Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #62 : Data Properties

Determine the range:  \(\displaystyle [5,-9,-1,-3,3,3,5]\)

Possible Answers:

\(\displaystyle 8\)

\(\displaystyle -4\)

\(\displaystyle 14\)

\(\displaystyle 29\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 14\)

Explanation:

The range is the difference between the highest and lowest numbers.

Identify the highest and lowest numbers.

The highest number is 5.

The smallest number is:  \(\displaystyle -9\)

Subtract the two numbers. Use parentheses to brace the negative number.

\(\displaystyle 5-(-9) = 14\)

The answer is:  \(\displaystyle 14\)

Example Question #61 : Data Properties

Determine the range of the following numbers:  \(\displaystyle [5\%, 6, \frac{1}{2},\pi]\)

Possible Answers:

\(\displaystyle 5.95-\pi\)

\(\displaystyle 5.5\)

\(\displaystyle \frac{\pi}{3}\)

\(\displaystyle 5.95\)

\(\displaystyle \frac{6-\pi}{4}\)

Correct answer:

\(\displaystyle 5.95\)

Explanation:

The range is the difference between the highest and lowest numbers in the data set.

Identify the numbers.

The value of \(\displaystyle 5\%\) is equivalent to \(\displaystyle 0.05\), which is the smallest number.

The largest number is 6.

Subtract both numbers to determine the range.

\(\displaystyle 6-0.05 = 5.95\)

The answer is:  \(\displaystyle 5.95\)

Example Question #161 : Algebra Ii

Determine the range of the numbers:  \(\displaystyle [9,26,-9,30,-17]\)

Possible Answers:

\(\displaystyle 53\)

\(\displaystyle 13\)

\(\displaystyle 47\)

\(\displaystyle 35\)

\(\displaystyle 43\)

Correct answer:

\(\displaystyle 47\)

Explanation:

Identify the largest and smallest numbers.

The largest number is 30, while the smallest number is negative 17.

The range is the difference between the largest and smallest numbers.

\(\displaystyle 30-(-17)=47\)

The answer is:  \(\displaystyle 47\)

Example Question #162 : Algebra Ii

Determine the range:  \(\displaystyle [-9,18,-32,-78,0]\)

Possible Answers:

\(\displaystyle 110\)

\(\displaystyle 78\)

\(\displaystyle 96\)

\(\displaystyle 137\)

\(\displaystyle 60\)

Correct answer:

\(\displaystyle 96\)

Explanation:

The range is defined as the difference between the largest and smallest numbers.

The largest number is 18.

The smallest number is negative 78.

Subtract both numbers to determine the range.

\(\displaystyle 18-(-78) = 18+78 = 96\)

The range is:  \(\displaystyle 96\)

Example Question #66 : Data Properties

Evaluate the range of the numbers:  \(\displaystyle [9,-8,-3,12,26,-10]\)

Possible Answers:

\(\displaystyle 38\)

\(\displaystyle 16\)

\(\displaystyle 15\)

\(\displaystyle 36\)

\(\displaystyle 26\)

Correct answer:

\(\displaystyle 36\)

Explanation:

The range is the difference of the highest and lowest numbers in the given set of numbers.

The highest number is 26. 

The smallest number is negative 10.

Subtract the highest number with the smallest number.  Use parentheses to brace the negative quantity.

\(\displaystyle 26-(-10) = 26+10 = 36\)

The answer is:  \(\displaystyle 36\)

Example Question #163 : Algebra Ii

Determine the range of the numbers:  \(\displaystyle [9,-7,13,-24,-56]\)

Possible Answers:

\(\displaystyle 65\)

\(\displaystyle 69\)

\(\displaystyle 32\)

\(\displaystyle 109\)

\(\displaystyle 43\)

Correct answer:

\(\displaystyle 69\)

Explanation:

The range is the difference between the highest and lowest numbers.

The highest number is 13.

