I think it May be b because it’s slope is rising by two
You would take 25.5 feet and convert it to inches (306 inches) then just divide that by 6 and you get 51 inches or 4 feet 3 inches depending on how the answer needs to be reported.
Answer:
0.89417
Step-by-step explanation:
Using the relation to obtain the Zscore :
Z = (x - mean) ÷ standard deviation / sqrt(n)
x = 0.8535
Mean = 0.8565
Standard deviation = 0.0518
Sample size, n = 465
P(x ≤ 0.8535) = (0.8535 - 0.8565) ÷ 0.0518/sqrt(465)
P(x ≥ 0.8535) = - 0.003 / 0.0024021
P(x ≥ 0.8535) = - 1.249
P(Z ≥ - 1.249) = 0.89417
Answer:
The ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.
Step-by-step explanation:
The question is:
A company knows that if it produces "x" monthly units its utility "u" could be calculated with the expression: u (x) = - 0.04x ^ 2 + 44x-4000 where "u" is expressed in dollars. Determine the ratio of the average change in profit when the level of production changes from 600 to 620 units per month. Remember that the slope of the secant line to the graph of the function represents the average rate of change.
Solution:
The expression for the utility is:
![u (x) = - 0.04x ^ {2} + 44x-4000](https://tex.z-dn.net/?f=u%20%28x%29%20%3D%20-%200.04x%20%5E%20%7B2%7D%20%2B%2044x-4000)
It is provided that the slope of the secant line to the graph of the function represents the average rate of change.
Then the ratio of the average change in profit when the level of production changes is:
![\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20change%20in%20profit%7D%3D%5Cfrac%7Bu%28x_%7B2%7D%29-u%28x_%7B1%7D%29%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
Compute the values of u (x₁) and u (x₂) as follows:
<em>x</em>₁ = 600
![u (x_{1}) = - 0.04x_{1} ^ {2} + 44x_{1}-4000](https://tex.z-dn.net/?f=u%20%28x_%7B1%7D%29%20%3D%20-%200.04x_%7B1%7D%20%5E%20%7B2%7D%20%2B%2044x_%7B1%7D-4000)
![= - 0.04(600) ^ {2} + 44(600)-4000\\=-14400+26400-4000\\=8000](https://tex.z-dn.net/?f=%3D%20-%200.04%28600%29%20%5E%20%7B2%7D%20%2B%2044%28600%29-4000%5C%5C%3D-14400%2B26400-4000%5C%5C%3D8000)
<em>x</em>₂ = 620
![u (x_{2}) = - 0.04x_{2} ^ {2} + 44x_{2}-4000](https://tex.z-dn.net/?f=u%20%28x_%7B2%7D%29%20%3D%20-%200.04x_%7B2%7D%20%5E%20%7B2%7D%20%2B%2044x_%7B2%7D-4000)
![= - 0.04(620) ^ {2} + 44(620)-4000\\=-15376+27280-4000\\=7904](https://tex.z-dn.net/?f=%3D%20-%200.04%28620%29%20%5E%20%7B2%7D%20%2B%2044%28620%29-4000%5C%5C%3D-15376%2B27280-4000%5C%5C%3D7904)
Compute the average rate of change as follows:
![\text{Average change in profit}=\frac{u(x_{2})-u(x_{1})}{x_{2}-x_{1}}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20change%20in%20profit%7D%3D%5Cfrac%7Bu%28x_%7B2%7D%29-u%28x_%7B1%7D%29%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![=\frac{7904-800}{620-600}\\\\=\frac{-96}{20}\\\\=-\frac{24}{5}\\\\=-24:5](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7904-800%7D%7B620-600%7D%5C%5C%5C%5C%3D%5Cfrac%7B-96%7D%7B20%7D%5C%5C%5C%5C%3D-%5Cfrac%7B24%7D%7B5%7D%5C%5C%5C%5C%3D-24%3A5)
Thus, the ratio of the average change in profit when the level of production changes from 600 to 620 units per month is -24 : 5.