Translate into an algebraic expression: One sixth of the sum of A and B

Mathematics

2 answers:

BabaBlast [244]3 years ago

7 0

(a+b)/6

Add the two together and divide by six; thus one-sixth the SUM of A & B

WARRIOR [948]3 years ago

5 0

$\frac{1}{6} (a+b)$
Opening brackets;
$\frac{1}{6} a+ \frac{1}{6}b$

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1) The population of a town was7652in 2016. The population grows at a rate of 1.6%annually.(a)Use the exponential growth model t

marshall27 [118]

Answer:

1. a) population of the town in 2024 = 8697

2.) the earthquake with a magnitude of 8 is a 100 times stronger than an earthquake with a magnitude of 6.

Step-by-step explanation:

1) the population of a town was, $N_{0} = 7652$ in 2016.

a) Exponential growth model is given by $N(t) = N_{0} e^{kt}$ where t is the time in years after 2016.

Year 2016 is when t = 0.

k = growth rate constant = 1.6% = 0.016

i) therefore the population of the town in 2024

= $N = N_{0} e^{kt} = 7652e^{0.016\times8} = 8697$ ( to the nearest whole number)

2.) log (I $\times$ M $\times$ S) = magnitude of earthquake where I is the Intensity of the earthquake and S is the intensity of a standard earthquake

therefore I $\times$ M $\times$ S = $10^{magnitude\hspace{0.1cm}of\hspace{0.1cm}earthquake}$

therefore $\frac{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}1 }{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}2} = \frac{10^{8} }{10^{6} } = 100$