Answer:
0.290
Step-by-step explanation:
You just have to divide 3.49/12
The slope represents how much the value decreases per year.
The y-intercept represents the initial value of the car.
Answer:
Option C: 126
Step-by-step explanation:
Total displays to be assembled = 280
25% of the displays are assembled during the first hour, this value becomes:
![0.25\times280=70](https://tex.z-dn.net/?f=0.25%5Ctimes280%3D70)
Remaining displays = ![280-70=210](https://tex.z-dn.net/?f=280-70%3D210)
40% of the remaining displays during the second hour, the value becomes:
![0.40\times210=84](https://tex.z-dn.net/?f=0.40%5Ctimes210%3D84)
Hence, number of displays that will not have been assembled by the end of the second hour = ![210-84=126](https://tex.z-dn.net/?f=210-84%3D126)
Therefore, the answer is 126.
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.
2418 * 9 = 21,762
hope it helps