Algebra and Trigonometry Enhanced with Graphing Utilities (7th Edition)
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and ; To evaluate functions, plug in the value. ... more
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In order for a relation between two sets to be a ... more
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Sequence ; A sequence is a list of things in a ... more
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The terms of a sequence are represented by the ... more
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Factorial () is a special math symbol for in ... more
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An alternating sequence has terms that alternate ... more
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Summation ; is the notation used when adding all ... more
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, , and for ; is obtained when adding k, n times... more
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3,628,800 ; Factorial () is a special math symbol ... more
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362,880 ; Factorial () is a special math symbol ... more
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504 ; Factorial () is a special math symbol for ... more
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132 ; Factorial () is a special math symbol for ... more
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1260 ; Factorial () is a special math symbol for ... more
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806,400 ; Factorial () is a special math symbol ... more
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; On the sequence , the first five terms are ... more
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; On the sequence , the first five terms are ... more
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; To find the nth term of a sequence, find the ... more
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; The numerator of each fraction is always 1, so ... more
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; The numerator of each fraction is always 1, so ... more
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; The numerator of each fraction is a power of 2... more
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; The terms of this sequence have alternating ... more
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; This sequence is divided into two parts. One ... more
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; The terms of this sequence have alternating ... more
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; The terms of this sequence have alternating ... more
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; To find , use the previous term, . ; To find ... more
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; To find , use the previous two terms, and . ; ... more
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, , ,, ; To find , use its previous term, . ; To ... more
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, ,, , ; To find , use its previous term, . ; To ... more
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; Substitute the value of k starting with and ... more
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; Substitute the value of k starting with and ... more
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; To write the sum in summation notation, find ... more
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; To write the sum in summation notation, find ... more
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; To write the sum in summation notation, first ... more
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200 ; To find the sum of the sequence, the ... more
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400 ; To find the sum of the sequence, the ... more
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820 ; To find the sum of the sequence, the ... more
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; Use the properties of sequences first, move the... more
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1110 ; Using the properties of sequences first, ... more
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871 ; Using the properties of sequences first, ... more
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1560 ; Using the properties of sequences first, ... more
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959 ; Using the properties of sequences first, ... more
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3570 ; Using the properties of sequences first, ... more
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44,000 ; The following formulas of sum will be ... more
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89,964 ; The following formulas of sum will be ... more
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21 pairs ; Let be the number of mature rabbits ... more
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Fibonacci sequence ; Add the numbers of each ... more
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LetThen ; To show , let the left side equal to S... more
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; Use to find .. ; Use to find . ; Use to find... more
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; . To find , add to . That is, . Note that ... more
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; and .Substitute these values into the left side... more
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The Fibonacci sequence is a sequence that is ... more
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The numbers are called triangle numbers. If ... more
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; Compound interest formula:is the amount of ... more
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; The focus is to the right of the vertex, so the... more
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arithmetic ; An arithmetic sequence is a sequence ... more
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To find the nth term of an arithmetic sequence use... more
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17 ; Use the recursive formula to find . ; more
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The sum of the first n terms of an arithmetic ... more
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A Fibonacci sequence is a special recursive ... more
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is the common difference. ; The nth term of ... more
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1 is a constant , therefore is an arithmetic ... more
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1 is a constant , therefore is an arithmetic ... more
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2 is a constant, therefore is an arithmetic ... more
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3 is a constant, therefore is an arithmetic ... more
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is a constant, therefore is an arithmetic ... more
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is a constant, therefore is an arithmetic ... more
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is a constant, therefore is an arithmetic ... more
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is a constant, therefore is an arithmetic ... more
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is a constant, therefore is an arithmetic ... more
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1 is a constant, therefore is an arithmetic ... more
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; The nth term of an arithmetic sequence is found... more
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; The nth term of an arithmetic sequence is found... more
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; The nth term of an arithmetic sequence is found... more
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; The nth term of an arithmetic sequence is found... more