The smallest number is negative 56.

Subtract both numbers. 

\(\displaystyle 13-(-56) = 13+56 = 69\)

The range is:  \(\displaystyle 69\)

Example Question #64 : Data Properties

Determine the range of the numbers:  \(\displaystyle [\frac{1}{8}, -\frac{7}{3}, -\frac{11}{4}, 10]\)

Possible Answers:

\(\displaystyle \frac{37}{3}\)

\(\displaystyle \frac{23}{3}\)

\(\displaystyle \textup{The answer is not given.}\)

\(\displaystyle \frac{51}{4}\)

\(\displaystyle \frac{29}{4}\)

Correct answer:

\(\displaystyle \frac{51}{4}\)

Explanation:

The range is the difference between the highest and lowest numbers.

The highest number is:  \(\displaystyle 10\)

The lowest number will need to be determined by comparing the two negative fractions after converting both to a least common denominator.

Multiply the denominators.

\(\displaystyle 3\times 4 = 12\)

Convert the fractions and compare the numerators.

\(\displaystyle [ -\frac{7}{3}, -\frac{11}{4}] \rightarrow[ -\frac{7(4)}{3(4)}, -\frac{11(3)}{4(3)}]\rightarrow [-\frac{28}{12},-\frac{33}{12}]\)

We can see that \(\displaystyle -\frac{33}{12}\) is the smallest number.

Subtract the highest and lowest numbers.  Add a parentheses to brace the negative fraction.

\(\displaystyle 10-(-\frac{33}{12}) = \frac{120}{12}+\frac{33}{12} = \frac{153}{12}\)

Reduce the fraction.

\(\displaystyle \frac{153}{12} = \frac{3\times 51}{4 \times 3} = \frac{51}{4}\)

The answer is:  \(\displaystyle \frac{51}{4}\)

Example Question #66 : Data Properties

Identify the range of the numbers:  \(\displaystyle [9,-3,6,-1,0,13]\)

Possible Answers:

\(\displaystyle 10\)

\(\displaystyle 24\)

\(\displaystyle 13\)

\(\displaystyle 16\)

\(\displaystyle 4\)

Correct answer:

\(\displaystyle 16\)

Explanation:

In order to determine the range of the numbers, determine the difference between the highest and lowest numbers.

The highest number is 13, while the lowest number provided is negative three.

Subtract both numbers to determine the range.

\(\displaystyle 13-(-3) = 13+3 = 16\)

The answer is:  \(\displaystyle 16\)

Example Question #64 : Data Properties

Find the range of the following numbers:  \(\displaystyle [9,-9,-36,-48,-56]\)

Possible Answers:

\(\displaystyle 47\)

\(\displaystyle \textup{The range cannot be determined.}\)

\(\displaystyle 45\)

\(\displaystyle 158\)

\(\displaystyle 65\)

Correct answer:

\(\displaystyle 65\)

Explanation:

The range of the numbers is defined as the difference of the largest number and the smallest number.

Identify the largest number:  \(\displaystyle 9\)

Identify the smallest number:  \(\displaystyle -56\)

Subtract the largest number with the smallest number.

\(\displaystyle 9-(-56) = 9+56 = 65\)

The answer is:  \(\displaystyle 65\)

Example Question #161 : Algebra Ii

Determine the range of the numbers:  \(\displaystyle [-9,3,-99,11,33,24]\)

Possible Answers:

\(\displaystyle 132\)

\(\displaystyle 66\)

\(\displaystyle 96\)

\(\displaystyle 179\)

\(\displaystyle 108\)

Correct answer:

\(\displaystyle 132\)

Explanation:

The range is the difference between the largest and smallest numbers.

The largest number is: \(\displaystyle 33\)

The smallest number is:  \(\displaystyle -99\)

Subtract the two numbers.

\(\displaystyle 33-(-99) = 33+99 = 132\)

The answer is:  \(\displaystyle 132\)

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