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3 years ago

In how many unique ways can 4 boys and 4 girls sit around a circle table if all the boys sit together?

1 answer:

3 0

Working it completely in my head, I come up with 2,880 unique ways. I'll check it when I get back to a computer with an actual keyboard, and also explain my reasoning if anybody's interested.

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Herman is traveling 125 miles from his house to the beach by car. Herman plans to stop for lunch when the ratio of the distance

aliya0001 [1]

Answer:

250 miles

Step-by-step explanation:

The given distance between the house and the beach is 125 miles.

Let $x$ miles be the distance between the house and the lunch stop.

So, at the time of the lunch stop, he already traveled $x$ miles, the remaining distance is the distance between the lunch stop and the beach.

Let $y$ miles be the remaining distance, so

$y=125-x.$

Give that the ratio of the distance he has traveled, $x$ , to the distance he still has to travel, $y$ , is $2:3$ ,i.e

$x:y=2:3$

$\Rightarrow \frac x y =\frac 2 3$

$\Rightarrow \frac {x}{125-x}=\frac 2 3$

$\Rightarrow 3\times x=2\times(125-x)$

$\Rightarrow 3\times x=2\times125-2\timesx$

$\Rightarrow 3 x=250-2x$

$\Rightarrow 3x-2x=250$

$\Rightarrow x=250$

Hence, the distance traveled by Herman when he stops for lunch is 250 miles.

4 0

2 years ago

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 <u>100 times stronger</u> 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 $\frac{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}1 }{strength\hspace{0.1cm}of\hspace{0.1cm}earthquake\hspace{0.1cm}2} = \frac{10^{8} }{10^{6} } = 100$