Convert the given Celsius temperature to its equivalent temperature on the Fahrenheit scale. Where appropriate, round to the nearest tenth of a degree.

$$- 5 ^ { \circ } \mathrm { C }$$

Solve each system by the substitution method . Be sure to check all proposed solutions.

$$\left\{ \begin{array} { r } { x + 8 y = 6 } \\ { 2 x + 4 y = - 3 } \end{array} \right.$$

The radius of a sphere is doubled. What happens to the ratio of the volume of the sphere to the surface area of the sphere? (F) It remains the same. (G) It is doubled. (H) It is increased by a factor of 4. (J) It is increased by a factor of 8

The distance from Potsdam to larger markets and limited air service have hindered the town in attracting new industry. Air Express, a major overnight delivery service, is considering establishing a regional distribution center in Potsdam. But Air Express will not establish the center unless the length of the runway at the local airport is increased. Another candidate for new development is Diagnostic Research, Inc. (DRI), a leading producer of medical testing equipment. DRI is considering building a new manufacturing plant. Increasing the length of the runway is not a requirement for DRI, but the planning commission feels that doing so will help convince DRI to locate their new plant in Potsdam. Assuming that the town lengthens the runway, the Potsdam planning commission believes that the probabilities shown in the following table are applicable.

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.30} & \text{.10}\\ \text{No Air Express Center} & \text{.40} & \text{.20}\\ \end{matrix}$$

For instance, the probability that Air Express will establish a distribution center and DRI will build a plant is .30. The estimated annual revenue to the town, after deducting the cost of lengthening the runway, is as follows:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{\$600,000} & \text{\$150,000}\\ \text{No Air Express Center} & \text{\$250,000} & \text{-\$200,000}\\ \end{matrix}$$

If the runway expansion project is not conducted, the planning commission assesses the probability DRI will locate their new plant in Potsdam at .6; in this case, the estimated annual revenue to the town will be $450,000. If the runway expansion project is not conducted and DRI does not locate in Potsdam, the annual revenue will be$0 since no cost will have been incurred and no revenues will be forthcoming. a. What is the decision to be made, what is the chance event, and what is the consequence? b. Compute the expected annual revenue associated with the decision alternative to lengthen the runway. c. Compute the expected annual revenue associated with the decision alternative to not lengthen the runway. d. Should the town elect to lengthen the runway? Explain. e. Suppose that the probabilities associated with lengthening the runway were as follows:

$$\begin{matrix} \text{ } & \text{DRI Plant} & \text{No DRI Plant}\\ \text{Air Express Center} & \text{.40} & \text{.10}\\ \text{No Air Express Center} & \text{.30} & \text{.20}\\ \end{matrix}$$

What effect, if any, would this change in the probabilities have on the recommended decision?

A thin sheet of plastic is uniform and has the shape of an equilateral triangle. Consider two axes for rotation. Both are perpendicular to the plane of the triangle, axis A passing through the center of the triangle and axis B passing through one corner. If the angular speed

$$\omega$$

about each axis is the same, for which axis does the triangle have the greater rotational kinetic energy? Explain.

Find the exact value of each expression. Do not use a calculator.

$$\sin ^ { - 1 } \left( \cos \frac { 2 \pi } { 3 } \right)$$

Find each product or quotient. (1/8) (3/5)

Identify the following term or individuals and explain their significance. nativism

How would you explain to a patient with leukemia, who has a greatly elevated white blood cell count, the importance of avoiding bacterial infections?

True or False. If the statement is false, change it to make it true. The Subtraction Principle states that to subtract a number, you should add its absolute value.

Multiply, Estimate to check whether each answer is reasonable. $2.8 \cdot 8.2$

What is the maximum number of solutions of a system of equations that consists of a circle and a hyperbola?

If the reaction

$$\mathbf { X } \longrightarrow \mathbf { Y }$$

is spontaneous, what can be said about the reaction

$$\mathrm { Y } \longrightarrow \mathrm { X } ?$$

Each open sentence defines a relation, and x and y are real numbers. Graph each relation and tell whether it is a function. {(x, y): y=1-|x|}