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neonofarm [45]
1 year ago
10

How many gallons each of 30% alcohol and 5% alcohol should be mixed to obtain 25gal of 25% alcohol?

Mathematics
1 answer:
lozanna [386]1 year ago
4 0

Let x be the amount of the 30% alcohol and let y be the amount of 5% alcohol.

We want the total amount to by 25 gal, then we have:

x+y=25

We also want the resulting mix to be 25% alcohol, this is 0.25 in decimal form; also we know that the first type of alcohol is 30% and the second is 5%, then we have:

\begin{gathered} 0.3x+0.05y=0.25(25) \\ 0.3x+0.05y=6.25 \end{gathered}

Hence we have the system of equations:

\begin{gathered} x+y=25 \\ 0.3x+0.05y=6.25 \end{gathered}

To solve the system we solve the first equation for y:

y=25-x

then we plug this value of y in the second equation:

\begin{gathered} 0.3x+0.05(25-x)=6.25 \\ 0.3x+1.25-0.05x=6.25 \\ 0.25x=6.25-1.25 \\ 0.25x=5 \\ x=\frac{5}{0.25} \\ x=20 \end{gathered}

Once we have the value of x we plug it in the expression we found for y:

\begin{gathered} y=25-20 \\ y=5 \end{gathered}

Therefore, the mixture will have 20 gallons of 30% alcohol and 5 gallons of 5% alcohol.

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Answer:

The matched options to the given problem is below:

Step1: Choose a point on the parabola

Step2: Find the distance from the focus to the point on the parabola.

Step3: Use (x, y).

Find the distance from the point on the parabola to the directrix.

Step4: Set the distance from focus to the point equal to the distance from directrix to the point.

Step5: Square both sides and simplify.

Step6: Write the equation of the parabola.

Step by step Explanation:

Given that the focus (-1,2) and directrix x=5

To find the equation of the parabola:

By using focus directrix property of parabola

Let S be a point and d be line

focus (-1,2) and directrix x=5 respectively

If P is any point on the parabola then p is equidistants from S and d

Focus S=(-1,2), d:x-5=0

Step1: Let P(x,y) be any point on parabola

Step2: Therefore the d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)

Step3: The perpendicular distance from p to d is

\frac{|x-5|}{\sqrt{(-1)^2+2^2}}

=\frac{|x-5|}{\sqrt{5}}\hfill (2)

Step4: equating (1) and (2)

\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}

Step5: squaring on both sides

(x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}

5[(x+1)^2+(y-2)^2]=(x-5)^2

5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0

12x+y^2-2y-24=0

Step6: Equation of the parabola is

y^2-2y+12x-24=0

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Help me out please an thank you
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Answer:

Answer is D

Step-by-step explanation:

because its sideways its x = y^2

and because its facing right its positive.

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3 years ago
seven people arrive to dinner, but the circular table only seats six. if two seatings such that one is a rotation of the other a
Alenkinab [10]

6 different people chosen from 7 can sit around the circular table in 840 ways.

Given that there are 7 people who have arrived for dinner.

But the circular table only seats 6.

Hence 1 person can be left out.

This can be done in 7 ways, which is a simple case of permutation.

A permutation is a combination of objects arranged in a particular sequence. The elements of sets are arranged in this case in a linear or sequential sequence.

Now 6 people will have to sit on the circular table.

Now from the properties of combination we know that , if n people sit around a circular table, then they can sit in n! ways.

Therefore 6 people can sit around a circular table in 6! ways.

6! = 120

Therefore total number of ways = 120 × 7 = 840

Hence 6 different people chosen from 7 can sit around the circular table in 840 ways.

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5 0
1 year ago
Two friends are collecting cards. Frank has 7 more than half the number of cards as his friend. Together they have 42 cards. How
Naddika [18.5K]

Answer:

The number of cards Frank has is 18 and the number of cards his friend has is 24.

Step-by-step explanation:

<u><em>The correct question is </em></u>

Two friends are collecting cards. Frank has 6 more than half the number of cards as his friend. Together they have 42 cards. How many cards does each friend have?

Let

x ----> the number of cards that Frank has

y ----> the number of cards that his friend has

we know that

Together they have 42 cards

x+y=42 ----> equation A

Frank has 6 more than half the number of cards as his friend

x=\frac{y}{2} +6 ---> equation B

Solve the system by substitution    

Substitute equation B in equation A

\frac{y}{2} +6+y=42

solve for y

\frac{3}{2}y=42-6\\\\\frac{3}{2}y=36\\\\y=36(2)/3=24

<em>Find the value of x</em>

x=\frac{24}{2} +6=18

therefore

The number of cards Frank has is 18 and the number of cards his friend has is 24.

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3 years ago
What is 235 divided by 5?
Alex Ar [27]
The answer to this question is: 47
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