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MaRussiya [10]
3 years ago
6

A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost? Verify your answe

r using mathematical reasoning and language.
Mathematics
1 answer:
shutvik [7]3 years ago
3 0

Answer:

$162÷24=$6.75

$6.75-per each

five pairs of socks-$6.75x5=$33.75

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Find the general term of {a_n}
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From the given recurrence, it follows that

a_{n+1} = 2a_n + 1 \\\\ a_{n+1} = 2(2a_{n-1} + 1) = 2^2a_{n-1} + 1 + 2 \\\\ a_{n+1} = 2^2(2a_{n-2}+1) + 1 + 2 = 2^3a_{n-2} + 1 + 2 + 2^2 \\\\ a_{n+1} = 2^3(2a_{n-3} + 1) + 1 + 2 + 2^2 = 2^4a_{n-3} + 1 + 2 + 2^2 + 2^3

and so on down to the first term,

a_{n+1} = 2^na_1 + \displaystyle \sum_{k=0}^{n-1}2^k

(Notice how the exponent on the 2 and the subscript of <em>a</em> in the first term add up to <em>n</em> + 1.)

Denote the remaining sum by <em>S</em> ; then

S = 1 + 2 + 2^2 + \cdots + 2^{n-1}

Multiply both sides by 2 :

2S = 2 + 2^2 + 2^3 + \cdots + 2^n

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S - 2S = 1 - 2^n \implies S = 2^n - 1

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xz_007 [3.2K]

Hey there!

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New equation: 3q + 102 = 2

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Cancel out: 102 - 102 because it gives us 0

Keep: 2 - 102 because it helps us solve for our q

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New equation: 3q = -100

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3q/3 = -100/3

Cancel out: -3q/3 because it gives us 1

Keep: -100/3 because it gives us the answer for q

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Good luck on your assignment and enjoy your day!

~LoveYourselfFirst:)

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