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1,260 ; Find and . ; . ; Find the common ... more
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900 ; Find and . ; Find the common difference, d, ... more
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324 ; Find and . ; Find the common difference,d, ... more
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301 ; Find and . ; Find the common difference,d, ... more
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30,919 ; Find and . ; Find the common difference, ... more
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10,036 ; Find and . ; Find the common difference, ... more
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4,901 ; Find and . ; Find the common difference, ... more
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6,080 ; Find and by plugging in and in . ; Use ... more
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1,120 ; Find and by plugging in and in . ; Use... more
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15,960 ; Find . ; To find the 120th term (), find ... more
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; Find . ; To find the 46th term (), find the ... more
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; In an arithmetic sequence, the difference ... more
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24 terms ; Plug in , , and in and . ; ; A ... more
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13 or 27 terms ; Plug in , , and in and . ; A ... more
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1,185 ; This is an arithmetic sequence of 30 terms... more
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2,160 ; This is an arithmetic sequence of 40 terms... more
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210 color A triangles190 color B triangles ; The ... more
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; n is the number of feet in thousands.The ... more
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11 ; This is an arithmetic sequence.Find and... more
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1,647 ; This is an arithmetic sequence with .To ... more
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30 ; This is an arithmetic sequence with and . ... more
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8 years ; This is an arithmetic sequence.is the ... more
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; To create an arithmetic sequence, write ... more
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Similarities:Arithmetic sequences and linear ... more
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; In an account where interest is compounded, the... more
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The graph is an ellipse with center , vertices at... more
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; The inverse of matrix is . ; more
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; For the infinite geometric series adds up to... more
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The recursive geometric sequence formula is .To ... more
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Geometric sequences have common ratios that may be... more
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The sum of the first n terms of a geometric ... more
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3 is a constant, so is a geometric sequence with ... more
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is a constant. is a geometric sequence with ... more
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is a constant. is a geometric sequence with ... more
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is a constant. is a geometric sequence with ... more
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2 is a constant. is a geometric sequence with ... more
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3 is a constant. is a geometric sequence with ... more
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is a constant. is a geometric sequence with ... more
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9 is a constant. is a geometric sequence with ... more
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is a constant. is a geometric sequence. ; The ... more
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is a constant. is a geometric sequence with ... more
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2,187 ; Find the common ratio, r, by dividing ... more
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1 ; Find the common ratio, r, by dividing ... more
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512 ; Find the common ratio, r, by dividing ... more
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0.00000004 ; Find the common ratio, r, by dividing... more
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100,000 ; Find the common ratio, r, by dividing ... more
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or . ; Plug in the information of both terms in .... more
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; Find .Find the common ratio, r, by dividing ... more
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; The first term is 2 and the last term is , ... more
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8191.75 ; Find .Find the common ratio, r, by ... more
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2,391,484.333 ; Find .Find the common ratio, r, by... more
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1.995432683 ; Find and the common ratio, r, by ... more
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28,697,812 ; Find , the common ratio, r, and n ... more
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; Find .Find the common ratio, r, by dividing ... more
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4.998589445 ; Find .Find the common ratio, r, by ... more
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Converges ; Find the common ratio, r, by dividing ... more
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Converges6 ; Find the common ratio, r, by dividing... more
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Converges16 ; Find the common ratio, r, by ... more
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Converges9 ; Find the common ratio, r, by dividing... more
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Converges ; Find the common ratio, r, by dividing ... more
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Converges ; Find the common ratio, r, by dividing ... more
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Diverges ; Find the common ratio, r, by dividing ... more
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Diverges ; Find the common ratio, r, by dividing ... more
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Converges ; The geometric series is written in ... more
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Converges12 ; The geometric series is written in ... more
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Diverges ; The geometric series is written in ... more
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Diverges ; The geometric series is written in ... more
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Converges ; The geometric series is written in ... more
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Converges ; The geometric series is written in ... more
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Converges6 ; Rewrite the geometric series so that ... more
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Converges6 ; Rewrite the geometric series so that ... more
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Arithmetic sequence1,375 ; Sequences can be ... more
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Arithmetic ; Sequences can be arithmetic, ... more
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Neither ; Sequences can be arithmetic, geometric, ... more
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Neither ; Sequences can be arithmetic, geometric, ... more
