exactly 512 small cubes perfectly fill a lidless cubical box. All of the small cubes were removed except those touching the bott
1 answer:
Answer: 216
Step-by-step explanation:
Since, a cube is a 3D structure,
We can understand this problem by assuming the figure in the coordinate axis.
In which, The cubes in the box along x-axis = 10
Along y-axis = 10
Along z-axis = 10
Total cubes along each x, y, z directions those are not appearing on surface are (10-2), (10-2), (10-2) = 8, 8, 8
Therefore total cubes which are not shown on the surface of the cube=
Since, the box that are not in the surface are removed.
Thus, the total boxes that are removed = 216
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Answer:
Pease check my assumptions.
Step-by-step explanation:
I will assume that f(x)=x2 is actually f(x) = x^2.
Same for g(x)=(12x)^2 [Is it g(x)=12x^2 ???]
See the attached image.
Note that (12x)^2 results in a narrower, steeper graph. That's because (12x)^2 can be rewritten as 144x^2, so every value is multiplied by 144, compared to just x^2.
Answer:
a)
The 95% confidence interval would be given by (0.487;0.553)
b) After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
Part a
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The confidence interval for the mean is given by the following formula:
If we replace the values obtained we got:
The 95% confidence interval would be given by (0.487;0.553)
Part b
After see the confidence interval we see that the lower limits 0.487>0.44 with 0.44 or 44% the estimated proportion for 1960, we can conclude that we have a significant increase in the adult proportion had never smoked cigarettes at 5% of significance.