Find the distance between the points.

$$(1,12),(6,0)$$

The numbers in Set N are multiples of 5.

The numbers in Set P are multiples of 9.

Which number of the three possibilities could be a number of both Set N and Set P ?

A. 27

B. 25

C. 90

Use a rotation matrix to rotate the vector

$$\left[\begin{array}{l} -2 \\ -3 \end{array}\right]$$

counterclockwise by the angle $\pi / 9.$

Mayfield Corporation finished job no. 314 on June 1. On June 10, the company sold job no. 314 for $\$ 10,000$, cash. Total manufacturing costs allocated to this job at the time of the sale amounted to $\$ 6,500$.

a. Record the transfer of job no. 314 from Work in Process to Finished Goods on June 1.

Find the complement of the following set.

The set {x|x is an integer strictly between 0 and 8} if U is the set of all integers.

In the earlier exercise, you used the Correlation and Regression applet to create three scatterplots having a correlation of about r = 0. 7 between the horizontal variable x and the vertical variable y. Create three similar scatterplots again, and click the "Show least-squares line" box to display the regression lines. Correlation r = 0. 7 is considered reasonably strong in many areas of work. Because there is a reasonably strong correlation, we might use a regression line to predict y from x. In which of your three scatterplots does it make sense to use a straight line for prediction?

Find the rotation–dilation matrix within the given matrix.

$$\left[\begin{array}{rr} 1 & -2 \\ 1 & 3 \end{array}\right]$$

A chiral sample gives a rotation that is close to $180^{\circ}$. How can one tell whether this rotation is $+180^{\circ}$ or $-180^{\circ} ?$

Solve each percent problem. What is 20% of 3?

Determine whether the first set is a subset of the second set. {0, 1, 5, 9}, the set of natural numbers

Work the given problem on independent events.

According to data from the U.S. Department of Transportation, Delta Airlines was on time approximately 87% of the time in 2012 . Use this information, and assume that the event that a given flight takes place on time is independent of the event that another flight is on time to answer the following questions

(a) Elisabeta Gueyara plans to visit her company's branch offices; her journey requires 3 separate flights on Delta Airlines. What is the probability that all of these flights will be on time?

(b) How reasonable do you believe it is to suppose the independence of being on time from flight to flight?

Solve the problem.

The polar equation

$$r=\frac{a\left(1-e^2\right)}{1+e \cos \theta}$$

can be used to graph the orbits of the planets, where $a$ is the average distance in astronomical units from the sun and $e$ is a constant called the eccentricity. The sun will be located at the pole.

Plot the orbits of Earth, Jupiter, Uranus, and Pluto on the same polar grid. How does Earth's distance from the sun compare to the other planets' distances from the sun?

Xon, a small oil equipment company, purchased a new petroleum drilling rig for $2,000,000. Xon will depreciate it using MACRS depreciation. The drilling rig has been leased to a firm, which will pay Xon$750,000 per year for 8 years. After 8 years the drilling rig will belong to the firm. Xon has a 40% combined incremental tax rate and a 20% after-tax MARR. (a) Does the investment appear to be satisfactory? (b) Some claim that the coal and/or oil industries are inherently unsustainable and harmful to the environment. Develop a short position summary to support and challenge this perspective.

Why is the flow of smoke from a cigarette frequently laminar near the source but turbulent further away? Explain.