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Arithmetic sequence ; Sequences can be arithmetic... more
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Arithmetic sequence ; Sequences can be arithmetic... more
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Neither ; Sequences can be arithmetic, geometric, ... more
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Arithmetic sequence2,550 ; Sequences can be ... more
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Geometric ; Sequences can be arithmetic, geometric... more
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Geometric ; Sequences can be arithmetic, geometric... more
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Geometric ; Sequences can be arithmetic, geometric... more
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Neither ; Sequences can be arithmetic, geometric, ... more
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Geometric ; Sequences can be arithmetic, geometric... more
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Geometric0 ; Sequences can be arithmetic, ... more
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; In geometric sequences, consecutive terms have ... more
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2 ; In geometric sequences, consecutive terms have... more
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; The starting salary is 42,000.After 1 year, the... more
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; The starting cost is 15,000.The cost at the end... more
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; In the annuity formula , i is the percent ... more
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; In the annuity formula , i is the percent ... more
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; In the annuity formula , i is the percent ... more
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; The account pays 6% compounded monthly. Find n... more
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124.98 ; In the annuity formula , i is the percent... more
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grains do not fit on the board. ; The number of ... more
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; The square is divided into quarters of quarters... more
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10 ; The multiplier is the sum of the geometric ... more
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20 ; The multiplier is the sum of the geometric ... more
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; The price is an infinite geometric series.Find... more
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; The price is an infinite geometric series.Find... more
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December 20 ; Amount given on day 1 is 1000.Amount... more
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; This is an arithmetic sequence with and ... more
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The salary is greater with A () than B () after 5 ... more
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Alpha has a total of , which is less than the ... more
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The option that will result in the most money is ... more
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Total paid for 22 days: On day 22: The risk to ... more
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Yes.The sequence has , common difference and ... more
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; Make up any geometric sequence by choosing a ... more
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Example 1 Example 2No sumTo determine whether it ... more
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Similarities:The base, b, in exponential functions... more
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2.121 ; Identify the base, b, and the argument, a... more
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; To find the inverse of a 3 by 3 matrix A, write... more
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; The vertices of the hyperbola are and .The ... more
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54 ; Choose to expand one row.In this case, row 1 ... more
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Condition 1: Left side: , Right side: , True ... more
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Condition 1: Left side: , Right side: , True ... more
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Condition 1: Left side: , Right side: , True ... more
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Condition 1Left side: , Right side: , True ... more
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Condition 1:Left side: , Right side: , True ... more
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Condition 1:Left side: , Right side: , True ... more
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Condition 1:Left side: , Right side: , True ... more
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Since both conditions of the Principle of ... more
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Both conditions of the Principle of Mathematical ... more
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Both conditions of the Principle of Mathematical ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since both conditions of the Principle of ... more
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Since is divisible by 2 and is divisible by 2... more
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Since is divisible by 3 and is divisible by 3... more
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Since is divisible by 2 and is divisible by 2... more
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Since is divisible by 6 and is divisible by 6... more
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Since follows , then by the Principle of ... more
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is true for all . ; Let represent the given ... more
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is a common factor in the expression, thus, by ... more
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; Let represent the given statement. Show that ... more
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Let represent the given statement. Show that is ... more
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is not prime. The statement holds true for all ... more
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; Let represent the given statement. Show that ... more
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Pascal triangle ; The Pascal triangle is a device ... more
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The correct expression for is . ; The correct ... more
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Binomial Theorem ; The theorem is used as an ... more
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10 ; Plug the values of and into the formula. ; ... more
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35 ; Plug the values of and into the formula. ; ... more
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21 ; Plug the values of and into the formula. ; ... more
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36 ; Plug the values of and into the formula. ; ... more
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50 ; Plug the values of and into the formula. ; ... more
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4950 ; Plug the values of and into the formula... more
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1 ; Plug the values of and into the formula. ; ... more
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1 ; Plug the values of and into the formula. ; ... more
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; Use the Binomial Theorem to expand the ... more
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; Use the Binomial Theorem to expand the given ... more
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17,010 ; Use the formula , where and . The power ... more
