91Ó°ÊÓ

Compute the sum-of-squares error \((S S E)\) by hand for the given set of data and linear model. $$ (0,-1),(1,3),(4,6),(5,0) ; \quad y=-x+2 $$

A table of values for a linear function is given. Fill in the missing value and calculate \(m\) in each case. $$ \begin{array}{|c|c|c|c|} \hline x & -2 & 0 & 2 \\ \hline f(x) & 4 & & 10 \\ \hline \end{array} $$

Use technology to compute the sum-ofsquares error (SSE) for the given set of data and linear models. Indicate which linear model gives the better fit. $$ (1,1),(2,2),(3,4) ; \quad \text { a. } y=1.5 x-1 \quad \text { b. } y=2 x-1.5 $$

A piano manufacturer has a daily fixed cost of \(\$ 1,200\) and a marginal cost of \(\$ 1,500\) per piano. Find the cost \(C(x)\) of manufacturing \(x\) pianos in one day. Use your function to answer the following questions: a. On a given day, what is the cost of manufacturing 3 pianos? b. What is the cost of manufacturing the 3rd piano that day? c. What is the cost of manufacturing the 11 th piano that day? d. What is the variable cost? What is the fixed cost? What is the marginal cost? e. Graph \(C\) as a function of \(x\). HINT [See Example 1.]

Say whether or not \(f(x)\) is defined for the given values of \(x .\) If it is defined, give its value. \(f(x)=x-\frac{1}{x^{2}}\), with domain \((0,+\infty)\) a. \(x=4\) b. \(x=0\) c. \(x=-1\)

The Audubon Society at Enormous State University (ESU) is planning its annual fund-raising "Eat-a-thon." The society will charge students 50 e per serving of pasta. The only expenses the society will incur are the cost of the pasta, estimated at \(15 \mathrm{~d}\) per serving, and the \(\$ 350\) cost of renting the facility for the evening. a. Write down the associated cost, revenue, and profit functions. b. How many servings of pasta must the Audubon Society sell in order to break even? c. What profit (or loss) results from the sale of 1,500 servings of pasta?

Find the regression line associated with each set of points in exercise. Graph the data and the best-fit line. \((\) Round all coefficients to 4 decimal places.) $$ (0,-1),(1,3),(4,6),(5,0) $$

The total weekly revenue earned at Royal Ruby Retailers is given by $$ R(p)=-\frac{4}{3} p^{2}+80 p $$ where \(p\) is the price (in dollars) RRR charges per ruby. Use this function to determine: a. The weekly revenue, to the nearest dollar, when the price is set at \$20/ruby. b. The weekly revenue, to the nearest dollar, when the price is set at \(\$ 200\) /ruby. (Interpret your result.) c. The price \(\mathrm{RRR}\) should charge in order to obtain a weekly revenue of \(\$ 1,200\).

The amount of iodine 131 remaining in a sample that originally contained \(A\) grams is approximately $$ C(t)=A(0.9175)^{t} $$ where \(t\) is time in days. a. Find, to the nearest whole number, the percentage of iodine 131 left in an originally pure sample after 2 days, 4 days, and 6 days. b. Use a graph to estimate, to the nearest day, when one half of a sample of 100 grams will have decayed.

\(\nabla\) Income Taxes The income tax function \(T\) in Exercise 53 can also be written in the following form: \(T(I)=\left\\{\begin{array}{ll}0.10 I & \text { if } 0349,700\end{array}\right.\) What was the tax owed by a single taxpayer on a taxable income of \(\$ 25.000 ?\) On a taxable income of \(\$ 125.000 ?\)