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olya-2409 [2.1K]
2 years ago
13

There is a proportional relationship between the volume of a sample of helium in liters and the mass of that sample in grams. if

the mass of a sample is 5 grams, its volume is 28 liters. (5, 28) is shown on the graph below. what is the constant of proportionality in this relationship,
in this situation, what is the meaning of the number you found in question 1?(explain in the short answer) Add at least three more points to the graph above, and label with their coordinates.(Show your work)
Write an equation that shows the relationship between the mass of a sample of helium and its volume. Use m for mass and v for volume.(Please answer in v = form)

Mathematics
1 answer:
love history [14]2 years ago
6 0

Answer:

  • v = 5.6m

Step-by-step explanation:

<u>Proportional relationship equation:</u>

  • y = kx, where k- constant of proportionality

<u>Use the given point to work out the value of k:</u>

  • 28 = 5k
  • k = 28/5
  • k = 5.6

<u>In our case the equation is:</u>

  • v = 5.6m, where v- volume, m- mass
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Phantasy [73]

Answer:

8.9

Step-by-step explanation:

1)\ S = 80 => l = \sqrt{80}

2)\ l = \sqrt{80} = 8.9

4 0
3 years ago
What is Permutations and Combinations?
marissa [1.9K]

Answer:

See below

Step-by-step explanation:

Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.

Permutation can be expressed in math as:

\displaystyle{_n P _r = \dfrac{n!}{(n-r)!} \ \ \ (n \geq r) }

where n is a number of total object and r is a number of selected object to arrange. Hence. n cannot be less than r.

Now let's see an example of permutation, suppose we have letter A, B and C. I'd like to know how many ways these words can be arranged:

Since there are 3 letters total and 3 selected letters to arrange then:

\displaystyle{_3 P _3 = \dfrac{3!}{(3-3)!}}\\\\\displaystyle{_3 P _3 = \dfrac{3 \times 2 \times 1}{0!}}\\\\\displaystyle{_3 P _3 = \dfrac{6}{1}}\\\\\displaystyle{_3 P _3 = 6}

Therefore, there are 6 ways to arrange the letters - we can also demonstrate visually:

ABC - 1

ACB - 2

BAC - 3

BCA - 4

CAB - 5

CBA - 6

Notice that if you do visually, you'll get the same answer as the calculation of permutation!

----

Combination can be expressed mathematically as:

\displaystyle{_n C _r = \dfrac{n!}{(n-r)!r!} = \dfrac{_n P _r}{r!} \ \ \ (n \geq r) }

The difference between permutation and combination is that you only find how many ways you can select object in combination. Therefore, no arrange and doesn't care about order, just ways to select.

Suppose we have same 3 letters: A, B and C. I want to find how many ways I can select these 3 letters:

Since there are 3 letters total and 3 selected letters:

\displaystyle{_3 C _3 = \dfrac{3!}{(3-3)!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{0!3!}}\\\\\displaystyle{_3 C _3 = \dfrac{3!}{3!}}\\\\\displaystyle{_3 C _3 = 1}

Hence, there is only one way to select 3 letters. This makes sense because if you have 3 letters then you can only select 3 letters only one way.

5 0
2 years ago
What is the slope of a line that is perpendicular to the
alexgriva [62]

Answer:

The slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

Step-by-step explanation:

From the line equation, let us take two points

  • (0, 2)
  • (4, 1)

Finding the slope between two points

\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:1\right)

m=\frac{1-2}{4-0}

m=-\frac{1}{4}

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

The slope of the perpendicular line will be:

-\frac{1}{-\frac{1}{4}}=4

Thus, the slope of a line that is perpendicular to the line

shown in the graph is = 4

Hence, option 'd' is true.

5 0
3 years ago
A line passes through the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because x 2
yaroslaw [1]

Answer:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Step-by-step explanation:

Points:

  • (7, 10) and (7, 20)

Slope-intercept form:

  • y= mx+b

slope is:

  • m= (y2-y1)/(x2-x1)= (20-10)/(7-7)= 10/0,

denominator of the fraction is zero, we can't divide by zero, so this line has no slope

----------

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

  • no, numerator is not zero

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

  • no, it has no slope

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

  • no, numerator is not zero

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

  • yes
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3 years ago
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Joe ate 7 pies on wednesday. If that is only 1/4 of the world record for pie eating what is the pie record
Lina20 [59]

Answer:

7 pie is the world record. That is 1/4 under the record and your Answer.

Step-by-step explanation:

Who come up with these dump questions??

4 0
3 years ago
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