Fajitas A recipe for six servings of beef fajitas requires $16$ oz of beef sirloin.
a) If the recipe were to be made for nine servings, how many ounces of beef sirloin would be needed? b) How many servings of beef fajitas can be made with $32$ oz of beef sirloin?

The prize was for the closest guest. The exact answer was $14,016.2163$ kilograms. 15) Charles guessed thirteen thousand, forty-one, and six ten-thousandths kilograms. Mary guessed fourteen thousand, nine hundred ninety-one and twenty-three hundredths kilograms. By how much did each of them miss the exact answer? Whose guess was closer?

Solve the following exercise.

In the x y plane, mark all nine of these linear combinations:

$$c\left[\begin{array}{l} 2 \\ 1 \end{array}\right]+d\left[\begin{array}{l} 0 \\ 1 \end{array}\right] \quad \text { with } c=0,1,2 \text { and } d=0,1,2 .$$

Monica has a daisy with nine petals. She asks Jerry to play the following game: They will take turns picking either one petal or two petals that are next to each other.

The player who picks the last petal wins. Does the first player always win? Can the first player ever win? Discuss.

Nine boxes are each labelled with a different whole number from 1 to 9. Five people are allowed to take one box each. In how many different ways can this be done if: a. there are no restrictions b. the first three people decide that they will take even numbered boxes?

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that σ = 2 psi. A random sample of nine specimens is tested, and the average breaking strength is found to be 98 psi. Find a 95% two-sided confidence interval on the true mean breaking strength.

Use a graphing calculator program for Newton's method to approximate the root of each equation, beginning with the given x0 and continuing until two successive approximations agree to nine decimal places.

$$\begin{aligned} &e^{x}+4 x-100=0\\ &x_{0}=3 \end{aligned}$$

Write an equation for each sentence. Solve each equation by inspection.

a) Five more than a number is 22.

b) Seven less than a number is 31.

c) Six times a number is 54.

d) A number divided by eight is 9.

e) Nine more than three times a number is 24.

Suppose you have a $3 \times 3$ checkerboard (so it has 9 squares). You put one penny on the first square, then 3 pennies on the next square, then $3^{2}$ pennies on the next square, and so on until there are pennies on all nine squares. Write an expression that gives the total number of pennies on the board. Find the sum.

Use a graphing calculator program for Newton's method to approximate the root of each equation, beginning with the given $x_0$ and continuing until two successive approximations agree to nine decimal places.

$$\begin{aligned} &x^{3}=5 \ln x+10\\ &x_{0}=2 \end{aligned}$$

Use a graphing calculator program for Newton’s method to approximate the root of each equation beginning with the given $x_0$ and continuing until two successive approximations agree to nine decimal places.

$$\begin{aligned} &e^{2 x}+3 x=0\\ &x_{0}=0 \end{aligned}$$

Using the discussion earlier, answer the questions below:

a) Write an equation for each sentence.

b) Sketch balance scales to represent each equation.

c) Solve each equation. Verify the solution.

i) Nine more than a number is 17.

ii) Three times a number is 21.

iii) Seven more than two times a number is 19.

Use a graphing calculator program for Newton’s method to approximate the root of each equation beginning with the given $x_0$ and continuing until two successive approximations agree to nine decimal places.

$$\begin{aligned} &x+\ln x-5=0\\ &x_{0}=2 \end{aligned}$$

Use a graphing calculator program for Newton's method to approximate the root of each equation, beginning with the given x0 and continuing until two successive approximations agree to nine decimal places.

$$\begin{aligned} &x^{4}=2+\sin x\\ &x_{0}=0 \end{aligned}$$