Answer:
Step-by-step explanation:
The given system is:
Since I prefer to use smaller numbers I'm going to divide both sides of the first equation by 3 and both sides of the equation equation by 6.
This gives me the system:
We could solve the first equation for 
and replace the second with that.
Let's do that.
Subtract 
on both sides:
So we are replacing the second in the second equation with 
which gives us:
Now recall the first equation we arranged so that was the subject. I'm referring to .
We can now find given that using the equation .
Let's do that.
with :
So the solution is (8,-1).
We can check this point by plugging it into both equations.
If both equations render true for that point, then we have verify the solution.
Let's try it.
with 
:
is a true equation so the "solution" looks promising still.
with :
is also true so the solution has been verified since both equations render true for that point.
The total amount of the resulting mixture can be calculated by adding up the volume of the given substances assuming that volume addition is applicable given the properties of the fluids used.
That is,
T = 6 quarts + 10 quarts = 16 quarts
The total volume of the resulting mixture is 16.
Then, we do the component (antifreeze) balance by adding up the resulting antifreeze from the substances to the total. We let x be the percentage of antifreeze in the final mixture.
6(0.52) + 10(0.32) = 16(x)
The value of x from the equation is 0.395.
Therefore, the answer to this item is 39.5%.
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Add '-1' to each side of the equation.
1 + -1 + 3d = 10 + -1
Combine like terms: 1 + -1 = 0
0 + 3d = 10 + -1
3d = 10 + -1
Combine like terms: 10 + -1 = 9
3d = 9
Divide each side by '3'.
d = 3
Simplifying
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Answer:
perimeter-
perimeter outer rectangle = 2 (l+b)
=2×8+9
= 2×17
2×17 =34 cm sq.
perimeter of inner rectangle = 2 (l+b)
= 2×5+3
=2× 8
= 16 cm sq.
perimeter of shaded portion= 34 - 16
= 18 cm sq.
area-
<em>area</em><em> </em><em>of</em><em> </em><em> </em><em>inner</em><em> </em> rectangle =l×b
l×b = 3×5
3×5=15
15 cm sq.
area of outer rectangle =l×b
l×b= 9×8
9×8= 72
72 cm sq.
area of shaded portion = 72 -15 =57 cm sq.
hey there! In second method i have done first area of inner rectangle but you have to do first area of outer rectangle...
hope it helps you....
Answer:
The probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes <em>n</em> > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
The standard deviation of this sampling distribution of sample proportion is:
Let <em>p</em> = the proportion of keypads that pass inspection at a cell phone assembly plant.
The probability that a randomly selected cell phone keypad passes the inspection is, <em>p</em> = 0.77.
A random sample of <em>n</em> = 111 keypads is analyzed.
Then the sampling distribution of 
is:
Compute the probability that the proportion of passed keypads is between 0.72 and 0.80 as follows:
Thus, the probability that the proportion of passed keypads is between 0.72 and 0.80 is 0.6677.
