Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Equation of regression line :
Yˆ = −114.05+2.17X
X = Temperature in degrees Fahrenheit (°F)
Y = Number of bags of ice sold
On one of the observed days, the temperature was 82 °F and 66 bags of ice were sold.
X = 82°F ; Y = 66 bags of ice sold
1. Determine the number of bags of ice predicted to be sold by the LSR line, Yˆ, when the temperature is 82 °F.
X = 82°F
Yˆ = −114.05+2.17(82)
Y = - 114.05 + 177.94
Y = 63.89
Y = 64 bags
2. Compute the residual at this temperature.
Residual = Actual value - predicted value
Residual = 66 - 64 = 2 bags of ice
Answer:
Step-by-step explanation:
Use the following formula:
slope: 
Let:

Plug in the corresponding numbers to the corresponding variables:

is your answer.
~
6 5/6 just subtract 2 from the whole (8)
Answer:



Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
The procedure to optimize a function (find its maximum or minimum) consists in
:
- Produce a function which depends on only one variable
- Compute the first derivative and set it equal to 0
- Find the values for the variable, called critical points
- Compute the second derivative
- Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum
We know a cylinder has a volume of 4
. The volume of a cylinder is given by

Equating it to 4

Let's solve for h

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

Replacing the formula of h

Simplifying

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

Rearranging

Solving for r

![\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4%7D%7B%5Cpi%20%7D%7D%5Capprox%201.084%5C%20feet)
Computing h

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.
The minimum area is


Answer:
.
Step-by-step explanation:
It is given that the sum of 10 and one-third of a number is 25.
Let as consider n be the unknown number.
One-third of a number
Sum of 10 and one-third of a number
The sum of 10 and one-third of a number is 25. It can be written as
Therefore, the required equation is
.