You can solve it using an arithmetic sequence.
The nth term of the sequence is equal to the number of penguins in the nth row. It's equal to the number of the row.
![a_n=n](https://tex.z-dn.net/?f=a_n%3Dn)
There was one penguin in the first row.
![a_1=1](https://tex.z-dn.net/?f=a_1%3D1)
The sum of the sequence:
![S=\frac{n(a_1+a_n)}{2}=\frac{n(1+n)}{2}=\frac{n+n^2}{2}](https://tex.z-dn.net/?f=S%3D%5Cfrac%7Bn%28a_1%2Ba_n%29%7D%7B2%7D%3D%5Cfrac%7Bn%281%2Bn%29%7D%7B2%7D%3D%5Cfrac%7Bn%2Bn%5E2%7D%7B2%7D)
There were 250 penguins - set the sum equal to 250 and solve:
![\frac{n+n^2}{2}=250 \ \ \ |\times 2 \\ n+n^2=500 \\ n^2+n-500=0 \\ \\ a=1 \\ b=1 \\ c=-500 \\ b^2-4ac=1^2-4 \times 1 \times (-500)=1+2000=2001 \\ \\ n=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-1 \pm \sqrt{2001}}{2 \times 1}=\frac{-1 \pm \sqrt{2001}}{2} \\ n=\frac{-1 -\sqrt{2001}}{2} \ \lor \ n=\frac{-1+\sqrt{2001}}{2} \\ n \approx -22.87 \ \lor \ n \approx 21.87](https://tex.z-dn.net/?f=%5Cfrac%7Bn%2Bn%5E2%7D%7B2%7D%3D250%20%5C%20%5C%20%5C%20%7C%5Ctimes%202%20%5C%5C%0An%2Bn%5E2%3D500%20%5C%5C%0An%5E2%2Bn-500%3D0%20%5C%5C%20%5C%5C%0Aa%3D1%20%5C%5C%20b%3D1%20%5C%5C%20c%3D-500%20%5C%5C%20b%5E2-4ac%3D1%5E2-4%20%5Ctimes%201%20%5Ctimes%20%28-500%29%3D1%2B2000%3D2001%20%5C%5C%20%5C%5C%0An%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%3D%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B2001%7D%7D%7B2%20%5Ctimes%201%7D%3D%5Cfrac%7B-1%20%5Cpm%20%5Csqrt%7B2001%7D%7D%7B2%7D%20%5C%5C%0An%3D%5Cfrac%7B-1%20-%5Csqrt%7B2001%7D%7D%7B2%7D%20%5C%20%5Clor%20%5C%20n%3D%5Cfrac%7B-1%2B%5Csqrt%7B2001%7D%7D%7B2%7D%20%5C%5C%0An%20%5Capprox%20-22.87%20%5C%20%5Clor%20%5C%20n%20%5Capprox%2021.87)
The number of rows can't be a negative number so n≈21.87.
So, there were 21 full rows and one not full.
Calculate the number of penguins in 21 rows:
![S_{21}=\frac{21+21^2}{2}=\frac{21+441}{2}=\frac{462}{2}=231 \\ \\ 250-231=19](https://tex.z-dn.net/?f=S_%7B21%7D%3D%5Cfrac%7B21%2B21%5E2%7D%7B2%7D%3D%5Cfrac%7B21%2B441%7D%7B2%7D%3D%5Cfrac%7B462%7D%7B2%7D%3D231%20%5C%5C%20%5C%5C%0A250-231%3D19)
There were 19 penguins in the last row.
The answer:
There were 22 rows of penguins. The last row wasn't full, it contained 19 penguins.
Answer:
Your answer would be the first option.
A right angle is 90 degrees
An obtuse angle is more than 90 degrees and that angle is more that 90 degrees
Answer:
The answer is x = y² .
Step-by-step explanation:
In order to make x the subject, you have to square to both sides to get rid of square root :
![y = \sqrt{x}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Csqrt%7Bx%7D%20)
![{y}^{2} = {( \sqrt{x}) }^{2}](https://tex.z-dn.net/?f=%20%7By%7D%5E%7B2%7D%20%20%3D%20%20%7B%28%20%5Csqrt%7Bx%7D%29%20%7D%5E%7B2%7D%20)
![{y}^{2} = x](https://tex.z-dn.net/?f=%20%7By%7D%5E%7B2%7D%20%20%3D%20x)
![x = {y}^{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%7By%7D%5E%7B2%7D%20)
Answer:
Step-by-step explanation:
Normally Z scores in a std normal distribution curve lie between -3 and 3 comprising more than 99% of total area.
Any entry outside (-3,3) can be considered as an extreme observation.
Here we have hence a) -4.3 is the most extreme observation.
-------------------------
Given that 84 separates the lowest 75% of the scores from the highest 25% of the scores,
This means 84 is the 75th percentile and similarly 65 is the 25th percentile.
Thus we have 84 has the percentile rank of 75
Option C
No this is not a linear equation