Step-by-step explanation:
4/5 + 2/3 = 2215 = 1 715 ≅ 1.4666667. Spelled result in words is twenty-two fifteenths (or one and seven fifteenths).
Answer:
Predicted values:
![\hat y_1 = 49.3 (1.47)^1 =72.471](https://tex.z-dn.net/?f=%5Chat%20y_1%20%3D%2049.3%20%281.47%29%5E1%20%3D72.471)
![\hat y_2 = 49.3 (1.47)^2 =106.5324](https://tex.z-dn.net/?f=%5Chat%20y_2%20%3D%2049.3%20%281.47%29%5E2%20%3D106.5324)
![\hat y_3 = 49.3 (1.47)^3 =156.6026](https://tex.z-dn.net/?f=%5Chat%20y_3%20%3D%2049.3%20%281.47%29%5E3%20%3D156.6026)
![\hat y_4 = 49.3 (1.47)^4 =230.2058](https://tex.z-dn.net/?f=%5Chat%20y_4%20%3D%2049.3%20%281.47%29%5E4%20%3D230.2058)
![\hat y_5 = 49.3 (1.47)^5 =338.4025](https://tex.z-dn.net/?f=%5Chat%20y_5%20%3D%2049.3%20%281.47%29%5E5%20%3D338.4025)
![\hat y_6 = 49.3 (1.47)^6 =497.4517](https://tex.z-dn.net/?f=%5Chat%20y_6%20%3D%2049.3%20%281.47%29%5E6%20%3D497.4517)
![\hat y_7 = 49.3 (1.47)^7 =731.254](https://tex.z-dn.net/?f=%5Chat%20y_7%20%3D%2049.3%20%281.47%29%5E7%20%3D731.254)
![\hat y_8 = 49.3 (1.47)^8 =1074.943](https://tex.z-dn.net/?f=%5Chat%20y_8%20%3D%2049.3%20%281.47%29%5E8%20%3D1074.943)
Residuals:
![e_1 = 65-72.471=-7.471](https://tex.z-dn.net/?f=e_1%20%3D%2065-72.471%3D-7.471)
![e_2 = 90-106.5324=-16.5324](https://tex.z-dn.net/?f=e_2%20%3D%2090-106.5324%3D-16.5324)
![e_3 = 162-156.6026 = 5.3974](https://tex.z-dn.net/?f=e_3%20%3D%20162-156.6026%20%3D%205.3974)
![e_4 = 224-230.2058 = -6.2058](https://tex.z-dn.net/?f=e_4%20%3D%20224-230.2058%20%3D%20-6.2058)
![e_5 = 337-338.4025 = -1.4025](https://tex.z-dn.net/?f=e_5%20%3D%20337-338.4025%20%3D%20-1.4025)
![e_6 = 466-497.4617 = -31.4517](https://tex.z-dn.net/?f=e_6%20%3D%20466-497.4617%20%3D%20-31.4517)
![e_7 = 780-731.254 = 48.7459](https://tex.z-dn.net/?f=e_7%20%3D%20780-731.254%20%3D%2048.7459)
![e_8 = 1087-1074.493 = 12.0566](https://tex.z-dn.net/?f=e_8%20%3D%201087-1074.493%20%3D%2012.0566)
Step-by-step explanation:
For this case we assume the following exponential function:
![\hat y_i = 49.3 (1.47)^x](https://tex.z-dn.net/?f=%5Chat%20y_i%20%3D%2049.3%20%281.47%29%5Ex%20)
Where x represent the hours and y the predicted values for each hour. We can find the estimated values like this:
![\hat y_1 = 49.3 (1.47)^1 =72.471](https://tex.z-dn.net/?f=%5Chat%20y_1%20%3D%2049.3%20%281.47%29%5E1%20%3D72.471)
![\hat y_2 = 49.3 (1.47)^2 =106.5324](https://tex.z-dn.net/?f=%5Chat%20y_2%20%3D%2049.3%20%281.47%29%5E2%20%3D106.5324)
![\hat y_3 = 49.3 (1.47)^3 =156.6026](https://tex.z-dn.net/?f=%5Chat%20y_3%20%3D%2049.3%20%281.47%29%5E3%20%3D156.6026)
![\hat y_4 = 49.3 (1.47)^4 =230.2058](https://tex.z-dn.net/?f=%5Chat%20y_4%20%3D%2049.3%20%281.47%29%5E4%20%3D230.2058)
![\hat y_5 = 49.3 (1.47)^5 =338.4025](https://tex.z-dn.net/?f=%5Chat%20y_5%20%3D%2049.3%20%281.47%29%5E5%20%3D338.4025)
![\hat y_6 = 49.3 (1.47)^6 =497.4517](https://tex.z-dn.net/?f=%5Chat%20y_6%20%3D%2049.3%20%281.47%29%5E6%20%3D497.4517)
![\hat y_7 = 49.3 (1.47)^7 =731.254](https://tex.z-dn.net/?f=%5Chat%20y_7%20%3D%2049.3%20%281.47%29%5E7%20%3D731.254)
![\hat y_8 = 49.3 (1.47)^8 =1074.943](https://tex.z-dn.net/?f=%5Chat%20y_8%20%3D%2049.3%20%281.47%29%5E8%20%3D1074.943)
Now we can find the residuals with this formula:
![e_i = Y_i -\hat y_i](https://tex.z-dn.net/?f=%20e_i%20%3D%20Y_i%20-%5Chat%20y_i%20)
And replacing we got:
![e_1 = 65-72.471=-7.471](https://tex.z-dn.net/?f=e_1%20%3D%2065-72.471%3D-7.471)
![e_2 = 90-106.5324=-16.5324](https://tex.z-dn.net/?f=e_2%20%3D%2090-106.5324%3D-16.5324)
![e_3 = 162-156.6026 = 5.3974](https://tex.z-dn.net/?f=e_3%20%3D%20162-156.6026%20%3D%205.3974)
![e_4 = 224-230.2058 = -6.2058](https://tex.z-dn.net/?f=e_4%20%3D%20224-230.2058%20%3D%20-6.2058)
![e_5 = 337-338.4025 = -1.4025](https://tex.z-dn.net/?f=e_5%20%3D%20337-338.4025%20%3D%20-1.4025)
![e_6 = 466-497.4617 = -31.4517](https://tex.z-dn.net/?f=e_6%20%3D%20466-497.4617%20%3D%20-31.4517)
![e_7 = 780-731.254 = 48.7459](https://tex.z-dn.net/?f=e_7%20%3D%20780-731.254%20%3D%2048.7459)
![e_8 = 1087-1074.493 = 12.0566](https://tex.z-dn.net/?f=e_8%20%3D%201087-1074.493%20%3D%2012.0566)
If you are going by looks the number line is just a horizontal line that usually had little dashes on it that show where the number is. A coordinate plane has two lines. One line goes up and down and another goes left and right. points can be places anywhere on or not on the lines of a coordinate plane
2 one , going up and down