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Romashka-Z-Leto [24]
2 years ago
8

How many ways can 6 people sit on a bench if 3 of them have to sit side by side

Mathematics
1 answer:
pickupchik [31]2 years ago
4 0

Answer:

144 ways

Step-by-step explanation:

Let's think of the 3 persons sitting together as "one". So essentially we have 3 + "1" = "4" persons to arrange.

THey can be arranged in 4! ways, which is:

4! = 4 * 3 * 2 * 1 = 24 ways

Now, the 3 persons themselves can be arranged in 3! ways, which is:

3! = 3 * 2 * 1 = 6 ways

Total ways = 4! * 3! = 24 * 6 = 144 ways

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(1 point) Rework problem 15 in section 2 of Chapter 5 of your textbook about the growing suburb and the declining city using the
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Answer:

16 years

Step-by-step explanation:

Let x represent the number of years. The suburb population is growing at a rate of 5000 per year after x years, it can be represented by the equation:

320000 + 5000x

The city population is declining at a rate of 14000 per year after x years, it can be represented by the equation:

624000 - 14000x

The number of years for the city and suburb population to be equal can be gotten from:

320000 + 5000x = 624000 - 14000x

14000x + 5000x = 624000 - 320000

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In 16 years the populations of the suburb and the city be equal

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Adrienne has several receipts from recent transactions that she entered in her records. The receipts include an ATM receipt for
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Which number below has a value between 6.6 and 6.7?
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The answer is √44

Step-by-step explanation:

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Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere.
Advocard [28]
The volume of a sphere is given by:

V= \frac{4}{3} \pi r^{3}

So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution<span>) that lies on the same plane. We know from calculus that:

</span>V=\pi \int_{a}^{b}[f(x)]^{2}dx
<span>
Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:

</span>x^{2}+y^{2}=r^{2}
<span>
Isolationg y:

</span>y= \sqrt{r^{2}-x^{2}}<span>

So,

</span>f(x)=y=\sqrt{r^{2}-x^{2}}<span>

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<span>
</span>V=\pi \int_{a}^{b}(r^{2}-x^{2})dx<span>

being -r and r the limits of this integral. 

</span>V=\pi \int_{-r}^{r}(r^{2}-x^{2})dx
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Solving:

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