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1760 ; Use the formula , where and . The power on... more
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41,472 ; Use the formula , where and . The power ... more
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; Use the formula , where and . The power on the... more
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; The expansion of the given binomial has , or ... more
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; The expansion of the given binomial has , or ... more
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; The expansion of the given binomial has , or ... more
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; The expansion of the given binomial has , or ... more
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495 ; Write the general term in the expansion of ... more
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; Write the general term in the expansion of the ... more
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3360 ; Write the general term in the expansion of ... more
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252 ; Write the general term in the expansion of ... more
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1.00501 ; Use the hint provided to write the given... more
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0.98806 ; Rewrite the given number as . Then, use ... more
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; Use the hint provided to rewrite as . Expand ... more
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; Rewrite 0 as . Expand using the Binomial ... more
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1 ; Expand each term in the expression.Use the ... more
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ExpressionCalculator, Approximation ; Find ... more
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or to three decimal places ; Take the natural log... more
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; Construct the augmented matrix for the system... more
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Bounded ; Find the intercepts of the last two ... more
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; Evaluate the expression by substituting... more
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; Evaluate the expression by substituting... more
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Arithmetic Sequence, , ; Identify the first three... more
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Neither. ; Identify the first three terms by ... more
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Geometric Sequence, , ; Identify the first three ... more
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Arithmetic Sequence, , ; Let denote the given ... more
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; Let denote the given sequence. Check if it is ... more
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Neither. ; Let denote the given sequence. Check ... more
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; Use the property of sequences, i.e. , to split ... more
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; Use the formula to create an equation defined ... more
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The series converges; sum is ; First, determine ... more
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The series converges; sum is ; First, determine ... more
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The sequence diverges. ; First, determine the ... more
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The sequence converges, sum is . ; An infinite ... more
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; Show that the given series holds true for , ... more
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; Show that the given series holds true for , ... more
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; Show that the given series holds true for , ... more
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; The binomial coefficient represented by can be... more
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; The expansion of a power of a binomial, that is... more
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; The expansion of a power of a binomial, that is... more
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144 ; In the expansion of a power of a binomial, ... more
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84 ; In the expansion of a power of a binomial, ... more
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360 ; Since the number of blocks needed after each... more
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; The maturity value of an annuity, represented ... more
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; The annual earnings of the person increases by ... more
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; Evaluate the expression by substituting... more
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; Evaluate the expression by substituting... more
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; Substitute to the formula defined in the ... more
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; Substitute to the formula defined in the ... more
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; First, find a pattern that describes the ... more
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Neither. ; Let denote the given sequence. Check ... more
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Geometric Sequence, , ; Let denote the given ... more
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Arithmetic Sequence, , javascript:void(0) ; Let ... more
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Arithmetic Sequence, , ; Let denote the given ... more
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Geometric Sequence, , ; Let denote the given ... more
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Neither ; Let represent the given sequence. ... more
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Converges; ; From the given sequence, . The common... more
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; The expansion of is given by . Use this ... more
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Show that the given series is true for .Then, ... more
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; The worth of the car is reduced to a fraction ... more
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8000 lb ; The weight is increased by a specific ... more
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; Note that the absolute value of a function is ... more
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; To eliminate the , take the natural logarithm ... more
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; Every -intercept is of the form , so the line ... more
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; Since the center and another point on the ... more
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; Find the distance between the center (the ... more
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; The vertex and the focus both lie on the line... more
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, ; According to the given source, the value of ... more
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; The value of is equal to the difference ... more
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; According to the given source, the net ... more
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331,890,517 ; Use the recursive formula from the ... more
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The projected population for 2019 is acceptable ... more
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The birth rate, mortality rate, and net migration ... more
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The difference in the rate of growth of population... more
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It is highly unlikely for any drastic changes in ... more