Solve the following problems about equivalence mod n.

a. Use the definition of equivalence mod n to explain why each statement is true.

i. 23 $\equiv$ 8 mod 5

ii. 76 $\equiv$ 4 mod 9

iii. -3 $\equiv$ 24 mod 27

b. Find four integers that are equivalent to 2 mod 27. At least one of the numbers should be a negative integer.

c. Working with others, brainstorm a possible equivalent, yet different, definition or description of "equivalent mod n. "

Solve each system of equations using Cramer’s Rule if it is applicable. If Cramer’s Rule is not applicable, say so.

$$\left\{\begin{array}{l}{3 x-6 y=24} \\ {5 x+4 y=12}\end{array}\right.$$

A soap bubble of radius $R_1=10 \mathrm{~cm}$ has a charge of $3 \mathrm{nC}$ uniformly spread over it. Because of electrostatic repulsion, the soap bubble expands until it bursts at a radius $R_2=20 \mathrm{~cm}$. From the results of Earlier Problem , calculate the work done by the electrostatic force in expanding the soap bubble.

Identify the following terms or individuals and explain their significance:

socialism

What is Stirliing's Approximation? Why is it useful? When is it applicable?

Let X denote the number of patients who suffer an infection within a floor of a hospital per month with the following probabilities:

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3}\\ \text{P(X = x)} & \text{0.7} & \text{0.15} & \text{0.1} & \text{0.05}\\ \end{matrix}$$

Determine the following: (a) F(x) (b) Mean and variance (c) P(X > 1.5) (d) $P(X \leq 2.0)$

Scores on a standardized test are normally distributed with a mean of $80$ and a standard deviation of $12$.

Approximately what percent of students scored between $65$ and $101$ points ?

A) $85.42 \%$

B) $95.99 \%$

C) $14.57 \%$

D) $89.44 \%$

Benzene can be prepared from acetylene. $3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{C}_{6} \mathrm{H}_{6}(g)$). Determine the equilibrium constant at 25 $^{\circ} \mathrm{C}$ and at 850 $^{\circ} \mathrm{C}$. Is the reaction spontaneous at either of these temperatures? Why is all acetylene not found as benzene?

Explain the reactivity of the noble gases in terms of valence electrons.

Solve each equation. Give solutions in exact form. $\log _{2}\left(\log _{2} x\right)=1$

Vous regardez la tele avec Juliette . Elle a perdu ses lunettes et elle ne voit pas bien . Confirmez pour elle le personnage de l emission.

Modele : la chanteuse c est Natasha st - Pier ? oui c est elle

L acteur c est Johnny Depp ?

Check whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If a linear system has graphs with equal slopes, the system must be inconsistent.

How many valence electrons does sulfur have?

Answer the following questions in complete sentences that include the word por, where applicable. Por lo general, ¿gastas mucho cuando vas de compras? ¿Por qué? _____