Show that the set of irrational numbers is an uncountable set.

Determine the appropriate rotation formulas to use so that the new equation contains no xy-term. $34 x^{2}-24 x y+41 y^{2}-25=0$

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.

Determine whether the statement is true or false. Use the following sets of numbers.

$N=$ set of natural numbers.

$Z=$ set of integers

$I=$ set of irrational numbers

$Q=$ set of rational numbers

$\mathbb{R}=$ set of real number

$$Z \subseteq \mathbb{P}$$

Find the time requested, to the nearest 0.1 year. The time it would take $6,000 to grow to$10,000 at 4.75% interest compounded monthly

(a) Prove that the set of all irrational numbers, $\mathbb{R} \backslash \mathbb{Q}$, is uncountable,

(b) Prove that $\mathbb{R} \backslash \mathbb{Q} \sim \mathbb{R}$.

Find the distance between the points.

$$(6.2,5.4),(-3.7,1.8)$$

Find the rotation–dilation matrix within the given matrix.

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

Write always, sometimes, or never to complete a true statement.

A sequence of a rotation and a dilation will $\underline{\text{?}}$ result in an image that is the same size and orientation as the preimage.

Solve the problem. Prove that $(\cosh (x)+\sinh (x))^{n}=\cosh (n x)+\sinh (n x)$.

The previous two problems suggest that using LEDs is a good idea from a purely financial perspective unless you live in an area where power is relatively inexpensive, but there is another wrinkle. Suppose you have a residence with a lot of incandescent bulbs that are used on average 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can't tell which bulbs are older or newer). At what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today?

Use a rotation matrix to rotate the vector

$$\left[\begin{array}{r} 4 \\ -1 \end{array}\right]$$

counterclockwise by the angle $\pi / 3.$

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.

Use a rotation matrix to rotate the vector

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

counterclockwise by the angle $\pi / 9.$