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3 years ago

What is required of a proportional relationship that is not required of a general linear relationship?

1 answer:

8 0

The proportional relationship should require they y-intercept and is then 0 and the linear relationship should be in a straight line to be a linear! Hope this helps!

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A system contains n atoms, each of which can only have zero or one quanta of energy. How many ways can you arrange r quanta of e

My name is Ann [436]

Answer:

$\mathbf{a)} 2\\ \\ \mathbf{b)} 184 \; 756 \\ \\\mathbf{c)} \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

Step-by-step explanation:

If the system contains $n$ atoms, we can arrange $r$ quanta of energy in

$\binom{n}{r} = \dfrac{n!}{r!(n-r)!}$

ways.

$\mathbf{a)}$

In this case,

$n = 2, r=1$ .

Therefore,

$\binom{n}{r} = \binom{2}{1} = \dfrac{2!}{1!(2-1)!} = \frac{2 \cdot 1}{1 \cdot 1} = 2$

which means that we can arrange 1 quanta of energy in 2 ways.

$\mathbf{b)}$

In this case,

$n = 20, r=10$ .

Therefore,

$\binom{n}{r} = \binom{20}{10} = \dfrac{20!}{10!(20-10)!} = \frac{10! \cdot 11 \cdot 12 \cdot \ldots \cdot 20}{10!10!} = \frac{11 \cdot 12 \cdot \ldots \cdot 20}{10 \cdot 9 \cdot \ldots \cdot 1} = 184 \; 756$

which means that we can arrange 10 quanta of energy in 184 756 ways.

$\mathbf{c)}$

In this case,

$n = 2 \times 10^{23}, r = 10^{23}$ .

Therefore, we obtain that the number of ways is

$\binom{n}{r} = \binom{2\times 10^{23}}{10^{23}} = \dfrac{(2\times 10^{23})!}{(10^{23})!(2\times 10^{23} - 10^{23})!} = \dfrac{(2\times 10^{23})!}{(10^{23}!)(10^{23})!}$

3 0

3 years ago

Sarah and Jane both brought new storage containers for packing away winter clothing. Sarah’s storage containers are cubic meters

kobusy [5.1K]

Answer: the answer is Sarah

Step-by-step explanation:

Just got it correct on Plato

4 0

3 years ago

Who can help me with these questions

damaskus [11]

#15(A)
First Bike
$380 - $190 ($380 * 0.50) = $190

2nd Bike
$380 - $114 ( $380 * 0.30) = $266
$266 - $53.20 ($266 * 0.20) = $212.80

#15 (B)
Eliza should buy the first bike because it is cheaper. $190 < $212.80

#16
$57 + $28.50 ($57 * .50) = $85.50

6 0

2 years ago

Can someone graph this? I'll give brainliest.

vodomira [7]

It's nice of you to offer, but no thanks.

To correctly graph this, you need to set up a simple equation and table of values. Luckily, this equation is dead-simple; I'll define y as the total cost and x as the number of water bottles sold.

$y=1.5x$

Since 1.50$ is the cost for one bottle, multiplying that with your variable that defined the amount of bottles, x, gets you the total, y. Now that we have a basic equation, we can begin plugging in values.

Recall that a function is basically just something that takes in a value and returns another one; in our case, it takes the amount of bottles and returns the total cost. Now, plug in the x-values present on the graph (specifically only whole numbers, since you can't have a half bottle). I can't make a proper table but I'll make do.

x y

--------

0 0

1 1.5

2 3

3 4.5

4 6

5 7.5

-----------

Great, now that you have a table of values all you have to do is plug them into the graph, which I've attached. It's pretty crude since I drew it in mspaint but I'm sure you get the point at this point.

7 0

3 years ago

Can 29 be broken down to an even number

Novay_Z [31]

29 can not be broken down to an even number

8 0

3 years ago