A researcher wants to know if the octane level of gasoline affects the gas mileage of a car. She randomly selects 10 cars and puts 5 gallons of 87-octane gasoline in the tank. On a closed track, each car is driven at 50 miles per hour until it runs out of gas. The experiment is repeated, with each car getting 5 gallons of 92-octane gasoline. The miles per gallon for each car are then computed. The results are shown. Would you recommend purchasing 92 octane? Why or why not?

$$\begin{matrix} \text{87 Octane} & \text{92 Octane} & \text{87 Octane} & \text{92 Octane}\\ \text{18.0} & \text{18.5} & \text{23.4} & \text{22.8}\\ \text{23.2} & \text{23.1} & \text{23.1} & \text{23.5}\\ \text{31.5} & \text{31.9} & \text{19.0} & \text{19.5}\\ \text{24.9} & \text{26.7} & \text{26.8} & \text{26.2}\\ \text{24.1} & \text{25.1} & \text{31.8} & \text{30.7}\\ \end{matrix}$$

What strategies would you offer to a friend who wanted to increase his or her need for achievement level? Explain why.

Choose the correct term to complete each sentence. If corresponding elements of matrices are equal, the matrices are _____.

What are some tools that economists use to draw meaning from large amounts of data?

A retail store currently has annual sales of $160,000. The sales manager's goal is to increase sales by 15% for the following year. Write and solve an equation to find how much the store manager wants to do in sales volume next year.

Calculate $\frac{d y}{d x}$. You need not expand your answers. $y=\frac{\sqrt{x}+1}{\sqrt{x}-1}$

A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to minimize the combined area of the circle and the square?

Write the number in standard notation.

$$5 \times 10^{-2}$$

A fluid with a density of 2000 kg/m$^{3}$ flows steadily between two flat plates. The bottom plate is fixed and the top one moves at a constant speed in the x direction. The velocity is $\mathrm{V=0.20 y \hat{i} m / s}$ where y is in meters. The acceleration of gravity is $\mathrm{g}=-9.8 \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}^{2}$. The only nonzero shear stresses, $\tau_{y x}=\tau_{x y}$, are constant throughout the flow with a value of 5 N/m$^{2}$. The normal stress at the origin (x = y = 0) is s $\sigma_{x x}=-100 \mathrm{kPa}$. Use the x and y components of the equations of motion to determine the normal stress throughout the fluid. Assume that $\sigma_{x x}=\sigma_{y y}$.

Basket stars are active at night. During the day, basket stars curl up their arms and become a compact mass. What are possible explanations for this behavior?

Name one advantage of using a flow poof rather than a two-column proof.

a. Write the formula for the area of a rectangle. b. A professional basketball court is a rectangle that is 50 feet wide and 94 feet long. What is the area of the basketball court?

Use the given function f to: Find the domain and the range of $f(x)=\log (-2 x)$

The quality-control manager of a candy company wants to discover whether a filling machine over-or underfills 16-ounce bags randomly. The following data represent the filling stat us of 18 consecutive bags: A A A A A R R R A A A A A A A A A A. A bag is rejected (R) if it is either overfilled or underfilled and accepted (A) if it is filled according to specification. Test the randomnes of the filling machine in the way that it over- or underfills at the $\alpha$=0.05 level of significance.