Answer:
81
Step-by-step explanation:
27 total of pupils.
girls 1×27=27
boys 2×27=54
total 54+27=81
F(x)+g(x)=(x+5)+(11x-5)=x+11x+5-5=12x using the commutative property.
Expand everything in the limit:
We have 
approaching 0, and in particular 
, so we can cancel a factor in the numerator and denominator:
Alternatively, if you already know about derivatives, consider the function 
, whose derivative is 
.
Using the limit definition, we have
which is exactly the original limit with 
. The derivative is 
, so the value of the limit is, again, -14.
<span>let x = the number of liters of the 20% solution.
let y = the number of liters of the 60% solution.
you want x + y to be equal to 40 liters.
x is the number of liters total in the first solution.
y is the number of liters total in the second solution.
you want .2 * x + .6 * y to be equal to .35 * 40
.2 * x is the number of liters of acid in the first solution.
.6 * y is the number of liters of acid in the second solution.
.35 * 40 is the number of liters of acid in the final solution.
you have two equations that need to be solved simultaneously.
they are:
x + y = 40
.2x + .6y = .35*40
simplify these equations to get:
x + y = 40
.2x + .6y = 14
you can solve by substitution or by elimination or by graphing.
i will solve this one by graphing.
this means to graph both equations and find the intersection.
the graph looks like this:
the graph says the intersection is at the coordinate point of (25,15).
this means that x = 25 and y = 15.
x is the number of liters of the 20% solution.
y is the number of liters of the 60% solution.
the formula of .2x + .6y = 14 becomes .2 * 25 + .6 * 15 = 14.
simplify this equation to get 14 = 14.
this confirms the solution is good.
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