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(a)  We can use a system here to solve this. 

Let x=amount of red potion used

Let y=total amount of potion in solution

 
200 + x =  y
0.15(200) + 0.75x = 0.25y

.15(200) because 15% of the blue potion=.15 and there is 200mL. 

.75x because 75% of the red potion=.75 and there is x amount of it 

.25y because we want 25% of the total potion=.25 and there is y amount of it

We can substitute for y in the second equation:
0.15(200) + 0.75x = 0.25(200 + x)

Simplify: 
30 + 0.75x = 50 + 0.25x
-20 = -0.5x
x = 40

Knowing that x=40, we know that y=240, meaning our answer is 240.

b.) We can again use a system for this problem

Let x=Amount of red potion

Let y=Amount of blue potion

x + y = 400
0.3(400) = 0.15y + 0.75x

.3(400)=30% of the 400 mL 

.15y=15% of the magic syrup

.75x=75% of the magic syrup

We can substitute for x in this equation: 
120 = 0.15y + 0.75(400 - y)

Simplify: 

120 = 0.15y + 300 - 0.75y
-180 = -0.6y
y = 300, x = 100

There are 300 mL of blue potion used and 100 mL of red potion used. 

c.) Let x=amount of red potion

Let y=amount of blue potion

0.15x + 0.75y = 0.35(x + y)
.35(x+y) because the total amount of the potion is x+y

Simplify: 

0.15x + 0.75y = 0.35x + 0.35y
0.4y = 0.2x
2y = x

Whenever there is a ratio of 2 (blue potion):1 (red potion), there will be a 35% amount of magical syrup.

For example, 200 mL of blue potion and 100 mL of red potion would work. 

https://web2.0calc.com/questions/distributions_2

Let  be the distance to the beach, in miles. Then the time it took to drive to the beach, at 40 miles per hour, is d/40 (in hours).

If I had driven at 30 miles per hour instead, then it would take me d/30  hours. Note that 1 hour is equivalent to 60 minutes, so 20 minutes is equivalent to  of an hour. Therefore,

d/40=d/30-1/3

Multiplying both sides by 120 to get rid of the fractions, we get

3d=4d-40

so, d=40. As a check, we see that at 40 mph it took me 1 hour to drive 40 miles, and at 30 mph it would have taken me 1 hour and 20 minutes, as required.

Hope this helps.

Which numbers are missing from your list:

2, 3, 5, 6, 7, 10, 11, ...

All the missing numbers are squares, cubes and perfect powers. Do you think you can continue the list?

What is "the product of her rolls..........??"

b) 

17.3  -  13.561 ==3.739 ==3.7 trillion

A==7

B==24

C==25

7^2  +  24^2 ==25^2

Perimeter ==7  +  24  +  25 ==56

Area ==7  x  24/2 ==84

Perimeter / Area ==56 / 84 ==2 / 3

#2 is correct but #1 is 0.1475 because you forgot the percent symbol.

.1 

14(1/3)

Multiplying these together gets us

4.666 (repeating)

.2 

42.5% in its simplest form is 17/40

Hope i could help!

Let me help. 

24=3/4r 

we can multiply both sides by the reciprocal of 3/4 which is 4/3

4/3*24=3/4r*4/3

This leaves us with

32=r 

Hope I could help!

2011  -  1986 ==25 years

In that period of 25 years, the inflation rate went up by:

224.939 / 109.60 ==2.05236314 - or more than doubled

$130,000 / 2.05236314 ==$63,341.62 - average price of a house in 1986 dollars.

60%=60/100=6/10

110*6/10=11*6

66

You got your equation all mixed up:

40T = 30(T + 20/60), solve for T

T = 1 hour.

From left-side of the equation, you have:

1 hour x 40 miles =40 miles - distance to the beach.

One six-sided die tossed 7 times should give you this many pemutations:

6^7 = 279,936 possible sequences.

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Take the first equation, and multiply it by 8. This gives us \(8x + 8y + 24x = 80\). 

Subtracting the second equation from this gives us \(12x + 19z = 73\). 

Now, take the third equation and multiply it by 19. This gives us \(19kx + 19z = 57\)

These two equations won't have any solutions when the coefficient of x in both equations is equal. This will mean that two of the same things sum to two different values, which is impossible. 

This means that \(12 = 19k\), meaning \(k = \color{brown}\boxed{12 \over 19}\)

I'm not sure if understand your question! But here a list of all 36 permutations of 2 rolled dice:

(1, 1) ,  (1, 2) ,  (1, 3) ,  (1, 4) ,  (1, 5) ,  (1, 6) ,  (2, 1) ,  (2, 2) ,  (2, 3) ,  (2, 4) ,  (2, 5) ,  (2, 6) ,  (3, 1) ,  (3, 2) ,  (3, 3) ,  (3, 4) ,  (3, 5) ,  (3, 6) ,  (4, 1) ,  (4, 2) ,  (4, 3) ,  (4, 4) ,  (4, 5) ,  (4, 6) ,  (5, 1) ,  (5, 2) ,  (5, 3) ,  (5, 4) ,  (5, 5) ,  (5, 6) ,  (6, 1) ,  (6, 2) ,  (6, 3) ,  (6, 4) ,  (6, 5) ,  (6, 6) ,  Total == 36 possible outcomes.

Use it as an aid to help you with your question, if yo understand it. Good luck.

This question makes no sense to me.