The drag force $F_D$ on a sphere depends on the velocity $V$, the viscosity $\mu$, the density $\rho$, the surface roughness height $e$, the freestream fluctuation intensity $I$ (a dimensionless quantity), and the diameter $D$. Find an expression for $F_D$.

What could a hospital learn from benchmarking a Ritz-Carlton Hotel? Southwest Airlines? Disneyland?

Use the results of the said exercise to solve the given problem.

A carpet cleaner uses $8$ oz of shampoo to clean an area $31 \ \mathrm{ft}$ by $31 \ \mathrm{ft}$. How much shampoo would be needed for an area $93 \ \mathrm{ft}$ by $93 \ \mathrm{ft}$ ?

Solve the below triangle:

$$a=9, c=12, \beta=23^{\circ}$$

Interested in the possible relationship between the size of his tip versus the size of the check and the number of diners in the party, a food server has recorded the following for a sample of 8 checks:

$$\begin{aligned} &\text { Observation }\\ &\begin{array}{cccc} \text { Number } & \boldsymbol{y}=\text { Tip } & \boldsymbol{x}_1=\text { Check } & \boldsymbol{x}_2=\text { Diners } \\ \hline 1 & \$ 7.5 & \$ 40 & 2 \\ 2 & 0.5 & 15 & 1 \\ 3 & 2.0 & 30 & 3 \\ 4 & 3.5 & 25 & 4 \\ 5 & 9.5 & 50 & 4 \\ 6 & 2.5 & 20 & 5 \\ 7 & 3.5 & 35 & 5 \\ 8 & 1.0 & 10 & 2 \end{array} \end{aligned}$$

g. Analyze the residuals. Does the analysis support the applicability of the multiple regression model to these data?

Is the sum of two binomials always a binomial? Explain.

Expand each binomial. $(11 x-1)^{3}$

Give a geometric definition for each of the fo llowing: point, line, line segment, plane, and space. Give an example of an everyday object that approximates each of these geometrical objects.

In the following exercise, sketch the solid that has the given description in spherical coordinates.

$$0 \leq \theta \leq \pi, 0 \leq \phi \leq \pi / 2,1 \leq \rho \leq 3$$

Evaluate the integral in this exercise. To transform the integral into a recognizable basic form, it may be necessary to use one or more algebraic substitution techniques, completing the square, separating fractions, long division, or trigonometric substitution.

$$\int \frac{d x}{x^2 \sqrt{1-x^2}}$$

Determine whether each arrangement of objects is a linear or circular permutation. Then determine the number of arrangements for each situation. 12 decorative symbols around the face of a clock

Evaluate the integral in this exercise. To transform the integral into a recognizable basic form, it may be necessary to use one or more algebraic substitution techniques, completing the square, separating fractions, long division, or trigonometric substitution.

$\int \frac{d x}{(x-1) \sqrt{x^2-2 x}}$

The following sentencs is missing its end mark. The sentence also may have inappropriately abbreviated words. Add an end mark to the sentence. Then, on the line provided, write out any inappropriately abbreviated words. If no correction of abbreviations is necessary, write C. Example 1. Planning a party for four-yr-olds is certainly a challenge$\color{#c34632}!$ $\underline{\text{\color{#c34632}four-year-olds}}$

When my little sister turned four, I agreed to help plan her birthday party__________________________________________

Sketch the solid described by the given inequalities.

$$1 \leqslant \rho \leqslant 3, \quad 0 \leqslant \phi \leqslant \pi / 2, \quad \pi \leqslant \theta \leqslant 3 \pi / 2$$