Answer:
a) , b)
, c)
, d)
, e)
, f)
Step-by-step explanation:
The velocity function can be derived by the differentiating the height function:
Velocities after 2 and 4 seconds are, respectively:
a)
b)
The maximum height is reached when velocity is zero. Then:
c)
The maximum height is:
d)
The time required to hit the ground is:
Roots of the second-order polynomial are:
Only the first root is physically reasonable.
e)
The velocity when the projectile hits the ground is:
f)
Answer:
n=369
Step-by-step explanation:
1) Notation and definitions
number of the selected labourers opt for a new incentive scheme.
random sample taken
estimated proportion of the selected labourers opt for a new incentive scheme.
true population proportion of the selected labourers opt for a new incentive scheme.
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".
The population proportion have the following distribution
2) Solution tot he problem
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 margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=369
