Answer:
A sample of 17 must be selected.
Step-by-step explanation:
We have that to find our 
level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Z-table as such z has a p-value of 
.
That is z with a pvalue of 
, so Z = 2.054.
Now, find the margin of error M as such
In which 
is the standard deviation of the population and n is the size of the sample.
The standard deviation from a previous study is 4 hours.
This means that 
How large a sample must be selected if he wants to be 96% confident of finding whether the true mean differs from the sample mean by 2 hours?
A sample of n is required.
n is found for M = 2. So
Simplifying both sides by 2:
Rounding up:
A sample of 17 must be selected.
32 meters tall.
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m. You're looking for the last side, the hypotenuse. So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
Which is, 49 + 576 = c^2
Add, 625 = c^2.
Take the square root of 625, which is 25. So, the length of the hypotenuse (last side) is 25m. Add the 7m that is sticking out of the ground, to get 32m.
Answer: x = 57
Step-by-step explanation:
Since CD = AC, triangle ACD is isosceles, therefore
ADC = DAC
ADC + DAC + 112 = 180
ADC + DAC = 180 -112 = 68
ADC + DAC = 68/2 = 34
DEB = 180 - 34 - 23 = 123 (sum of interior angles of a triangle = 180)
Therefore, x = 180 - 123 = 57 (DEB and x are supplementary angles)
