Chlorine consists of the following isotopes:

$$\begin{array}{lll}\text { Isotope } & \text { Isotopic } & \text { Fractional } \\ \text { Chlorine-35 } & \text { Mass (amu) } & \text { Abundance } \\ \text { Chlorine-37 } & 34.96885 & 0.75771 \\ \end{array}$$

What is the atomic mass of chlorine?

A uniform brass disk of radius $R$ and mass $M$ with a moment of inertia $I$ about its cylindrical axis of symmetry is at a temperature $T=20 .^{\circ} \mathrm{C}$. Determine the fractional change in its moment of inertia if it is heated to a temperature of $100 .{ }^{\circ} \mathrm{C}$.

A diffraction pattern is formed on a screen 120 cm away from a 0.400-mm-wide slit. Monochromatic 546.1-nm light is used. Calculate the fractional intensity $I / I_{\max }$ at a point on the screen 4.10 mm from the center of the principal maximum.

Considering a population that begins growing exponentially at a base rate of $6.0 \%$ per year and then follows a logistic growth pattern. If the carrying capacity is $80 \mathrm{mil}$ lion, find the actual fractional growth rate when the population is $10$ million, $50$ million, and $70$ million.

The fractional change of reacting mass to energy in a fission reactor is about $0.1 \%$, or 1 part in a thousand. For each kilogram of uranium that is totally fissioned, how much energy is released? If energy costs 3 cents per megajoule, how much is this energy worth in dollars?

Consider an apportionment problem with two states A and B. Suppose that state A has standard quota

$$q_1$$

and state B has standard quota

$$q_2$$

, neither of which is a whole number. (Of course,

$$q_1+q_2=M$$

must be a whole number.) Let

$$f _ { 1 }$$

represent the fractional part of

$$q_1$$

and

$$f_2$$

the fractional part of

$$q_2$$

. (a) Find values

$$q_1$$

and

$$q_2$$

such that Lowndes's method and Hamilton's method result in the same apportionment. (b) Find values

$$q_1$$

and

$$q_2$$

such that Lowndes's method and Hamilton's method result in different apportionments. (c) Write tan inequality involving

$$q_1, q_2, f_1$$

, and

$$f_2$$

that would guarantee that Lowndes' method and Hamilton's method result in different apportionments.

The fractional population of an excited state of energy $E_{n}$ compared to the population of the ground of energy $E_{0}$ is $N_{n} / N_{o}=e^{-\left(E_{n}-E_{o}\right) / k T}$. At approximately what temperature $T$ are 20 percent of hydrogen atoms in the first excited state?

Simplify each of the following expressions. Be sure that your answer has no negative or fractional exponents. a. $64^{1 / 3}$ b. $\left(4 x^{2} y^{5}\right)^{-2}$ c. $\left(2 x^{2} \cdot y^{-3}\right)\left(3 x^{-1} y^{5}\right)$

a. If the resistance of 1000 ft of wire is about 1 $\Omega$ at room temperature $\left(68^{\circ} \mathrm{F}\right),$ at what temperature will it double in value? b. What gage wire was used? c. What is the approximate diameter in inches, using the closest fractional form?

Simplify each integrand as follows: If the integrand involves fractional powers such as $x^{p / q}$ and $x^{r / s}$, make the substitution $x=u^{n}$, where n is the least common denominator of $\frac{p}{q}$ and $\frac{r}{s}$. Then find each integral. $\int \frac{d x}{3 \sqrt{x}-\sqrt[3]{x}}$

Juan got $\frac{3}{4}$ of the problems correct on the last test. Julio got $\frac{5}{8}$ of the problems correct on the last test. What fractional part more of the test questions did Juan get correct than Julio?

Assuming m=85 kg, l=8.0 m and k=850 N/m, determine x/l (the fractional stretch of the rope) and kx/ mg (the force that the rope exerts on the climber compared to his own weight) at the moment the climber's fall been stopped.

A $0.735-\mathrm{kg}$ block oscillates on the end of a spring whose spring constant is $k=41.0 \mathrm{~N} / \mathrm{m}$. The mass moves in a fluid which offers a resistive force $F=-b v$, where $b=0.662 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}$. What is the fractional decrease in amplitude per cycle?

Explain the significance of state bank, legal tender, national bank, national currency, gold certificate, silver certificate, central bank, bank run, bank holiday, fractional reserve system, legal reserves, reserve requirement, member bank reserve (MBR), and excess reserves.