Confidence interval decreases, error decreases
Option: a
<u>Explanation:</u>
Increasing of sample size will decrease the width of the confidence intervals because it also decreases the standard error of the interval. So whenever the 'sample size' is increases then the 'confidence interval' decreases as well as the 'error' decreases.
Confidence interval gives us the unknown average population or percentage of the population. This gives us just how much the average rate is varying. Confidence interval gives the location as well as the precision of a measure. The smaller sample sizes gives more wider intervals.
Answer:
Distance covered by the bird before meeting the water is: 51.264 ft
Step-by-step explanation:
Notice that if the bird catches the fish in 2 seconds, then the fish was able to dive down a total of 6 feet before being caught:

So the bird needs to fly in the direction of the hypotenuse of a right angle triangle (see attached image) that has one leg of length (24 ft + 6 ft) = 30 ft, and another one 22.5 ft (half the width of the river.
Such hypotenuse is (using Pythagoras theorem):

Now, in order to find the distance D the bird covers from the top of the tree to the water (marked in red in our image), we use similar triangles. The bigger triangle is that of legs 60 ft and 22.5 ft and hypotenuse 64.08 ft.
The smallest triangle we use in the proportion is the one shaded yellow in the image, which has one leg equal to 24 ft, and unknown hypotenuse:
So we make the proportion between known legs, and hypotenuses:

Answer:
5/2 x^2y^2
Step-by-step explanation:
( x^2 - 3/5y^2)^2 + (3/4 x^2 + 4/5 y^2)^2 - (5/4x^2 - y^2)^2
= x^4 - 6/5x^2y^2 + 9/25y^4 + 9/16x^4 + 6/5x^2y^2 + 16/25y^4 - ( 25/16x^4
- 5/2x^2y^2 + y^4)
Distributing the negative over the parentheses:-
= x^4 - 6/5x^2y^2 + 9/25y^4 + 9/16x^4 + 6/5x^2y^2 + 16/25y^4
- 25/16x^4
+ 5/2x^2y^2 - y^4
Bringing like terms together
x^4 + 9/16x^4 - 25/16x^4 - 6/5x^2y^2 + 6/5x^2y^2 + 5/2x^2y^2 + 16/25y^4 + 9/25y^4
- y^4
Adding like terms:-
= 5/2 x^2y^2 Answer