Given set S = <span>{A, B, C, D, E, F, G, H}
There are 8 elements in set S and we are to choose 3 letters at random, the number of ways to choose such is x. It is simply similar to choosing 5 letters at random, which is also equal to x. Since order doesn't matter, n! / (n-m)! where n = 8 and m = 3, which is 336 ways. </span>
Solving a system of equations we will see that we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
<h3>
How many liters of each solution do we need to use?</h3>
First, we need to define the variables:
- x = liters of the 35% acid used.
- y = liters of the 80% acid used.
We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use <u>40 liters of the 80% acid solution</u>, and the other <u>20 liters are of the 35% acid solution</u>.
If you want to learn more about systems of equations:
brainly.com/question/13729904
#SPJ1
Plot a graph of y-axis against x-axis.
The graph should be a straight line passing through:
(-2,0.8) , (-1,-0.4) , (0,0) , (1,0.4) and (2,0.8)
I don’t really understand the question at hand but let me try to help
X is equal to 4 we know this because because the sign in between the number means greater than or equal to so 3 x 4 equals 12 and that makes the equation on right true and on the left x is also equal to for which also makes the statement on the right true as well so I think X = 4
I hope I was able to help and If not I’m sorry
It is a polynomial, and the degree is quartic
hope this helps
