2 fraction that is equal to 1/4
2 answers:
You might be interested in
Answer:
233.48s
3.84 min
Step-by-step explanation:
In order to solve this problem, we can start by drawing what the situation looks like. See attached picture.
We can model this situation by making use of a trigonometric function. Trigonometric functions have the following shape:
where:
A= amplitude =-20m because the model starts at the lowest point of the trajectory.
f= the function to use, in this case we'll use cos, since it starts at the lowest point of the trajectory.
t= time
angular speed.
in this case:
where T is the period, in this case 6 min or
so:
and
= phase angle
C= vertical shift
in this case our vertical shift will be:
2m+20m=22m
in this case the phase angle is 0 because we are starting at the lowest point of the trajectory. So the equation for the ferris wheel will be:
Once we got this equation, we can figure out on what times the passenger will be higher than 13 m, so we build the following inequality:
so we can solve this inequality, we can start by turning it into an equation we can solve for t:
and solve it:
and we can take the inverse of cos to get:
which yields two possible answers: (see attached picture)
so
or
so we can solve the two equations. Let's start with the first one:
t=63.25s
and the second one:
t=296.73s
so now we can build our possible intervals we can use to test the inequality:
[0, 63.25] for a test value of 1
[63.25,296.73] for a test value of 70
[296.73, 360] for a test value of 300
let's test the first interval:
[0, 63.25] for a test value of 1
2>13 this is false
let's now test the second interval:
[63.25,296.73] for a test value of 70
15.16>13 this is true
and finally the third interval:
[296.73, 360] for a test value of 300
12>13 this is false.
We only got one true outcome which belonged to the second interval:
[63.25,296.73]
so the total time spent above a height of 13m will be:
196.73-63.25=233.48s
which is the same as:
see attached picture for the graph of the situation. The shaded region represents the region where the passenger will be higher than 13 m.
Answer:
a. The 99% confidence interval for the population proportion is (0.7872, 0.8610).
D. Yes, we can conclude that the population proportion exceeds 75% because 75% is below the lowest believable value of the confidence interval.
b. The 99% confidence interval would be wider than a 95% confidence interval.
As the confidence level increases, the width interval increases, as we are requiring more confidence with the same information (there is no new sample). This means that, to be more confident, the only way is to include more values in the interval.
Step-by-step explanation:
We have to calculate a 99% confidence interval for the proportion.
The sample proportion is p=0.8241.
The standard error of the proportion is:
The critical z-value for a 99% confidence interval is z=2.5758.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 99% confidence interval for the population proportion is (0.7872, 0.8610).
We can conclude that there is, at least, 99% chances that the true proportion is higher than 0.7872. So there is at least 99% chances that the population proportion is higher than 0.75.