We have been given that a colleague has been tutoring six students in 11th grade to prepare for the ACT. Student scores were as follows: 20, 18, 16, 15, 23, 20. We are asked to find the mean of the ACT scores.
We will use mean formula to solve our given problem.
![\text{Mean}=\frac{\text{Sum of terms}}{\text{Number of terms}}](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Cfrac%7B%5Ctext%7BSum%20of%20terms%7D%7D%7B%5Ctext%7BNumber%20of%20terms%7D%7D)
![\text{Mean}=\frac{20+18+16+15+23+20}{6}](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Cfrac%7B20%2B18%2B16%2B15%2B23%2B20%7D%7B6%7D)
![\text{Mean}=\frac{112}{6}](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D%5Cfrac%7B112%7D%7B6%7D)
![\text{Mean}=18.66666](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%3D18.66666)
Upon rounding to nearest whole number, we will get:
![\text{Mean}\approx 19](https://tex.z-dn.net/?f=%5Ctext%7BMean%7D%5Capprox%2019)
Therefore, the mean of the ACT scores is 19 and option 'c' is the correct choice.
For any circle with Cartesian equation
![(x-a)^2 + (y-b)^2 = r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%20%2B%20%28y-b%29%5E2%20%3D%20r%5E2)
,
we have that the centre of the circle is
![(a,b)](https://tex.z-dn.net/?f=%28a%2Cb%29)
, and the radius of the circle is
![r](https://tex.z-dn.net/?f=r)
.
So in the case that
![(x-5)^2 + y^2 = 38](https://tex.z-dn.net/?f=%28x-5%29%5E2%20%2B%20y%5E2%20%3D%2038)
,
we essentially have that
![a = 5, b = 0, r^2 = 38](https://tex.z-dn.net/?f=a%20%3D%205%2C%20b%20%3D%200%2C%20r%5E2%20%3D%2038)
.
So the centre of the circle is
![(5,0)](https://tex.z-dn.net/?f=%285%2C0%29)
, and the radius is
![\sqrt{38}](https://tex.z-dn.net/?f=%5Csqrt%7B38%7D)
.
The highest common factor is 13
Answer:
D is -31 also i checked to make sure.
the total tax is 14.71
the total cost is 272.71