 9800, 9900
Now we need to identify a pattern. We can pair the first and the last element:
Now, notice what happens when we pair the second and the second from the last element:
This pattern is going to work for the whole list! If there are 100 total accounts, that means that we can make 50 such pairs. That means that we have 50 pairs of $10900. The total account amount is therefore:
The mean will be equal to this total value divided by the number of accounts (100):
Example Question #10 : Mean
Find the mean of the following data set
The mean is the average of a set of data. In order to calculate this value, we need to take the sum of all the numbers and divide that by the number of values we have:
This gives us:
which finally gives us a mean of:
Example Question #201 : Algebra Ii
Find the mean of the following numbers:
150, 88, 141, 110, 79
71
110
88
141
113.6
113.6
The mean is the average. The mean can be found by taking the sum of all the numbers (150 + 88 + 141 + 110 + 79 = 568) and then dividing the sum by how many numbers there are (5).
Our answer is 113 3/5, which can be written as a decimal.
Therefore 113 3/5 is equivalent to 113.6, which is our answer.
Example Question #202 : Algebra Ii
If you roll a fair die six million times, what is the average expected number that you roll?
3
2.5
4.5
3.5
4
3.5
The outcomes from rolling a die are {1,2,3,4,5,6}.
The mean is (1+2+3+4+5+6)/6 = 3.5.
Rolling the die six million times simply suggests that each number will appear approximately one million times. Since each number is rolled with equal probability, it doesn't matter how many times you perform the experiment; the answer will always remain the same.
Example Question #1 : How To Find The Missing Number In A Set
If the mean of the following set is 12, what is 
(1,14,3,15,16,
Since we are given the mean, we need to find the sum of the numbers. From there we can figure out 
We can use this to find the sum by plugging in
So our sum is 96.
So we know that our total sum minus the sum of the given numbers is equal to 
So, 
Example Question #284 : Basic Arithmetic
Reginald has scores of {87, 79, 95, 91} on the first four exams in his Spanish class. What is the minimum score he must get on the fifth exam to get an A (90 or higher) for his final grade?
71
90
98
95
82
98
To find the fifth score, we need to set the average of all of the scores equal to 90.
Multiply both sides of the equation by 5.
Subtract 352 from both sides of equation.
Example Question #285 : Basic Arithmetic
The mean of the following set is 8. What is 
Cannot be determined
8
9
2
1
1
Let 
We know the mean is 8, and there are five values in the set, including the unknown 
Simplify.
Plug back into equation at top.
Example Question #12 : Mean
Angela scored the following on her past tests.
What is the current average (mean) score of her exams?
To find the average, add up all of the scores, then divide by how many scores there were:
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