Point estimate for the difference between two population proportions is the difference between the two sample proportions, written as:
and the standard deviation is given by
When np and n(1-p) is greater than 5, then the sampling distribution is approximately normal and we can use standard normal methods.
Thus, the propability of a test <span>for the difference between two population proportions is given by
</span>
The maximum volume of the box is 40√(10/27) cu in.
Here we see that volume is to be maximized
The surface area of the box is 40 sq in
Since the top lid is open, the surface area will be
lb + 2lh + 2bh = 40
Now, the length is equal to the breadth.
Let them be x in
Hence,
x² + 2xh + 2xh = 40
or, 4xh = 40 - x²
or, h = 10/x - x/4
Let f(x) = volume of the box
= lbh
Hence,
f(x) = x²(10/x - x/4)
= 10x - x³/4
differentiating with respect to x and equating it to 0 gives us
f'(x) = 10 - 3x²/4 = 0
or, 3x²/4 = 10
or, x² = 40/3
Hence x will be equal to 2√(10/3)
Now to check whether this value of x will give us the max volume, we will find
f"(2√(10/3))
f"(x) = -3x/2
hence,
f"(2√(10/3)) = -3√(10/3)
Since the above value is negative, volume is maximum for x = 2√(10/3)
Hence volume
= 10 X 2√(10/3) - [2√(10/3)]³/4
= 2√(10/3) [10 - 10/3]
= 2√(10/3) X 20/3
= 40√(10/27) cu in
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Complete Question
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Alright so first you want to find out how you take 30% off of $30. The first step is to ask yourself, what's 30% of $30? All you have to do is make the percentage into a decimal like you did and multiply .30 times 30. That gets you 9. So 9 is 30% of $30, but since it said the original 30 was marked down by that much, it means subtract. 30-9=21.
For the second part, you pretty much do the same thing but using the 21 you just got and taking away 20% this time. Same process so .20 times 21=4.2, and take the 4.2 away from 21 to get 21-4.2=16.8.
Convert that to dollars to see that the final price is $16.80.
Just a tip, a lot of people will forget the subtraction part after they find the percentage part. Most of these type questions are two steps like that so don't forget to subtract when needed. Lmk if you still have questions :)
Answer:
I have no idea
Step-by-step explanation:
This question doesn't have enough information for me to answer it.
80 because 16 divided by 20%
of means multiply but in this case divide
