Answer:
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ALGEBRA WORD PROBLEM
Dorian S. asked • 06/28/17
THREE LINEAR EQUATIONS WITH THREE VARIABLES
A chemist has three different acid solutions. The first acid solution contains 15% acid, the second contains 25%,
and the third contains 70%. He wants to use all three solutions to obtain a mixture of 40 liters containing 45%
acid, using 2 times as much of the 70% solution as the 25% solution. How many liters of each solution should be used?
How to set up as three linear equations to find the answer?
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Arthur D. answered • 06/28/17
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set up 2 equations
the first equation...
15%*x+25%*y+70%*2y=45%*40
0.15x+0.25y+1.4y=0.45*40
0.15x+1.65y=18
multiply all terms by 100
15x+165y=1800
divide all terms by 15
x+11y=120
the second equation...
x+y+2y=40
x+3y=40
x=40-3y
substitute into the first equation x+11y=120
40-3y+11y=120
40+8y=120
8y=120-40
8y=80
y=80/8
y=10 liters
x+3*10=40
x+30=40
x=40-30
x=10 liters
10 liters of 15%, 10 liters of 25%, and 20 liters of 70%
check:
10*15%=1.5
10*25%=2.5
20*70%=14
1.5+2.5+14=18
18/40=9/20=45/100=45%
45%*40=18
hope it helps
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Answer:
e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.
Step-by-step explanation:
The central limit theorem states that
"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."
This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.
Answer:
The measure of the sum of interior angles of a 11-gon is
.
Each interior angle is approximately
.
Step-by-step explanation:
A convex polygon has the measure of each interior angles to be less than
.
But,
sum of interior angles of polygon = (n - 2) x 
where n is the number of sides of the polygon.
For a convex 11-gon, we have;
sum of angles of a 11-gon = (11 - 2) x 
= 9 x 
= 
Sum of angles of a 11-gon = 
To check: convex polygons' interior angles are less than
.
so that,
each interior angle of 11-gon = 
= 
Answer:
m<C = 101°
m<E = 46°
Step-by-step explanation:
*This was the only problem I could figure out so I'm sorry*
C equals 101° b/c 1/2 a circle angle equals 180° which is the line. Angle F and Angle C are corresponding interior angles (same side angles) so if both of them together should equal 180. 180 - 79 (<F) = 101 (<C).
You do the same thing to find Angle E b/c it's corresponding interior angles to Angle D.
I hope you understand this explanation
The equation of a circle with center at (h,k) and radius r is

we are given
center is at (3,2)

solving for y



take the derivitive to find the slope at any point

we can use point slope form
for apoint (h,k) and slope m, the equation is
y-k=m(x-h)
not sure if you want in terms of what
I'll just say for a point (h,k)
so we get

where

that's the equation of the tangent line at (h,k) for arbitrary values of r
do the plots and other stuff yourself