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nikklg [1K]
3 years ago
5

Louie made 8.1 liters of fruit punch using only grape juice and carbonated water. He used 4.2 liters of grape juice. The equatio

n 4.2 + c = 8.1 can be used to represent this situation, where c is the number of liters of carbonated water used. How many liters of carbonated water did Louie use?
Mathematics
1 answer:
Dmitriy789 [7]3 years ago
7 0

Given:

The equation is:

4.2+c=8.1

Where c is the number of liters of carbonated water used.

To find:

How many liters of carbonated water did Louie use?

Solution:

We have,

4.2+c=8.1

We need to solve this equation for c to find the number of liters of carbonated water used by Louie.

Subtracting 4.2 from both sides, we get

4.2+c-4.2=8.1-4.2

c=3.9

Therefore, Louie used 3.9 liters of carbonated water.

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You randomly sample 5 people in your​ school, and none of them is a vegetarian. Does this mean that the probability of being a v
kap26 [50]

Answer:

B.

Step-by-step explanation:

The sample size taken for the school is too small.

5 people not being vegetarian does not mean NO OTHER students are vegetarian also. Thus, an assumption based on this probability of 5 people would not be correct unless fully supported. This makes option A wrong.

Answer B is correct because with small numbers, probability varies a lot and may change drastically with the addition of data.

For example: the 6th person we sample says he/she is a vegetarian.

This would change the probability drastically to 1/6 = 0.1667

Because this is a drastic change, and fluctuation is clear, answer B is correct.

C is wrong because probability is not subjective.

7 0
4 years ago
Find the 8th term of the geometric sequence. An=-2.5•4^n-1
Pachacha [2.7K]

8th term = 2.5×4^7 = 40960

8 0
4 years ago
Using the law of cosines, write an algebraic proof to show that the angles in an equilateral triangle must equal 60°. Use "∧" to
bekas [8.4K]

The algebraic proof shows that the angles in an equilateral triangle must equal 60° each

<h3>Laws of cosines </h3>

From the question, we are to use the law of cosines to write an algebraic proof that shows that the angles in an equilateral triangle must equal 60°.

Given any triangle ABC, the measures of angles A, B, and C by the law of cosines are

cos A = (b^2 + c^2 - a^2)/2bc

cos B= (a^2 + c^2 - b^2)/2ac

cos C = (a^2 + b^2 - c^2)/2ab  

Now, given that the triangle is equilateral, with each of the side lengths equal to s

That is, a = b = c = s

Then, we can write that

cos A = (s^2 + s^2 - s^2)/(2s×s)

cos A = (s^2 )/(2s^2)

cos A = 1/2

cos A = 0.5

∴ A = cos⁻¹(0.5)

A = 60°

Also

cos B = (s^2 + s^2 - s^2)/(2s×s)

cos B = (s^2 )/(2s^2)

cos B = 1/2

cos B = 0.5

∴ B = cos⁻¹(0.5)

B = 60°

and

cos C = (s^2 + s^2 - s^2)/(2s×s)

cos C = (s^2 )/(2s^2)

cos C = 1/2

cos C = 0.5

∴ C = cos⁻¹(0.5)

C = 60°

Thus,

A = 60°, B = 60° and C = 60°

Hence, the algebraic proof above shows that the angles in an equilateral triangle must equal 60° each.

Learn more on The law of cosines here: brainly.com/question/2866347

#SPJ1

3 0
2 years ago
What is the gcf of 48m^5n and 81m^2n^2
JulijaS [17]

Answer:

gcf is 3m^2n

Step-by-step explanation:

we are given

48m^5n and 81m^2n^2

Firstly, we will find factors of both expression

48m^5n=2\times 2\times2\times 2\times 3\times m^2\times m^3\times n

81m^2n^2=3\times 3\times 3\times 3\times m^2\times n\times n

now, we will find common factors among them

we can see that

For finding gcf, we always find common factors

so,

common terms are 3,m^2 and n

so, gcf is

=3\times m^2\times n

=3m^2n


8 0
3 years ago
How do you make this??
tatuchka [14]
For the 4/5 you do a number line all the way to 4/5 first u start off with 1/5 then 2/5 and so on
7 0
3 years ago
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