The two figures are congruent because the side lengths are the same, therefore making the angle measures the same.
Answer:
Overall rectangle: 100 ft × 8 16/23 ft ≈ 100 ft × 8.696 ft
Individual pen: 8 16/23 ft × 4 6/11 ft ≈ 8.696 ft × 4.545 ft
Step-by-step explanation:
Half the fence will be used in each of the orthogonal directions to make the pen. That is, the long side of the overall rectangle will be (400 ft/2)/2 = 100 ft. The short side of the overall rectangle will be (400 ft/2)/23 = 8 16/23 ft. (There are 21 partitions between the 22 pens, and 2 end fences, for a total of 23 fence segments of the short length.)
The long (100 ft) side of the overall rectangle is divided into 22 parts by the internal partitions, so each pen will have a short dimension of 100 ft/22 = 4 6/11 ft.
_____
We know half the fence will be used in each direction because we know the total area is a quadratic function of the side length. If the long side of the overall pen is x, then the short side is (400 ft -2x)/23, and the overall area is ...
... A = x(400 ft -2x)/23
The vertex of this quadratic function is halfway between the zeros, at x = 100 ft. That is, the two long sides of the pen total 200 ft, or half the overall length of fence.
Answer:
3.2
Step-by-step explanation:
Using the normal distribution, it is found that 0.0329 = 3.29% of the population are considered to be potential leaders.
In a <em>normal distribution</em> with mean 
and standard deviation 
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
In this problem:
- The mean is of 550, hence
.
- The standard deviation is of 125, hence
.
The proportion of the population considered to be potential leaders is <u>1 subtracted by the p-value of Z when X = 780</u>, hence:
has a p-value of 0.9671.
1 - 0.9671 = 0.0329
0.0329 = 3.29% of the population are considered to be potential leaders.
To learn more about the normal distribution, you can take a look at brainly.com/question/24663213
Answer:
6 1615/15377
Step-by-step explanation:
271,000√3 = 469385.768851
Turn that into a fraction 469385/ 768851
Simplify.
