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09 Nov 2021, 03:00
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C
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Difficulty:
45%
(medium)
Question Stats:
74% (03:04) correct
26%
(03:05)
wrong
based on 290
sessions
History
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In the well-known Thanksgiving equation below, M = the number of minutes after dinner until a person falls asleep, t = the ounces of turkey consumed by that person, s = the ounces of stuffing consumed by that person, c = the number of cocktails consumed by that person, v = the ounces of total vegetables consumed by that person, and K is a constant. Last year, Aunt Jane fell asleep exactly 17 minutes after dinner and she consumed 8 ounces of turkey, 6 ounces of stuffing, 5 cocktails, and 10 ounces of vegetables. This year Lauren is planning on eating 10 ounces of turkey, 6 ounces of stuffing, and 14 ounces of vegetables, while drinking 7 cocktails.
\(M=\frac{2^{t+s}+4^c}{K^v}\)
If Lauren sticks to her plan, how many minutes after dinner will Lauren fall asleep?
A. 1
B. 2
C. 5
D. 20
E. It cannot be determined from the information given
\(M=\frac{2^{t+s}+4^c}{K^v}\)
If Lauren sticks to her plan, how many minutes after dinner will Lauren fall asleep?
A. 1
B. 2
C. 5
D. 20
E. It cannot be determined from the information given
09 Nov 2021, 04:39
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Aunt Jane:
\(17 = \frac{ 2^{8+6} + 4^5 }{ K^{10}}\)
\(17 = \frac{ 2^{14} + 2^{10} }{ K^{10}}\)
\(17K^{10} = 2^{10}(2^4 + 1) \)
\(17K^{10} = 2^{10}(17) \)
\(K = 2\)
Lauren:
\(M = \frac{ 2^{10+6} + 4^7 }{ 2^{14}}\)
\(M = \frac{ 2^{16} + 2^{14} }{ 2^{14}}\)
\(M = \frac{ 2^{14}( 2^2 + 1) }{ 2^{14}}\)
\(M = 2^2 + 1\)
\(M = 5\)
Answer C
\(17 = \frac{ 2^{8+6} + 4^5 }{ K^{10}}\)
\(17 = \frac{ 2^{14} + 2^{10} }{ K^{10}}\)
\(17K^{10} = 2^{10}(2^4 + 1) \)
\(17K^{10} = 2^{10}(17) \)
\(K = 2\)
Lauren:
\(M = \frac{ 2^{10+6} + 4^7 }{ 2^{14}}\)
\(M = \frac{ 2^{16} + 2^{14} }{ 2^{14}}\)
\(M = \frac{ 2^{14}( 2^2 + 1) }{ 2^{14}}\)
\(M = 2^2 + 1\)
\(M = 5\)
Answer C
17 Feb 2025, 09:01
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