Answer:
33 1/3 L of the 40% solution, 16 2/3 L of the 25% solution
Step-by-step explanation:
Set up two equations...
Let x represent the number of Liters of the 40% solution
Let y represent the number of Liters of the 25% solution
We need 50 liters total, so
x + y = 50
and we need the 50 L to be 35% solution, so
0.4x = 0.25y = 0.35(50)
Solve the first equation for one variable...
x = 50 - y (subtract y from both sides in equation 1)
Now substitute that value into the second equation...
0.4(50 - y) + 0.25y = 17.5 (x becomes 50 - y, 0.35(50) = 17.5)
Now solve for y...
20 - 0.4y + 0.25y = 17.5
-0.15y = -2.5
y = 16.66666667
y = 16 2/3 L
So we need to plug that into the first equation to find 'x'
x + 16 2/3 = 50
x = 50 - 16 2/3
x = 33 1/3
Answer:
The third one, x+(x+1)+(x+2)=-21 because x, x+1 and x+2 are three consecutive numbers.
For the 3rd sum
Subtract
(10^5 - 10^2) = 10^3
And for the 4th sum
a) 2(2b+g)
b) b = - 2g/4
c). g = - 4b/2
Answer:
At least 13 chocolates must be removed
Step-by-step explanation:
If there are three flavors, the probability of drawing 1 would be: 1
1/3 = 0.333
Which means, that every 3 attempts, theoretically you should do 1 of each, but how they ask for 5 chocolates of each would be:
3 * 5 = 15
At least 15 chocolates must be extracted to theoretically guarantee 5 chocolates each, but how we are interested in knowing is that a single flavor has 5 chocolates, so we discard the last two chocolates that represent the other two flavors
Therefore, for there to be safely 5 chocolates of the same flavor, at least 13 chocolates must be removed.
Start at (-3,9). The increase in x from this point to the midpoint (3,3) is 6. Add 6 to the x-coordinate of (3,3), obtaining 9, which is the x-coordinate of the other endpoint of the line segment.
Next, notice that y decreases by 6 from 9 to 3 as we travel from (-3,9) to (3,3). Decrease y again by 6: 3 less 6 is -3. So the y-coordinate of the other endpoint is -3.
Thus, the coordinates of the other endpoint are (9, -3).
Let's check whether this is correct or not. According to the midpoint formula, e find the x-coordinate of the midpoint by summing up the endpoint x values and dividing this sum by 2: (-3+9)/2 = 3. This agrees with the given midpoint (3,3).
