To find: The function that models the area of rectangle in terms of length of one of its sides. The perimeter of rectangle is 20 ft.

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asked 2021-03-11

Let's say the widget maker has developed the following table that shows the highest dollar price p. widget where you can sell N widgets. Number N Price p $200 53.00$
$250 52.50$
$300 52.00$
$35051.50$ (a) Find a formula for pin terms of N modeling the data in the table. (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in month as a function of the number N of widgets produced in a month. $R=$ Is Ra linear function of N? (c) On the basis of the tables in this exercise and using cost, $C= 35N + 900$, use a formula to express the monthly profit P, in dollars, of this manufacturer asa function of the number of widgets produced in a month $p=$ (d) Is Pa linear function of N2 e. Explain how you would find breakeven. What does breakeven represent?

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asked 2021-03-11

An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds per square inch) and mileage (in thousands of miles). A mathematical model for the data is given by
$\displaystyle f{{\left({x}\right)}}=-{0.554}{x}^{2}+{35.5}{x}-{514}.$
$\begin{array}{|c|c|} \hline x & Mileage \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$
(A) Complete the table below.
$\begin{array}{|c|c|} \hline x & Mileage & f(x) \\ \hline 28 & 45 \\ \hline 30 & 51\\ \hline 32 & 56\\ \hline 34 & 50\\ \hline 36 & 46\\ \hline \end{array}$
(Round to one decimal place as needed.)
$A. 20602060xf(x)$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,45), (30,51), (32,56), (34,50), and (36,46). A parabola opens downward and passes through the points (28,45.7), (30,52.4), (32,54.7), (34,52.6), and (36,46.0). All points are approximate.
$B. 20602060xf(x)$
Acoordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2.
Data points are plotted at (43,30), (45,36), (47,41), (49,35), and (51,31). A parabola opens downward and passes through the points (43,30.7), (45,37.4), (47,39.7), (49,37.6), and (51,31). All points are approximate.
$C. 20602060xf(x)$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (43,45), (45,51), (47,56), (49,50), and (51,46). A parabola opens downward and passes through the points (43,45.7), (45,52.4), (47,54.7), (49,52.6), and (51,46.0). All points are approximate.
$D.20602060xf(x)$
A coordinate system has a horizontal x-axis labeled from 20 to 60 in increments of 2 and a vertical y-axis labeled from 20 to 60 in increments of 2. Data points are plotted at (28,30), (30,36), (32,41), (34,35), and (36,31). A parabola opens downward and passes through the points (28,30.7), (30,37.4), (32,39.7), (34,37.6), and (36,31). All points are approximate.
(C) Use the modeling function f(x) to estimate the mileage for a tire pressure of 29
$\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$ and for 35
$\displaystyle\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$
The mileage for the tire pressure $\displaystyle{29}\frac{{{l}{b}{s}}}{{{s}{q}}}\in.$ is
The mileage for the tire pressure $\displaystyle{35}\frac{{{l}{b}{s}}}{{{s}{q}}}$ in. is
(Round to two decimal places as needed.)
(D) Write a brief description of the relationship between tire pressure and mileage.
A. As tire pressure increases, mileage decreases to a minimum at a certain tire pressure, then begins to increase.
B. As tire pressure increases, mileage decreases.
C. As tire pressure increases, mileage increases to a maximum at a certain tire pressure, then begins to decrease.
D. As tire pressure increases, mileage increases.

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asked 2021-02-25

Means $=59.47444, SDS = 12.91711, Min = 23.599, Max = 82.603$ AND Means $= 67.00742, SDS = 12.7302, Min = 39.613, Max = 82.603$ Means Based on your findings write a preliminary statistical report that comprises of the Methods, Results/Analysis and Conclusions sections. Include a comparison of the two distributions in (1) and (2) in terms of their central tendencies and variability. While your audience is one that lacks statistical expertise you are still expected to correctly interpret the data and statistical analyses, in a manner that is understandable to your audience. Be mindful to present an impartial report that distinguishes conclusive and inferential statements for the audience.

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asked 2021-03-05

Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.
$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 200 & 53.00\\ \hline 250 & 52.50\\\hline 300 & 52.00\\ \hline 350 & 51.50\\ \hline \end{array}$
(a) Find a formula for p in terms of N modeling the data in the table.
$\displaystyle{p}=$
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
$\displaystyle{R}=$
Is R a linear function of N?
(c) On the basis of the tables in this exercise and using cost, $\displaystyle{C}={35}{N}+{900}$, use a formula to express the monthly profit P, in dollars, of this manufacturer as a function of the number of widgets produced in a month.
$\displaystyle{P}=$
(d) Is P a linear function of N?

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asked 2021-02-25

In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is, rather, a function of N. Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold.
$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 250 & 52.50\\ \hline300 & 52.00\\\hline 350 & 51.50\\ \hline 400 & 51.00\\ \hline \end{array}$
(a) Find a formula for p in terms of N modeling the data in the table.
$\displaystyle{p}=$
(b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month.
$\displaystyle{R}=$

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Answer 1

Concept used: Area of rectangle is defined as, $\displaystyle{A}={l}\ \cdot\ {b}$ Here, A is area, l is length and b is width. Calculation: Consider the length of one of its sides of rectangle as x. The perimeter of a rectangle is defined as, $\displaystyle{P}={2}\ {\left({l}\ +\ {b}\right)}$ Here, P is perimeter. The perimeter of rectangle is given as 20 ft. Substitute 20 for P and x for l in above equation to the value of b. $\displaystyle{20}={2}\ {\left({x}\ +\ {b}\right)}$
$\displaystyle{\frac{{{20}}}{{{2}}}}={x}\ +\ {b}$
$\displaystyle{10}={x}\ +\ {b}$
$\displaystyle{b}={10}\ -\ {x}$ Therefore, the value of b is $\displaystyle{\left({10}\ -\ {x}\right)}$ Substitute x for l and $\displaystyle{10}\ -\ {x}$ for b in equation to obtain the model that express area of the rectangle $\displaystyle{A}={x}\ {\left({10}\ -\ {x}\right)}$
$\displaystyle={10}{x}\ -\ {x}^{{{2}}}$ Here, x is always greater than zero and less than 10 to define the area therefore the value of x is always lies in between 0 and 10. Conclusion: Thus, the function that models the are of rectangle in terms of length of one of its sides is $\displaystyle{A}={10}{x}\ -\ {x}^{{{2}}}$.

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To find: The function that models the area of rectangle in terms of length of one of its sides. The perimeter of rectangle is 20 ft.

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