Answer:
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
Step-by-step explanation:
We are given a linear regression model that relates daily high temperature, in degrees Fahrenheit and number of lemonade cups sold.
![y = -34+ \frac{3}{5} x](https://tex.z-dn.net/?f=y%20%3D%20-34%2B%20%5Cfrac%7B3%7D%7B5%7D%20%20x)
Where y is the number of cups sold and x is the daily temperature in Fahrenheit.
Residual value:
A residual value basically shows the position of a data point with respect to the regression line.
A residual value of 0 is desired which means that the regression line best fits the data.
The Residual value is calculated by
Residual = Observed value - Predicted value
The predicted value of number of lemonade cups is obtained as
![y = -34+ \frac{3}{5} (95)\\\\y = -34+ 3 (19)\\\\y = -34+ 57\\\\y = 23](https://tex.z-dn.net/?f=y%20%3D%20-34%2B%20%5Cfrac%7B3%7D%7B5%7D%20%2895%29%5C%5C%5C%5Cy%20%3D%20-34%2B%203%20%2819%29%5C%5C%5C%5Cy%20%3D%20-34%2B%2057%5C%5C%5C%5Cy%20%3D%2023)
So the predicted value of number of lemonade cups is 23 and the observed value is 21 so the residual value is
Residual = Observed value - Predicted value
Residual = 21 - 23
Residual = -2
The negative residual value indicates that the data point lies below the regression line.
It said that Congress had no right to make slavery illegal anywhere because the Founding Fathers had not intended slaves to be, and that blacks, even if they were free, could not be citizens of the U.S.
The two numbers are -6 and 7
<em><u>Solution:</u></em>
Given that eight times a number plus five times another number is -13
The sum of two numbers is 1
To find: the two numbers
Let the two numbers be "a" and "b"
From given information,
Eight times a number plus five times another number = -13
eight times a number "a" + five times another number "b" = -13
8a + 5b = -13 ---- eqn 1
Also given that sum of two numbers is 1
sum of two numbers = 1
a + b = 1 ---- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "b"</u></em>
From eqn 2,
a = 1 - b ----- eqn 3
Substitute eqn 3 in eqn 1
8(1 - b) + 5b = -13
8 - 8b + 5b = -13
8 - 3b = -13
-3b = -13 - 8
-3b = -21
<h3>b = 7</h3>
Substitute b = 7 in eqn 3
a = 1 - 7
<h3>a = -6</h3>
Thus the two numbers are -6 and 7
Answer- 40.3
2³=2×2×2=8
-3×2³=-3×8=-24
64.3-3×2³=64.3-3×8=64.3-24=40.3