A mill is a unit of money that is used in assessing taxes. One mill is equal to $\frac{1}{10}$ of a cent or $\frac{1}{1000}$ of a dollar.

29. Money is usually written using decimals. Express each fraction above as a decimal using the correct money symbol.

30. Find the number of cents and the number of dollars equal to 375 mills.

31. Find the number of cents and the number of dollars equal to 775 mills.

32. Find the number of cents and the number of dollars equal to 1,000 mills.

Calculate the total number of electrons that can occupy three "p" orbitals.

The proton has a magnetic moment of $1.41 \times 10^{-26} \mathrm{~A} \cdot \mathrm{m}^2$. $(a)$ If the proton is placed in a uniform magnetic field of $0.80 \mathrm{~T}$, plot the torque as a function of the angle $\theta$. $(b)$ If the magnetic moment is initially oriented antiparallel to the field, how much energy will be released when the proton flips into the parallel orientation?

Use the key terms to complete the following sentence:

The __________ is the rate banks are charged to borrow money from the Fed.

Compute Topp Company’s price-earnings ratio if its common stock has a market value of $20.54 per share and its EPS is$3.95. Its key competitor, Lower Deck, has a PE ratio of 9.5. For which company does the market have higher expectations of future performance?

Answer these questions about the interest calculation s.

What number of years was the money on deposit in both accounts?

Let n be a positive integer whose decomposition into prime factors has no repeated prime. Let B = {x | x is a divisor of n}. For example, if $n=21=3 \cdot 7,$ then B = {1, 3, 7, 21}. Let the following operations be defined on B:

$$x+y=\operatorname{lcm}(x, y) \quad x \cdot y=\operatorname{gcd}(x, y) \quad x^{\prime}=n / x$$

Then + and $\cdot$ are binary operations on B and $\prime$ is a unary operation on B. a. For n = 21, find (i) $3 \cdot 7$ (ii) $7 \cdot 21$ (iii) 1 + 3 (iv) 3 + 21 (v) $3^{\prime}$ b. Prove that the commutative, associative, and distributive properties hold for both + and $\cdot.$ c. Find the value of the “0” element and the “1” element, then prove properties 4 and 5 for both + and $\cdot.$ d. Consider a value for n whose decomposition has repeated primes. In particular, let $n=12=2 \cdot 2 \cdot 3.$ Prove that, using the above definitions for + and $\cdot,$ it’s not possible to define a complement for 6 in the set {1, 2, 3, 4, 6, 12}. Therefore a Boolean algebra cannot be constructed with n = 12 using the process described.

Use algebraic procedures to determine the exact solution or solutions of the equation.

$$5^{-x}=121$$

A torque of $0.97 \mathrm{~N} \cdot \mathrm{m}$ is applied to a bicycle wheel of radius $35 \mathrm{~cm}$ and mass $0.75 \mathrm{~kg}$. Treating the wheel as a hoop, find its angular acceleration.

Compare the procedures of differentiation and integration. Which seems to be the most complicated or difficult and why?

At the start of 2010 Karim had $\$ 5000$ to invest. He decided to invest part of the money in a savings account that offered $1.5 \%$ simple interest per year. He added $\$ 1000$ to this amount and fixed it for 10 years in bonds that offered $2.5 \%$ compound interest per year. The rest of the money he invested in shares.

At the end of the first year, Karim decided to sell the shares at their current value and reinvest the money in the savings account. Evaluate the total value of his investment at the end of 2020.

Another word for $stability$ (line 12) would be__.

(A) shelter
(B) money
(C) firmness
(D) amusement

Find the maximum torque on a $400$-turn circular coil of radius $0.75 \mathrm{~cm}$ that carries a current of $1.6 \mathrm{~mA}$ and is in a region with a uniform magnetic field of $0.25 \mathrm{~T}$.

Water at $20^{\circ} \mathrm{C}$ flows at $30\ \mathrm{gal} / \mathrm{min}$ through the $0.75$-in diameter double pipe hend of Fig. P3.154. The pressures are $p_1=30\ \mathrm{lbf} / \mathrm{in}^2$ and $p_2=24\ \mathrm{lbf} / \mathrm{in}^2$. Estimate the torque $T$ at point $B$ necessary to keep the pipe from rotating.